### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Highway Traffic Operations CE 578

UI

GPA 3.54

### View Full Document

## 27

## 0

## Popular in Course

## Popular in Civil Engineering

This 67 page Class Notes was uploaded by Savanna Cruickshank on Friday October 23, 2015. The Class Notes belongs to CE 578 at University of Idaho taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/227783/ce-578-university-of-idaho in Civil Engineering at University of Idaho.

## Popular in Civil Engineering

## Reviews for Highway Traffic Operations

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/23/15

Highway Capacity Manual 2000 CHAPTER 22 FREEWAY FACILITIES CONTENTS I INTRODUCTION 221 Scope of the 991 Limitations of the 991 II METHODOLOGY 992 Performance Measures 223 Segmenting Freeway Facilities 994 Freeway Facility Demands and Estimation of Traffic Demand 225 226 227 Adjustments of Segment Capacity Permanent Capacity Reduction Construction Activities Capacity Reduction 227 ShortTerm Work Zones 227 LongTerm Construction Zones 228 Lane Width P 39 39 228 Adverse Weather Capacity Reduction 228 Rain 999 Snow 229 Fm 229 Environmental Capacity Reduction 229 Capacity Reductions Due to Traffic Accidents or Vehicular 2210 Applying Capacity Reductions 2211 DemandCapacity Ratio 2212 Undersaturated Conditions 2214 F Conditions 2215 Flow 2215 Segment Initialization 2216 Mainline Flow Calculation 2216 Mainline Input 2216 Mainline Output 2216 Mainline Output from Ramps 2216 Mainline Output from Segment Storage Mainline Output from FrontClearing Queue Mainline Flow Determining OnRamp Flnw Determining OffRamp Flnw Determining Segment Flnw Determining Segment Service Measures 2218 Determining Freeway Facility Performance Measures 2218 Ill APPLICATIONS 9919 Computational Steps 9919 Traffic Management Strategies 2221 IV EXAMPLE PROBLEMS 9923 Example Problem 1 9924 Example Problem 2 9928 Example Problem 3 9932 Example Problem 4 9934 Example Problem 5 9937 Chapter 22 Freeway Facilities Highway Capacity Manual 2000 Example Problem 6 V FIEFEFIENPFS APPENDIX A DETAILED COMPUTATIONAL MODULES FOR FREEWAY FACILITIES A1 Scope of Appendix Material A11 Limitations A12 Glossary Global Variables Segment Variables Node Variables OnRamp Variables OffRamp Variables Facilitywide Variables A2 Overall Procedure Description A21 Input Mndllle A22 Demand Estimation Module 2245 A23 Establish Spatial and Time Units A24 Demand Adjustment Module A25 Segment Capacity Estimation and Adjustment Module A26 DemandtoCapacity Ratio Module A3 Undersaturated Segment MOE Module A4 Oversaturated Segment MOE Module A41 Procedure Parameters A42 Flow Fetimatinn A421 Segment Initialization Exhibit A226 Steps 1 Through 4 2255 A422 Mainline Flow Calculations Exhibit A226 Steps 9 and 16 Through 2 1 2256 A4221 Mainline Input Exhibit A226 Step 9 2257 A4222 Mainline Output Exhibit A226 Steps 16 Through 21 2257 A42221 Mainline Output 1 Ramp Flows Exhibit A226 Step 16 2257 A42222 Mainline Output 2 Segment Storage Exhibit A226 Steps 20 and 21 2257 A42223 Mainline Output 3 FrontClearing Queues Exhibit A226 Steps 17 Through 19 A4223 Mainline Flow Exhibit A226 Steps 22 and 23 A423 OnRamp Calculations Exhibit A226 Steps 1O Through 15 2259 A4231 OnRamp Input Exhibit A226 Steps 10 and 11 2259 A4232 OnRamp Output Exhibit A226 Step 12 2259 A4233 OnRamp Flows Queues and Delays Exhibit A226 Steps 13 Through 15 2260 A424 OffRamp Flow Calculation Exhibit A226 Steps 5 Through 8 2261 A425 Segment Flow Calculation Exhibit A226 Steps 24 and 25 2261 A43 Segment and Ramp Penormance Measures Exhibit A226 Steps 26 Through 30 A5 Directional Facility Module EthbIt A226 2262 2263 Step 36 Chapter 22 Freeway Facilities 2211 Highway Capacity Manual 2000 Exhibits Exhibit 221 Freeway Facility Exhibit 222 TimeSpace Domain of a Freeway Facility Exhibit 223 Conversion of Freeway Sections into Freeway Segments Exhibit 224 Summary of Capacity Values for LongTerm Construction Zones 228 Exhibit 225 Capacities on German Autobahns Under Varying Conditions Iveh h In 9940 Exhibit 226 Proportion of Freeway Segment Capacity Available Under Incident Conditions 9911 Exhibit 227 SpeedFlow Curves for Different Weather Conditions 2212 Exhibit 228 Adjusted SpeedFlow Curves for Indicated Capacity Adjustments Exhibit 229 NodeSegment Representation of a Freeway Facility Exhibit 2210 Mainline and Segment Flow at On and OffRamps Exhibit 2211 Implementation of Freeway Facility Methodology Exhibit 2212 Required Input Data for Freeway Facility Analysis Exhibit A22 1 Overall Procedure I avnut Exhibit A22 2 Alternative SpeedFlow Curves for Indicated Capacity Adjustment Factors 9949 Exhibit A22 3 NodeSegment Representation of a Directional Freeway Facility 2250 Exhibit A22 4 Recommended Time Step Duration for Oversaturated Analysis 2250 Exhibit A22 5 Segment FlowDensity FIInr tinn Exhibit A22 6 F Analysis Procedure Exhibit A22 7 Definitions of Mainline and Segment Flows Exhibit A22 8 FlowDensity Function with a Shock Wave 22111 Chapter 22 Freeway Facilities Highway Capacity Manual 2000 I INTRODUCTION Freeway facilities are composed of connected segments consisting of basic freeway segments ramp segments and weaving segments When several of these segmenm occur in sequence they form a freeway facility A freeway facility is the fundamental unit of analysis in this chapter A freeway facility is analyzed by direction and the independent analysis of both directions constitutes the analysis of a twodirection freeway facility The reader is referred to Chapter 13 for discussion of freeway concepts SCOPE OF THE METHODOLOGY In Chapters 23 24 and 25 freeway components are addressed as isolated segments that are assumed to have no significant interaction A procedure that integrates the methodologies of Chapters 23 24 and 25 is provided in this chapter subject to several limitations The freeway facility has spatial and time dimensions subject to defined limits The spatial dimension consists of continuous connected segmenm of defined length type and width The segments could include basic freeway segments onramp junction segments offramp junction segments or weaving area segments Freeflow conditions must exist at the upstream and downstream ends of the freeway facility The maximum length of a freeway facility that should be considered is on the order of 9 to 12 mi so that traffic enters and leaves the freeway in the same time interval The temporal dimension consists of connected time intervals Undersaturated conditions must occur in the first and last time interval The analysis period to be considered is divided into 15min time intervals The material developed for this chapter resulted from research sponsored by the Federal Highway Administration 1 LIMITATIONS OF THE METHODOLOGY A complete discussion of freeway control systems or even the analysis of the performance alternatives is beyond the scope of this chapter The reader should consult references identified in a later section of this chapter The methodology does not account for delays caused by vehicles using alternate routes or vehicles leaving before or after the study time duration Certain freeway traffic conditions cannot easily be analyzed by the methodology Multiple overlapping bottlenecks are an example Therefore other tools may be more appropriate for specific applications beyond the capabilities of the methodology Refer to art of this manual for a discussion of simulation and other models User demand responses such as spatial temporal modal or total demand responses caused by traffic management strategies are not automatically incorporated within the methodology On viewing the facility traffic performance results the analyst can modify the demand input manually to analyze the effect of user demand responses or traffic growth The accuracy of the results depends on the accuracy of the estimation of the user demand responses The freeway facility methodology is limited to the extent that it can accommodate demand in excess of capacity The procedures address only local oversaturated flow situations not systemwide oversaturated flow conditions The completeness of the analysis will be limited if freeway segments in the first time interval the last time interval and the first freeway segment do not all have demandto capacity ratios less than 100 The rationale for these limitations is discussed in the section on demandcapacity ratio The analyst can given enough time analyze a completely undersaturated timespace domain manually although this is difficult It is not expected that analysm will ever manually analyze a timespace domain that includes oversaturation For heavily congested freeway facilities with interacting bottleneck queues the analyst may wish to review Part V of this manual before undertaking this methodology Background and concepts for this chapter are in Chapter 13 221 Chapter 22 Freeway Facilities Introduction Highway Capacity Manual 2000 METHODOLOGY Exhibit 221 summarizes the methodology for analyzing freeway facilities The methodology integrates the basic freeway segment1 ramp segment and weaving segment procedures into a freeway facility analysis The methodology adjusts vehicle speeds appropriately to account for effecm in adjacent segments The methodology can analyze freeway traffic management strategies only in cases for which 15min time intervals are appropriate and for which reliable data for capacity and demand estimates exist EXHIBIT 224 FREEWAY FACILITY METHODOLOGY Input Data 7 Demand 7 Geometric data 7 Timeispace domain Adiust demand according to spatia and time units established Compute segment capacities 4 according to Chapters 23 2 and 25 methodologies Adiust segment capacities Compute demandicapacity ratios Oversaturated Compute segment service measures and measures of effectiveness Compute oversaturated segment serVice measures and measures of effectiveness Compute freeway facility measures of effectiveness by time interval Chapter 22 Freeway Facilities Methodology Highway Capacity Manual 2000 The effect of various demand management techniques can be assessed by varying the demand associated with the technique The methodology is limited to applications for which data are available to quantify the effecm of demand management and whose complexity does not exceed the capabilities of the methodology This is especially true when periods of oversaturation occur The analysis should begin and end with no portion of the freeway having oversaturation Freeway control is frequently motivated by operational problems such as one or more bottlenecks with significant mainline congestion Ramp metering is a strategy to reduce the amount of congestion by limiting demand The effectiveness of a particular rampmetering strategy in improving freeway performance can be analyzed by the methodology The ability of the methodology to assess the total effects of the strategy depends on assumptions related to where excess demand would relocate If the demand is diverted to another time or location within the analysis period effecm can be accounted for The use of highoccupancy vehicle HOV lanes on freeways raises the issues of the operating characteristics of such lanes and the effects on the remainder of the freeway The issues are complex because HOV lanes come in many forms including separated facilities reserved freeway lanes concurrent flow and contraflow lanes and priority access ramp meter bypass lanes The methodology addresses separated facilities but not the interactions between the HOV lane and the mixedflow lanes There are a number of data requirements for conducting an analysis and some applications are beyond the capabilities of the methodology The issue of capacity must be addressed first This is a difficult issue because data are limited and by design most HOV freeway facilities operate below capacity to maintain a high level of service Singlelane HOV facilities generally have different speed characteristics because of the lack of passing opportunities Therefore it is recommended that singlelane analyses be conducted only when HOV lane demand is less than 1600 vehhln e methodology for analyzing freeway facilities is comprehensive in that it interacts with three other chapters of this manual and incorporates both undersaturated and oversaturated flow analysis capabilities In this portion of the chapter an overview of the methodology is given The timespace domain of a freeway facility is described with particular attention to facility geometrics facility traffic demands demandcapacity analysis and optional traffic management strategies Service measures levels of service LOS and performance measures are also discussed The purpose of this section is to describe the computational modules of the methodology To simplify the presentation the focus is on the function of and rationale for each module An expanded version of this section containing all the supporting analytical models and equations is presented in Appendix A PERFORMANCE MEASURES Facilitywide service measures and LOS designations are not incorporated in this chapter as they are in other chapters in Part III of this manual This is due to the complexity of assessing freeway facilities when oversaturated flow conditions are encountered A freeway facility may contain both uncongested and heavily congested segments and any average service measure for the entire length is likely to be misleading and difficult to classify by LOS The methodology provides estimates of speed travel time density flow rate vehicle and person volumetocapacity ratio and congestion status for each cell in the time space domain From these estimates vehicle hours person hours of travel as well as vehicle miles person miles of travel for each cell can be determined The previously discussed traffic performance measures can be aggregated by the analyst over the leng of the freeway facility over the study time duratiorL and over the entire timespace domain Singlelane HOV facilities can be analyzed only when flow rates are less than 1600 vehhln Systemwide measures can be generated but no LOS guidelines are given 223 Chapter 22 Freeway Facilities Methodology Highway Capacity Manual 2000 Freeway facilities up to 12 mi long can be analyzed with the methodology SEGMENTING FREEWAY FACILITIES The timespace domain of a freeway facility is used to provide an overview of the methodology A typical timespace domain is shown in Exhibit 222 EXHIBIT 22 2 TIME SPACE DOMAIN OF A FREEWAY FACILITY T me nterva OOmeJgtWNA Direction of Travel The horizontal scale indicates the distance along the freeway facility Traffic moves from left to right and the scale is divided into freeway sections A freeway section boundary occurs wherever there is a change in traffic demand ie onramp or offramp or a change in segment capacity ie lane drop or lane addition Freeway facilities up to 9 to 12 mi long can be analyzed by this methodology Estimates of traffic demand on longer freeway facilities cannot be reliably developed with the methodology because the travel time between some origins and destinations will exceed the standard time interval 15 min The vertical scale indicates the study time duration Time extends down the time space domain and the scale is divided into 15min intervals The study time duration can include any number of contiguous 15min intervals The number of sectionbased cells in the timespace domain is the product of the number of sections and the number of 15min intervals In Exhibit 222 there are 64 sectionbased cells e oundary conditions of the timespace domain are extremely important since the timespace domain will be analyzed as an independent freeway facility having no interactions with the upstream or downstream portions of any connecting facilities including freeways and surface streets or with time periods before or after the study time duration This means that no congestion should occur along the four boundaries of the timespace domain The cells located along the four boundaries should all have demands less than capacities and should contain undersaturated flow conditions Exhibit 222 shows the division of the freeway facility into connected freeway sections However to use the predictions of capacity and performance measures from the basic freeway ramp and weaving segment chapters the sections must be further divided into segments Each section contains one or more segments depending on the freeway geometrics First any weaving segment as defined in Chapter 24 Freeway Weaving is labeled as a weaving segment Next any onramp or offramp segment as defined in Chapter 25 Ramps and Ramp Junctions is labeled as an onramp or offramp segment The remaining portions of the freeway facility are labeled as basic freeway segments Chapter Chapter 22 Freeway Facilities Methodology 224 Highway Capacity Manual 2000 Special labeling of segments may be required under certain circumstances For example a long freeway section between an onramp and an offramp can be subdivided into three segments on ramp basic freeway and offramp A complication may occur when a short freeway section contains an onramp followed by an offramp without an auxiliary lane between the two ramps The problem arises if the length of the freeway section is insufficient to meet the requirements of the sum of the lengths of the onramp segment and the offramp segment as stated in Chapter 25 In that case the overlapping freeway segment is analyzed both as an on ramp segment and as an offramp segment and the more restrictive option is selected Similarly weaving sections with lengths exceeding 2500 ft can be analyzed as basic segments with the added auxiliary lane and ramp demands Other special types of freeway sections requiring special attention may be encountered In those cases Chapters 23 24 and 25 should be consulted The transformation of freeway sections into freeway segments for the freeway facility of Exhibit 222 is shown in Exhibit 223 The estimated segment capacities and traffic performance algorithms filter down through the timespace domain so that each cell has an estimated capacity and an algorithm for predicting traffic performance measures EXHIBIT 223 CONVERSION OF FREEWAY SECTIONS INTO FREEWAY SEGMENTS Freeway FaCIIIty B O B W B O B B O B O B A F A E A N A A F A N A S F S A S S S F S S V C C E C C C C C FREEWAY FACILITY DEMANDS AND ESTIMATION OF TRAFFIC DEMAND Traffic counts at each entrance to and exit from the freeway facility including the mainline entrance and the mainline exit for each time interval serve as input to the methodology Whereas entrance counts are considered to represent the current entrance demands for the freeway facility provided that there is not a queue on the freeway entrance the exit counts may not represent the current exit demands for the freeway facility because of freeway congestion Guidelines for handling long and short sections 225 Chapter 22 Freeway Facilities Methodology Highway Capacity Manual 2000 Estimation of traffic emand requires careful differentiation of volume as counted and demand Time interval scale factor in this chapter capacity computations are on a vehh basis Capacities can be selected to reflect a variety of controls or conditions For planning applications estimated traffic demands at each entrance to and exit from the freeway facility for each time interval serve as input to the methodology The sum of the input demands must be equal to the sum of the output demands in every time interval Once the entrance and exit demands are calculated the demands for each cell in every time interval can be estimated The segment demands can be thought of as filtering across the timespace domain and filling each cell in the timespace matrix emand estimation is required if the methodology uses actual freeway counm lf demand flows are known or can be projected they are used directly The demand estimation module converts the input set of freeway exit 15min traffic counts into a set of freeway exit 15min traffic demands Freeway exit demand is defined as the number of vehicles that desire to exit the freeway in a given 15min time interval This demand may not be represented by the 15min exit count because of upstream freeway congestion within the facility The procedure followed is to sum the freeway entrance demands along the entire freeway facility including the freeway mainline entrance and to compare it with the sum of the freeway exit counts along the entire directional freeway facility including the freeway mainline exit for each time interval The ratio of the total freeway entrance demands to the freeway exit counts in each time interval is called the time interval scale factor Theoretically the scale factor should approach 100 when the freeway exit counts are in fact freeway exit demands Scale factors greater than 100 indicate increasing levels of congestion within the freeway facility with exit traffic counts underestimating actual freeway exit demands Scale factors less than 100 indicate decreasing levels of congestion with exit traffic counts exceeding actual freeway exit demands To provide an estimate of freeway exit demand each freeway exit count is multiplied by the time interval scale factor Once the entrance and exit demands are determined the traffic demands for each freeway section in each time interval can be calculated On the timespace domain diagram the section demands can be viewed as projecting horizontally across the diagram with each cell containing an estimate of its 15min demand ADJUSTMENTS OF SEGMENT CAPACITY Segment capacity estimates are determined directly from Chapters 23 24 and 25 for basic weaving and ramp segments respectively All estimates of segment capacity should be carefully reviewed and compared with local knowledge and available traffic information for the study site particularly for known bottleneck segments Onramp and offramp roadway capacities are also determined in this module Onramp demands may exceed onramp capacities and limit the traffic demand entering the facility Offramp demands may exceed offramp capacities and cause congestion on the freeway although that effect is not accounted for in the methodology Unlike the computations performed in the basic freeway weaving and ramp chapters all capacity computations performed in this chapter are on the basis of vehicles per hour and not passenger cars The effect of a predetermined rampmetering plan can be evaluated in this methodology by overriding the computed ramp roadway capacities The capacity of each entrance ramp in each time interval is changed to the specified metering rate This feature not only permits the evaluation of a prespecified rampmetering plan but also permits the user to improve the rampmetering plan by experimentation Freeway design improvements can be evaluated within this methodology by modifying the design features of any portion or portions of the freeway facility For example the effect of adding auxiliary lanes at critical locations and full lanes over multiple segments can be assessed educedcapacity situations can also be investigated The capacity in any cell of the timespace domain can be reduced to represent incident situations such as construction Chapter 22 Freeway Facilities Methodology 226 Highway Capacity Manual 2000 and maintenance activities adverse weather and traffic accidentsvehicular breakdowns Conversely capacity can be increased to match field measurements In analyzing adjusted capacity use of an alternative speed ow relationship is important The computational details for this case are provided later in this chapter Permanent Capacity Reduction A lane drop is in many ways the simplest capacityreducing situation to deal with Capacity in both segments that with the smaller number of lanes and that with the larger number can be calculated using Chapter 23 24 or 25 methodologies So long as the arriving demand is less than the lower capacity no queue will form upstream of the lane op If the arriving demand begins to exceed the reduced capacity a queue will begin to form immediately upstream of the reducedcapacity section which will have become a bottleneck Some results suggest that a poorly designed merge at the lane drop can negatively affect the capacity of the segment with the smaller number of lanes because of the increase in friction and turbulence but this effect has not yet been quantified Construction Activities Capacity Reduction Capacity reductions due to construction activities can be divided into shortterm maintenance work zone lane closures and longterm construction zone closures One of the primary distinctions between shortterm work zones and longterm construction zones is the nature of the barriers used to demarcate the work area Longterm construction zones generally have portable concrete barriers shortterm work zones use standard channeling devices traffic cones drums in accordance with the Manual on Uniform Traffic Control Devices 2 Generally reduction of capacity brought about by reconstruction or major maintenance activities will last for several weeks or even months although some shortterm maintenance activities last only a few hours Short Term Work Zones Research 3 suggests that a capacity of 1600 pchln be used for shortterm freeway work zones regardless of the lane closure configurations For some types of closures capacity may be higher 3 e ase value should be adjusted for other conditions as follows Intensity of work activity The intensity of work activity refers to the number of workers on site the number and size of work vehicles in use and the proximity of work to the travel lanes in use Unusual types of work also contribute to the apparent intensity simply in terms of the rubbeniecking factor Research data did not result in explicit quantification of these effects but it is suggested that the capacity of 1600 pchln be adjusted by up to 10 percent for work activity that is more or less intense than normal 3 The research did not define what constitutes normal intensity Hence this factor should be applied on the basis of professional judgment recognizing that 1600 pchln is an average over a variety of conditions Effects of heavy vehicles It is recommended that the heavyvehicle adjustment factor fHV found elsewhere in the manual be used to account for the effect of heavy vehicles in the traffic stream moving through the work zone as shown in Equation 221 1 f 221 W 1PTETi1 where fHV heavyvehicle adjustment factor PT 2 proportion of heavy vehicles and ET 2 passengercar equivalent for heavy vehicles The value of ET can be taken from Chapter 23 Basic Freeway Segmenm Intensity of work will affect capaci y Hea vy vehicles should be accounte I r 227 Chapter 22 Freeway Facilities Methodology Highway Capacity Manual 2000 Entrance ramps within 500 it of a lane closure will affect capacity Presence of ramps If there is an entrance ramp within the taper area approaching the lane closure or within 500 ft downstream of the beginning of the full lane closure the ramp will have a noticeable effect on the capacity of the work zone for handling mainline traffic This arises in two ways First the ramp traffic will generally force its way in so it will directly reduce the amount of mainline traffic that can be handled Second the added turbulence in the merging area due to the entrance ramp may imelf reduce the capacity slightly If at all possible ramps should be located at least 1500 ft upstream rom the beginning of the full closure to maximize the total work zone throughput If that cannot be done then either the ramp volume should be added to the mainline volume to be served or the capacity of the work zone should be decreased by the ramp volume up to a maximum of half of the capacity of one lane on the assumption that at very high volumes mainline and ramp vehicles will alteniate Equation 222 is used to compute the resulting reduced capacity ca 1600 I7 R fHV N 222 where Ca va I adjusted mainline capacity vehh adjustment for heavy vehicles as defined in Equation 221 adjustment factor for type intensity and location of the work activity as discussed above ranges from 7160 to 160 pchln adjustment for ramps as described in the preceding paragraph and number of lanes open through the shortterm work zone R N LongTerm Construction Zones For longterm construction zones capacity values are given in Exhibit 224 lf traffic crosses over to lanes that are normally used by the opposite direction of travel the capacity is close to the 1550 vehhln value in Exhibit 224 5 If no crossover is needed but only a merge down to a single lane the value is typically higher and may average about 1750 vehhln 6 EXHIBIT 224 SUMMARY OF CAPACITY VALUES FOR LONGTERM CONSTRUCTION ZONES No of Normal Lanes Open Number of Studies Range of Values Average per Lane vennl n vennl n 3 2 7 I780 2060 I860 2 I 3 I550 Source Dudek 4 Lane Width Consideration An additional adjustment factor can be added to the longterm and shortterm reduction model for the effect of lane width 7 For traffic with passenger cars only headways increase by about 10 percent in going from llft widths to 105 or lOft widths and by an additional 6 percent in going to 9ft widths These increases in headways translate to 9 and 14 percent drops in capacity for the narrower lane widths within construction zones Adverse Weather Capacity Reduction There have been several research studies on the effect of rain snow and fog It has become clear that adverse weather can significantly reduce not only capacity but also operating speeds The following sections discuss the effects of each of these weather conditions and address the issue of when and how to take these effecm into account in applying the methodology Chapter 22 Freeway Facilities Methodology 228 Highway Capacity Manual 2000 Rain Research found that speeds are not particularly affected by wet pavement until visibility is also affected 8 This result suggests that light rain will not have much effect on speeds and presumably not on capacities unless it is of such extended duration that there is considerable water on the pavement Heavy rain on the other hand affects visibility immediately and can be expected to have a noticeable effect on traffic flow This expectation is bonie out by studies of freeway traffic Research found minimal reductions in maximum observed flows for light rain but significant reductions for heavy rain 9 Likewise the research found a small effect on operating speeds for light rain and larger effects for heavy rain These changes in operating speeds are important because they directly affect traffic performance For light rain a reduction in freeflow speeds of 12 mih was observed 9 At a flow rate of 2400 vehh the effect of light rain was to reduce speeds to about 51 mih compared with speeds of 55 to 59 mih under clear and dry conditions Under light rain conditions little if any effect was observed on flow or capacity For heavy rain the drop in freeflow speeds was 3 and 4 mih The result of heavy rain is to reduce speeds at 2400 vehh to 47 and 49 mih from respectively 55 and 59 mih These are reductions of 8 and 10 mih Maximum flow rates can also be affected and might be 14 to 15 percent lower than those observed under clear and dry conditions Snow For snow major differences were found depending on the quantity or rate of snowfall with light snow having minimal effects and heavy snow having potentially very large effects 9 If snowclearing operations cannot keep the road relatively clear during a heavy snowfall the snow accumulation on the highway obscures the lane markings Observation suggests that under these circumstances drivers often seek not only longer headways but also greater lateral clearance As a result a threelane freeway segment is used as if it had only two widely separated lanes This alone has a considerable effect on capacity Light snow was associated with a statistically significant drop of 06 mih in free flow speeds The effect on maximum observed flows was midway between the effecm of light and heavy rain or between a 5 and 10 percent reduction Heavy snow significantly influences the speedflow curve Freeflow speeds were reduced by 23 and 26 mih at the two stations from what they were under clear and dry conditions 63 and 66 mih respectively Maximum observed flows dropped from 2160 to 1200 vehhln at the station upstream of the queue At the station that might be a bottleneck itself for part of the peak period the maximum observed flows dropped from 2400 to 1680 vehhln This suggests a 30 percent drop in capacity due to heavy snow in an urban area where traffic will generally keep moving to some extent Fog Although no studies have quantified the effects of fog on capacity work has been done in Europe on fog waniing systems which use variable speed limit signs to reduce speeds during foggy conditions Those studies tend to report on the effectiveness of the speed waniing signs in reducing mean speeds not on what speeds or capacities are due to the fog alone For example they report effectiveness of fog warning devices of 5 to 6 mih in reducing speed but provide no information on capacity effecm 10 11 Environmental Capacity Reduction Research in Germany used speedflowdensity relationships to fit speed ow curves to the field observations 12 The capacity of each study site under a variety of conditions was estimated from these curves The results are useful not only in extending the research results cited on rain and wet pavement but also in identifying some other 229 Chapter 22 Freeway Facilities Methodology Highway Capacity Manual 2000 Mean duration of an incident was 37min but was highly variable causes of temporary capacity reduction that have not generally been discussed e g the difference between daylight and darkness and between weekdays and weekends A set of relationships for 10 to 15 percent heavy vehicles has been used for comparison in Exhibit 225 Although this exhibit shows the per lane capacities found in Germany the numbers clearly do not translate directly to North American conditions The most obvious difference is that capacity per lane is lower than would be found in North America In addition the capacity per lane for a sixlane freeway is lower than that of a fourlane freeway for all but one of the conditions These results are no doubt a consequence of the function the researchers were fitting together with the fact that there were few data near capacity because hourly data were analyzed What is important in the exhibit is the percentage reduction in capacity under each of the sew of conditions which is shown on the second line for each type of freeway and type of day weekday or weekend EXHIBIT 22 5 CAPACITIES ON GERMAN AUTOBAHNS UNDER VARYING CONDITIONS vehhIn Freeway Type Weekday or Daylight and Dry Dark and Dry Daylight and Wet Dark and Wet Weekend Sixelane freeway Weekday I489 I299 I3I O 923 Changea I3 I2 38 Sixelane freeway Weekend I380 I 084 IOI4 a Changea 2I 27 a Fourelane Weekday I739 I4I5 I42I 9I3 IIBBWW Changea I9 I8 47 Fourelane Weekend I55I I I58 IIO4 a WWW Changea Va 25 29 7 a The percentage reduction from daylight and dry conditions torthe same day of the week Source Brilon and Ponzlet 12 The estimates for weekdays and daylight for the reduction due to wet pavement 12 and 18 percent are consistent with the estimates discussed above for the effects of rain The reductions in capacity due to darkness are of the same order as those due to rain 13 and 19 percent for six and fourlane facilities respectively Since winter peakperiod commuter traffic occurs in darkness in many locations these capacity reductions are important to recognize The capacity of a freeway on weekends or holidays can be substantially less than when it carries commuter traffic Although the percentage change is not shown in the exhibit it amounts to a 7 to 10 percent reduction during dry daylight conditions Capacity Reductions Due to Traffic Accidents or Vehicular Breakdowns Capacity reductions due to traffic accidenm or vehicular breakdowns are generally shortlived ranging from less than 1 h before they can be cleared for a minor fender bender involving only passenger vehicles to as long as 12 h for a major accident involving fully loaded tractortrailer rigs For example on the basis of research the mean duration of a traffic incident was 37 min with just over half of the incidents lasting 30 min or less and 82 percent of the incidents lasting 1 h or less 13 When trucks were involved however the duration was longer accidenm involving trucks lasted 63 min on the average The effect of an incident on capacity depends on the proportion of the traveled roadway that is blocked by the stopped vehicles as well as on the number of lanes on the roadway at that point Exhibit 226 gives information on these effecm 14 15 Chapter 22 Freeway Facilities Methodology 2210 Highway Capacity Manual 2000 EXHIBIT 226 PROPORTION OF FREEWAY SEGMENT CAPACITY AVAILABLE UNDER INCIDENT CONDITIONS Number of Freeway Shoulder Shoulder One Lane Two Lanes anee Lanes Lanes by Direction Disablement Accrdent Blocked Blocked Blocked 2 095 081 035 000 NA 3 099 083 049 017 000 4 0 99 085 058 0 25 013 5 0 99 087 065 0 40 0 20 6 0 99 089 071 050 0 26 0 99 091 0 75 057 0 36 8 099 093 078 063 041 NA notapplrcable Source Rerss and Dunn 14 and Gordon et al 15 Note that in the case of a blocked lane the loss of capacity is likely to be greater than simply the proportion of original capacity that is physically blocked For example a fourlane in one direction freeway with two lanes blocked retains only 25 percent of its original capacity Exhibit 226 The added loss of capacity arises because drivers slow to look at the incident while they are abreast of it and are slow to react to the possibility of speeding up to move through the incident area The rubbernecking factor is also responsible for a reduction in capacity in the direction of travel opposite to that in which the accident occurred No quantitative studies of this effect have been published but experience suggests that it depends on the magnitude of the incident including the number of emergency vehicles present The reduction may range from 5 percent for a singlecar accident and one emergency vehicle to 25 percent for a multivehicle accident with several emergency vehicles Applying Capacity Reductions There are several ways to use the information on reduced capacities contained in the preceding material ranging from quick approximations through the application of the methodology described in this chapter to other quantitative approaches involving queuing analysis or shock wave analysis The quick approximations simply require reviewing the expected traffic demands and comparing them with the applicable capacity reduction If the demands do not exceed the reduced capacity there will not be any major difficulties in handling the traffic A more detailed analysis may be desired to estimate the expected traffic performance in which case use of the methodology would be appropriate The methodology works with the full speed ow curve for the undersaturated part of the relationship but in many of the cases described above only the effect on capacity has been identified by research reported to date The literature does not describe the effect of the factor incident construction on speeds and hence on the speed ow curve Without a full speedflow curve the analyst is forced to use other methods or to work around this limitation of the model Consider each of the capacity reductions in tum from the simplest to the most difficult to deal with Adverse weather is the easiest to deal with because the results cited above indicate effects on both speeds and capacity Consequently the analyst can simply use a speed flow curve for a lower freeflow speed FFS to model the effects of inclement weather Neither of the research studies reported a method that would equate to a reduction in FFS but their results can be reasonably well approximated that way 9 12 For light rain or snow for example speeds at capacity drop by 4 to 8 mih which can be approximated by a reduction in FFS of 6 mih For heavy rain the approximation would be a reduction in FFS of 12 mih For heavy snow the reduction would be 31 mih Exhibit 227 shows the approximate curves for these conditions using a constant density to determine the capacity for each curve Assumptions regarding effects on speeds 2211 Chapter 22 Freeway Facilities Methodology Highway Capacity Manual 2000 EXHIBIT 227 SPEEDFLOW CURVES FOR DIFFERENTWEATHER CONDITIONS Average PassengereCar Speed in h 0 400 800 i 200 1600 Flow Rate pchin 2000 2400 Note FPS 75 mih base conditions For the other temporary capacity reductions the research findings deal only with the change in capacity In most of these cases reasonable estimates of speed conditions can be made For example in construction zones a reduced speed is usually posted and lower speeds usually do occur particularly where actual construction operations are taking place Likewise for incidents traffic naturally slows as drivers pass the incidents and try to get a look at what happened Thus one can attempt to model these situations on the basis of a downwardshifted speedflow curve like those shown in Exhibit 228 If the analyst were not interested in the speeds the capacity reduction could be modeled by using a fractional number of lanes that would reflect the new capacity of the roadway rather than the real number of lanes For example in the case of a fourlane in one direction freeway facility with two lanes blocked Exhibit 226 shows that only 25 percent of the original capacity is available To reflect this the analyst could show only a single lane through the area of the incident even though it is in fact a fourlane segment However since most of the performance measures rely on or are based on speed this simplified approach will not permit a complete analysis Consequently use of a speed ow curve from the family shown in Exhibit 227 or 22 is recommen e The methodology and other methods have a role in analyzing the effect of incidents even when they are of short duration by assisting in the planning of responses to various types and locations of incidenm before they occur The advantage of planning is that it can minimize the need for improvising decisions about diversion plans and other methods of responding to incidents DEMANDCAPACITY RATIO Each cell in the timespace domain now contains an estimate of demand and capacity as well as an algorithm for calculating traffic performance measures A deman to capacity ratio can be calculated for each cell and the cell values should be reviewed to see whether in fact the timespace domain is free of congestion on its boundary and whether oversaturated flow conditions will occur anywhere in the timespace domain Chapter 22 Freeway Facilities Methodology 2212 Highway Capacity Manual 2000 EXHIBIT 228 ADJUSTED SPEEDFLOW CURVES FOR INDICATED CAPACITY ADJUSTMENTS SEE FOOTNOTE FOR ASSUMED VALUES Speed in h 5 I 30 A5 wu b CAP 100 207 p weNZ CAP 005 m CAP 000 To CAP 085 n I I I I I 0 400 800 i200 1600 2000 2400 Flow Rate pChIn Note Assumptions FPS 75 mih capamty adjustmenttactor CAP 0M 0 095 O 90 and O 85 The demandtocapacity ratio values should be less than 10 for all cells along the four boundaries of the timespace domain If they are not further analysis may be flawed and in some cases should not be undertaken For example if any cell in the first time interval has a demandtocapacity ratio value greater than 10 there may have been oversaturated conditions in earlier time intervals without transfer of unsatisfied demand into the timespace domain If any cell in the last time interval has a demandtocapacity ratio greater than 10 the analysis will not be complete since the unsatisfied demand within the timespace domain cannot be transferred to later time intervals If any cell in the last downstream segment has a demandtocapacity ratio greater than 10 there may be downstream bottlenecks that should be checked before proceeding with the analysis Finally if any cell in the first upstream segment has a demandtocapacity ratio greater than 10 then oversaturation will be extended upstream of the freeway facility but its effect will not be analyzed within the timespace domain These checks do not assure the analyst that the boundaries may not be violated later as the result of the more detailed analysis If the initial checks indicate that demands exceed capacities at the boundary segments the problem analysis domain should be adjusted As the analysis is undertaken the problem of demand exceeding capacity may occur again at the timespace domain boundaries requiring that the problem be reformulated or that other techniques as described in Part V of this manual be considered For example oversaturated conditions at a downstream bottleneck may be so severe as to extend upstream into or beyond the first freeway segment or beyond the last time interval other important check is to observe whether any cell in the entire timespace domain has a demandtocapacity ratio value greater than 10 If all cells have demand tocapacity ratio values less than 10 then the entire timespace domain contains undersaturated flow conditions and the analysis is greatly simplified If any cell in the timespace domain has a demandtocapacity ratio value greater than 10 then the timespace domain will contain both undersaturated and oversaturated flow conditions Analysis of oversaturated flow conditions is much more complex because of the interactions between freeway segments The analysis begins in the first cell in the upper lefthand corner of the timespace domain first segment in first time interval and continues downstream along the freeway facility for each segment in the first time interval The analysis then returns to the first upstream segment in the second time interval and continues downstream along the Demandcapacity should be less than 10 loraii cells along the four boundaries 0 the timespace domain 2213 Chapter 22 Freeway Facilities Methodology Highway Capacity Manual 2000 Fourstep process to analyze bottlenecks 1 Bottleneck cell analysis 2 Downstream demand modifications 3 Upstream llow modifications 4 Demand transfer to next time interval Shock wave analysis is used to analyze queue freeway for each segment in the second time interval This process is continued until all cells in the timespace domain have been analyzed As each cell is analyzed the question is asked Is the cell demandcapacity ratio less than or equal to 10 If the answer is yes then the cell is not a bottleneck and is assumed to be able to handle all traffic that wants to enter This process is continued in the sequence order described in the preceding paragraph until an answer of no is encountered indicating that the demandcapacity ratio in this cell is greater than 10 This cell is identified as a bottleneck and the traffic that wishes to enter cannot do so The following fourstep process is required to analyze each cell identified as a bottleneck bottleneck cell analysis downstream demand modifications upstream flow modifications and demand transfer to next time interval Since the demand in the bottleneck cell exceeds the bottleneck cell capacity the flow in the cell will be equal to capacity not demand Each bottleneck cell will have a volumecapacity ratio of exactly 10 On the basis of this volumecapacity ratio traffic performance measures can be estimated Since the bottleneck cell can only pass a flow equal to capacity not demand to the downstream segmenm in this time interval the demands for all downstream cells must be modified in accordance with the destinations of the unsatisfied demand at the bottleneck The unsatisfied demand at the bottleneck cell must be stored in the upstream segments and flow conditions and traffic performance measures in the upstream segments must be modified This is accomplished through shock wave analysis The unsatisfied demand stored upstream of the bottleneck cell must be transferred to the next time interval This is accomplished by adding the unsatisfied demand by desired destination to the origindestination table of the next time interval This fourstep process is implemented for each bottleneck encountered following the specified sequence of analyzing cells If no bottleneck cells are encountered then entire timespace domain will have undersaturated conditions and the sequence of analysis for oversaturation is not used If major bottlenecks are encountered the storage of unsatisfied demand may extend beyond the upstream boundary of the freeway facility or beyond the last time interval of the timespace domain In such cases the analysis will be flawed and the timespace domain should be reformulated Once traffic performance measures have been estimated for each cell in the time space domain they can be aggregated for the entire freeway facility for each time interval and for the entire study time duration The methodology for calculating these freeway traffic performance measures is described in the following section UNDERSATURATED CONDITIONS The analysis begins by examining the demandtocapacity ratios for all segments during the first time interval If all segments have a demandtocapacity ratio less than 10 then this time interval is completely undersaturated The flow or volume is equal to demand for each cell and undersaturated flow conditions occur Performance measures for the first segment during the first time interval are calculated by using the methodology for the corresponding segment type in Chapters 23 24 and 25 e analysis continues to the next downstream freeway segment in the same time interval and the performance measures are calculated for all subsequent downstream segments The analysis then resumes in the second time interval from the furthest upstream segment and moves downstream until all freeway segments in that time interval have been analyzed This patteni continues until the methodology encounters a time interval having one or more segments with a demandtocapacity ratio greater than 10 If this occurs the oversaturated analysis module is executed Chapter 22 Freeway Facilities Methodology 2214 Highway Capacity Manual 2000 When the analysis moves from isolated segments to a system additional constraints may be necessary A maximum achievable speed constraint is imposed to limit the predicted speed downstream of a segment experiencing low speeds This process prevents large speed fluctuations that can be predicted when applying the segmentbased methods in Chapters 23 24 and 25 OVERSATURATED CONDITIONS Once oversaturation is encountered the methodology changes its temporal and spatial units of analysis The spatial units become nodes and segments and the temporal unit moves from a time interval of 15 min to smaller time steps as recommended in Appendix A A node is defined as the junction of two segments There is always one more node than segment with a node analyzed at the beginning and end of the freeway facility as shown in Exhibit 229 The numbering of nodes and segments begins at the upstream end and moves to the downstream end with the segment upstream of Node i numbered i 7 l and the downstream segment numbered i as shown in Exhibit 2210 The oversaturated analysis moves from the first node to each downstream node for a time step After the completion of a time step the same nodal analysis is performed for the following time steps Many flow variables are computed in this analysis with the most prominent described in the next section EXHIBIT 229 NODE SEGMENT REPRESENTATION OF A FREEWAY FACILITY Seg I Sag 2 Sag 3 Sag 4 Seg 5 Sag 6 GGGG Ramp I Ramp 2 EXHIBIT 2240 MAINLINE AND SEGMENT FLOW AT ON AND OFFRAMPS Se 4 Node I Sag U Sag U 7 Node I Sag U MF MF ONRF OFRF I 7 I g I I SFI Mm SF I MFI0FRFI Flow Fundamentals Segment flow rates are calculated in each time step and are used to calculate the number of vehicles on each segment at the end of every time step The number of vehicles on each segment is used to track queue accumulation and discharge and to calculate the average segment density The conversion from time intervals to time steps occurs during the first oversaturated time interval and time steps continue in use until the end of the analysis The transition to time steps is essential because at certain points in the methodology future performance is estimated from past performance of an individual variable Use of time steps also allows more accurate tracking of queues Freeway analysis depends on the relationships between speed flow and density Chapters 23 24 and 25 define a relationship between these variables and the calculation of performance measures in the undersaturated regime The methodology uses this relationship in the calculations for undersaturated segments Calculations for segments Additional system considerations Speed on a segment may be constrained by a slower speed on an upstream segment Speed estimate is made for the full roadway width in a ramp influence area Node defined Time steps of less than 15 min are used 2215 Chapter 22 Freeway Facilities Methodology Highway Capacity Manual 2000 performing in the oversaturated regime use a simplified linear flowdensity relationship in the congested region as detailed in Appendix A Segment Initialization For the number of vehicles on each segment at the various time steps to be calculated the segments must contain the proper number of vehicles before the queuing analysis places unserved vehicles on segments The initialization of each segment is described below A simplified queuing analysis is initially performed to account for the effecm of upstream bottlenecks These bottlenecks meter traffic downstream To obtain the proper number of vehicles on each segment the segment s expected demand is calculated The expected demand is based on demands for and capacities of the segment including the effects of all upstream segments Expected demand represents the flow of traffic that would be expected to arrive at each segment if all queues were stacked vertically ie if queues had no upstream effects Thus all segmenm upstream of a bottleneck have expected demands equal to actual demands For the bottleneck and all further downstream segments a capacity constraint at the bottleneck which meters traffic to downstream segments is applied in the computation of expected demand From the expected segment demand the background density can be obtained for each segment using the appropriate segment density estimation procedures from Chapters 23 24 and 25 Mainline Flow Calculation Flows analyzed in oversaturated conditions are calculated for every time step and are expressed in vehicles per time step They are analyzed separately on the basis of the origin and destination of the flow across the node e flow from the mainline upstream Segment i 7 l to mainline downstream Segment i is the mainline flow ME The flow from the mainline to an offramp is the offramp flow OFRF The flow from an on ramp to the mainline is the onramp flow ONRF Each of these flows is shown in Exhibit 2210 with its origin and destination and relationship to Segment i and Node i The segment flow is the total output of a segment as shown in Exhibit 2210 The mainline flow is calculated as the minimum of six values These constraints are the mainline input Mainline Output 1 Mainline Output 2 Mainline Output 3 the upstream Segment i 7 1 capacity and the downstream Segment i capacity Mainline Input The mainline input is the number of vehicles that wish to travel through a node during the time step The calculation includes the effects of bottlenecks upstream of the subject node The effects include the metering of traffic during queue accumulation and the presence of additional traffic during queue discharge he mainline input is calculated by taking the number of vehicles entering the node upstream of the analysis node adding onramp flows or subtracting offramp flows if needed and adding to it the number of unserved vehicles on the upstream segment This is the maximum number of vehicles that desire to enter a node during a time step Mainline Output The mainline output is the maximum number of vehicles that can exit a node constrained by downstream bottlenecks or by merging traffic Different constraints on the output of a node result in three separate types of mainline outputs M01 M02 and M03 Mainline Output from Ramps Mainline Output 1 MOl is the constraint caused by the flow of vehicles from an onramp The capacity of an onramp segment is shared by two competing flows This Chapter 22 Freeway Facilities Methodology 2216 Highway Capacity Manual 2000 onramp flow limim the flow from the mainline at this node The total flow that can pass the node is estimated as the minimum of the Segment i capacity and the mainline outputs MOZ and M03 below calculated in the preceding time step Mainline Output from Segment Storage The output of mainline flow through a node is also constrained by the growth of queues on the downstream segment The presence of a queue limits the flow into the segment once the queue reaches its upstream end The queue position is calculated from shock wave analysis The M02 limitation is determined first by calculating the maximum number of vehicles allowed on a segment at a given queue density The maximum flow that can enter a queued segment is the number of vehicles leaving the segment plus the difference between the maximum number of vehicles allowed on a segment and the number of vehicles already on the segment The queue density is determined from the linear congested portion of the densityflow relationship shown in Appendix A Mainline Output from FrontClearing Queue The final limitation on exiting mainline flows at a node is caused by frontclearing downstream queues or M03 These queues typically occur when temporary incidenm clear Two conditions must be satisfied First the segment capacity minus the on ramp demand if present for the current time interval must be greater than the segment capacity minus onramp demand in the preceding time interval The second condition is that the segment capacity minus the ramp demand for the current time interval be greater than the segment demand in the same interval Frontclearing queues do not affect the segment throughput which is limited by the queue throughput until the recovery wave has reached the upstream end of the segment The shock wave speed is estimated from the slope of the line connecting the bottleneck throughput and the segment capacity points Mainline Flow The mainline flow across Node i is the minimum of the following variables Node i mainline input Node i Mainline Output 1 Node i Mainline Output 2 Node i Mainline Output 3 Segment i 7 1 capacity and downstream Segment i capacity Determining OnRamp Flow The onramp flow is the minimum of the onramp input and output Ramp input in a time interval is the ramp demand plus any unserviced ramp vehicles from a previous time interval Onramp output is limited by the ramp roadway capacity and the rampmetering rate It is also affected by the volumes on the mainline segments The latter is a very complex process that depends on the various flow combinations on the segment the segment capacity and the ramp roadway volumes Details of the calculations are presented in Appendix A Determining OffRamp Flow The offramp flow is determined by calculating a diverge percentage based on the segment and offramp demands The diverge percentage varies only by time interval and remains constant for vehicles that are associated with a particular time interval If there is an upstream queue then there may be metering of traffic to this offramp This will cause a decrease in the offramp flow When the vehicles that were metered arrive in the next time interval they use the diverge percentage associated with the preceding time interval The methodology ensures that all offramp vehicles prevented from exiting during the presence of a bottleneck are appropriately discharged in later time intervals Ramp diverge percentages may vary by time interval and this will be affected by queuing at bottlenecks 2217 Chapter 22 Freeway Facilities Methodology Highway Capacity Manual 2000 Threestep procedure Queues on ramps Facilitywide measures Trip time Vehicle and person distance of tra vel Vehicle and person hours of travel Determining Segment Flow The segment flow is the number of vehicles that flow out of a segment during the current time step These vehicles enter the current segment either to the mainline or to an offramp at the current node as shown in Exhibit 229 The number of vehicles on each segment is calculated on the basis of the following the number of vehicles that were on the segment in the previous time step the number of vehicles that have entered the segment in the current time step and the number of vehicles that can leave the segment in the current time step Because the number of vehicles that leave a segment must be known the number of vehicles on the current segment cannot be determined until the upstream segment is analyzed The number of unserved vehicles stored on a segment is calculated as the difference between the number of vehicles on the segment and the number of vehicles that would be on the segment at the background density Determining Segment Service Measures In the last time step of a time interval the segment flows in each time step are averaged over the time interval and the measures of effectiveness for each segment are calculated If there were no queues on a particular segment during the entire time interval then the performance measures are calculated from Chapters 23 24 and 25 as appropriate If there was a queue on the current segment during the time interval then the performance measures are calculated in three steps First the average number of vehicles over a time interval is calculated for each segment Next the average segment density is calculated by taking the average number of vehicles in all time steps in the time interval and dividing it by the segment length Finally the average speed on the current segment during the current time interval is calculated as the ratio of segment flow to density The final segment performance measure is the length of the queue at the end of the time interval if it exists which is calculated from shock wave theory Queue length on onramps can also be calculated A queue will form on the onramp roadway only if the flow is limited by a meter or by freeway traffic in the gore area If the flow is limited by the ramp roadway capacity unserved vehicles will be stored on a facility upstream of the ramp roadway most likely a surface street The methodology does not account for this delay If the queue is on the ramp roadway the queue length is calculated by using the difference in background and queue densities DETERMINING FREEWAY FACILITY PERFORMANCE MEASURES The previously discussed traffic performance measures can be aggregated over the length of the freeway facility over the time duration of the study interval or over the entire timespace domain Aggregating the estimated traffic performance measures over the entire length of the freeway facility provides facilitywide estimates for each time interval Averages and cumulative distributions of speed and density for each time interval can be determined and patterns of their variation over the connected time intervals can be assessed Trip times vehicle and person distance of travel and vehicle and person hours of travel can be computed and patterns of their variation over the connected time intervals can be assessed Aggregating the estimated traffic performance measures over the time duration of the study interval provides an assessment of the performance of each segment along the freeway facility Average and cumulative distributions of speed and density for each segment can be determined and patterns of the variation over connected freeway segments can be compared Average trip times vehicle and person distance of travel and vehicle and person hours of travel are easily assessed for each segment and compared Chapter 22 Freeway Facilities Methodology 2218 Highway Capacity Manual 2000 III APPLICATIONS The methodology is applied in the sequence indicated in Exhibit 2211 The process consists of nine steps and is based on the methodology described in the preceding section A detailed owchart that processes the oversaturation portion of the analysis is provided in Appendix A EXHIBIT 22I I IMPLEMENTATION OF FREEWAY FACILITY METHODOLOGY I CoIIect Input data ExnIbItZZ 12 Y 2 Demand estimation needed N 3 Estainsn spatIaI and time UTIIIS 4 Demand adjustments Convert counts to demand Adjust demands 5 HCM segment capacrty estimation on 23 24 or 25 5 Adjust HCM capacrties 7 Undersaturated segment SM AII segment and MOEs I07 dc s S Notes dc demand to capacrty ratio SM senIce measure MOE measure of e ectiveness COMPUTATIONAL STEPS 1 Collect input data for the directional facility Provide guidance on limits of congestion in time and space Document any demand and capacity adjustments that should be considered in the analysis The input data define the timespace domain of the Guidelines on required inputs and estimated values are given in Chapter 13 2219 Chapter 22 Freeway Facilities Applications Highway Capacity Manual 2000 Time steps can range from 15 to 60 s freeway facility The data include the specification of the facility in terms of length number of sections and geometric attributes Exhibit 2212 summarizes the inputs required to perform an analysis EXHIBIT 224 2 REQUIRED INPUT DATA FOR FREEWAY FACILITY ANALYSIS Geometric Data for Each Section Section Iengtn it MainIine number of Ianes MainIine average Iane wrdtn it MainIine IateraI cIearance it Terrain IeveI roIIing or mountainous Ramp numberotIanes Ramp acceIeration or deceIeration Iane Iengtn it Traffic Characteristics Data MainIinetreeetIow speed min optionaI VenicIe occupancy passengersyen Percent trucks and buses Va Percent recreationaI venicIes Driver popuIation commuter or recreationaI Ramp treeetIow speeds min Demand Data MainIine entry demand for each time intervaI Oneramp demands for each time intervaI Otteramp demands for each time intervaI Weavrng demand on weavrng segments 2 Check whether adjustmenm from counts to estimate demands are needed If the demands represent actual counts from a freeway facility for example from a freeway management system and the system is experiencing oversaturation an adjustment from counts to demands may be carried out in this step 3 Establish spatial and time analysis unis Convert sections to segments as described calculate time step for oversaturation and establish other time units such as time intervals and analysis duration Spatially the HCM analysis unit is a segment On the basis of the definitions of ramp influence areas 1500 ft upstream of offramps and downstream of onramps as indicated in Chapter 25 sections are subdivided into segments Similarly weaving sections are defined as having a maximum length of 2500 ft The analysis duration can vary from one to twelve 15min intervals Demand and capacity rates are fixed during an interval The time step for oversaturation analysis depends on the length of the shortest segment on the facility and can vary from 15 to 60 s 4 The procedure permits manual adjustments of segment demands This may encompass the application of overall growth factors to test the adequacy of the facility to meet projected demands or simulate the effect of demand diversion onto adjacent facilities The factors can be applied to individual origin and destination points 5 Calculate segment capacity using HCM methods and adjust capacity as needed Using the segment analysis methodologies of Chapters 23 through 25 segmentwide capacities in vehicles per hour are computed These values are assumed to reflect normal capacity conditions If the user is interested in adjusting capacities to reflect field measurements or to simulate a capacity reduction occurrence such as an incident or a work zone a capacity adjustment factor is introduced This factor changes both the capacity value and the speedflow relationship for the affected segment during the affected time intervals Chapter 22 Freeway Facilities Applications 2220 Highway Capacity Manual 2000 6 Generate an adjusted demandtocapacity dc matrix by segment and time interval Identify whether this facility is completely undersaturated or has some oversaturated time intervals Each segment demand is divided by its corresponding capacity in each time interval The resulting dc matrix is then used to evaluate the feasibility of the analysis and to identify which intervals have oversaturated segments The segment procedures are applied to undersaturated time intervals The analyst is referred to the speed density and LOS estimation methods for basic weaving and ramp segments in Chapters 23 24 and 25 respectively 7 For the first time interval with dc gt 10 for some segment begin using the reduced time step to carry out all computations Calculate the position of bottlenecks and queues in each time step Use appropriate flow regimes undersaturated for segmenm with no queues and oversaturated for segmenm with queues to estimate speeds and densities on each segment Aggregate measures of effectiveness MOEs for each segment by time interval Proceed to the next time interval until all time intervals in the period are analyzed The purpose of the oversaturated analysis is to calculate the actual flows on and the number of vehicles occupying each segment By comparing the current number of vehicles on a segment with the number of vehicles that would be expected on it at the background density segment queues can be identified and tracked each minute The smaller time step is necessary to ensure that fastgrowing queues do not jump over a short segment if not updated frequently e bottleneck analysis begins by setting the flowtocapacity ratio on that segment to 10 The unmet demand is transferred to the next time interval and the reduced flow rate through the bottleneck is propagated upstream in the form of a queue whose density depends on the severity of the bottleneck When an upstream onramp is encountered its flow rate is calculated on the basis of the level of congestion on the segment immediately downstream of the onramp and the magnitude of mainline and on ramp flows at that node Downstream of the bottleneck flows are metered at the bottleneck capacity rate which may result in starving subsequent mainline segments and offramp flows Only when the bottleneck effects clear when demands drop or capacity increases do the flows on downstream segmenm increase to serve the unmet demand from the preceding time interval Given adequate time the flows will catch up with demand and undersaturated operations will resume 9 Aggregate individual segment MOEs into a directional facility MOE for each time interval Examples include average speed density vehicle miles of travel VMT vehicle hours of travel VHT vehicle hours of delay VHD and travel time Facilitywide performance measure calculations by time interval are detailed in Appendix A TRAFFIC MANAGEMENT STRATEGIES The methodology for freeway facilities has incorporated procedures for the assessment of a variety of traffic management strategies The methodology permits the modification of previously calculated cell demands or capacities or both within the timespace domain to assess a traffic management strategy or a combination of strategies as described below A growth factor parameter has been incorporated to evaluate traffic performance when traffic demands are higher or lower than the demand calculated from the traffic counts This parameter would be used to undertake a sensitivity analysis of the effect of demand on freeway performance and to evaluate future scenarios In these cases all cell demand estimates are multiplied by the growth factor parameter 2 The effect of a predetermined rampmetering plan can be evaluated by modifying the ramp roadway capacities The capacity of each entrance ramp in each time interval is changed to the desired metering rate This feature permits both evaluation of a 2221 Chapter 22 Freeway Facilities Applications Highway Capacity Manual 2000 predetermined rampmetering plan and experimentation to obtain an improved ramp metering plan 3 Freeway design improvemenm can be evaluated within this methodology by modifying the design features of any portion or portions of the freeway facility For example the effect of adding an auxiliary lane at a critical location can be assessed The effect of adding merging or diverging lanes can also be assessed 4 Reducedcapacity situations can be investigated The capacity in any cell or cells of the timespace domain can be reduced to represent situations such as construction and maintenance activities adverse weather and traffic accidents and vehicle breakdowns 5 An independent HOV facility can be evaluated with this methodology The analysis is similar to that of a freeway facility without an HOV lane The methodology does not permit the analysis of concurrent HOV lanes User demand responses such as spatial temporal modal or total demand responses caused by a traffic management strategy are not automatically incorporated into the methodology On viewing the new freeway traffic performance results the user can modify the demand input manually to evaluate the effect of anticipated demand responses As stated earlier these traffic management strategies can be evaluated individually or in combinations For more complex traffic management strategies for which the chapter methodology is not appropriate such as concurrent HOVlane freeways or significant demand responses refer to Part V of this manual Chapter 22 Freeway Facilities Applications 2222 IV EXAMPLE PROBLEMS Highway Capacity Manual 2000 Problem N0 Descrrptron mmbwmgx Fully undersatu rated drrectronal freeway facrlrty wrtn 6 sectrons and fl segments Applrcatron of demand growth factors resultrng rn recurrrng oversaturatron Treatment of oversaturatron by means of geometrrc rmprovements of the facrlrty Effect of temporary capacrty reductron due to rncrdent Effect of reduced rncrdent response tr me on freeway facrlrty operatron Effect of ramp meterrng 0n freeway facrlrty operatron 2223 Chapter 22 Freeway Facilities Example Problems Highway Capacity Manual 2000 Chapter 22 Freeway Facilities Example Problems The Facility The Question EXAMPLE PROBLEM 1 freeway facility under existing conditions The Facts V The facts known about this freeway facility are shown in the exhibits below V Acceleration and deceleration lanes are 328 ft long V Each time interval is 15 min and all demands are expressed as hourly flow rates during each time interval SYSTEMWIDE INPUT DATA REQUIREMENTS The freeway facility is operating under capacity and traffic is expected to grow in the near future What is the capacity and levelofservice profile for the given directional Freewa Sectlon Sectlon Characterlstlcs t 2 3 4 5 6 Length ft t000 7200 2600 2300 tt50 3750 Number of lanes 3 3 3 3 3 3 Marnlrne FFS mln 68 68 68 68 68 68 Venrcle occupancy passveil t20 t 20 t20 t20 t20 t20 Lane wrdtn ft NA NA NA NA NA NA Lateral clearance ft NA NA NA NA NA NA Trucks Va 3 3 3 3 3 3 RVs Va 0 0 0 0 0 0 Terrar n Level Level Level Level Level Level Drrver populatlon Commuter Commuter Commuter Commuter Commuter Commuter Note Each ramp has one lane NA not avallable INPUT DEMANDS OneRamp O eRamp Tlme Entry Malnllne Ct 02 O3 Dt D2 EXlL Marnllne Interval O D t 4796 756 t456 648 656 560 6440 2 4772 973 M64 636 588 477 6480 3 4700 t002 t7t 2 596 636 802 6572 4 4t64 555 t548 580 520 608 57t9 5 3727 485 M80 484 632 448 4796 Outline of Solution The facility is analyzed assuming undersaturated conditions First the facility is divided into segments to enable the application of the segment analysis methods in Chapters 23 through 25 The performance results are summarized by each time interval and across time intervals using appropriate tables and charts The steps 2224 Highway Capacity Manual 2000 below follow Exhibit 2211 Note that speed and density values are soft converted from metric values Steps 1 Collection of input data The input data are summarized in the tables Note the heavy ramp demand volumes for OnRamp 02 which exceed 1700 vehh in Time Interval 3 These demands are still below the ramp roadway capacity estimated at about 2000 vehh for the ramp FFS of 44 mih Thus whereas there may be no capacity problem on the ramp roadway proper these demands may cause a merge problem on the segment immediately downstream of that ramp 2 Demand estimation No adjustments are necessary at this stage since the facility has been observed to operate under capacity 3 Establishment of spatial and time units Using the definition of ramp influence area the original 6 sections are further subdivided into 11 analysis segments The conversion is shown graphically in the exhibit below Section 4 with no auxiliary lanes and less than 900 m long contains an overlap segment 7 that is labeled R This segment s performance is calculated as the worse of Segments 6 and 8 The time intervals have been set at 15 min Furthermore since the shortest segment length is 820 ft a time step of 1 min is sufficient to carry out the oversaturated analysis 4 Demand adjustments The values in the Input Demands table are used directly to calculate segment demands by adding or subtracting ramp demands at each section CONVERSION OF FACILITY SECTIONS INTO SEGMENTS 1 Secllon 2 3 4 Length 7200 fl 26001t 230011 1150 fl 375011 5 HCM segment capacity estimation and adjustment The facility has five basic freeway segments numbered 1 3 5 9 and 11 three onramp segments 2 6 and 10 two offramp segments 4 and 8 and the overlap segment 7 For each segment type the appropriate HCM chapter 23 or 25 is consulted and the segment capacity computed The major difference in this chapter is that all segment capacities are expressed in units of vehicles per hour No adjustments of the estimated capacities are needed 6 Adjusted dc matrix After capacities are computed the dc matrix is generated for each segment and time interval Both segment capacity and dc ratios are shown in the exhibit below As suspected all segments have dc ratios less than 10 and therefore a complete undersaturated analysis can be carried out A review of the matrix indicates that Time Intervals 1 through 3 are critical and that Segments 6 through 8 10 and 11 have dc ratios above 090 during those three intervals Traffic demands subside considerably in Time Intervals 4 and 5 with a maximum dc ratio of 083 on Segment 8 in Time Interval 4 2225 Chapter 22 Freeway Facilities Example Problems Highway Capacity Manual 2000 ESTIMATED CAPACITY AND dC RATIO MATRIX Segment Number and Type Tlme 4 2 8 4 5 6 7 8 9 40 44 Interval B ONR B OFR B ONR R OFR B ONR B 4 069 080 080 080 070 094 094 094 088 098 098 2 069 088 088 088 074 094 094 094 084 098 098 8 068 082 082 082 078 098 098 098 086 095 095 4 060 068 068 068 060 088 088 088 074 082 082 5 054 064 064 064 052 069 069 069 062 069 069 Capacrty 6946 6946 6946 6946 6946 6946 6946 6946 6946 6946 6946 Note Capaerty values are taken from metne versron of HCM 2000 7 Undersaturated segment service measure and MOEs The methods in Chapters 23 through 25 are applied to estimate individual segment speeds densities and travel times Thetwo exhibits below summarize the results for segment speed density the service measure and LOS for the entire timespace domain ESTIMATED SEGMENT SPEEDS mih Segment Number and Type Trme 4 2 8 4 5 6 7 8 9 40 44 Interval B ONR B OFR B ONR R OFR B ONR B 4 684 587 660 599 679 540 540 54 7 646 566 589 2 684 580 649 600 674 554 554 589 648 564 585 8 682 580 654 599 676 488 488 567 688 559 574 4 688 602 682 608 680 564 564 572 660 586 654 5 688 609 682 604 680 595 582 582 668 604 679 Note Values are soft convened trom metne values ESTIMATED SEGMENT DENSITIES vehmiln AND LOS Segment Number and Type Tlme 4 2 8 4 5 6 7 8 9 40 44 Interval B ONR B OFR B ONR R OFR B ONR B 4 285 809 280 808 240 848 864 864 800 864 864 C D D D C D E E D E E 2 288 849 295 849 254 848 856 856 808 862 869 C D D D C D E E D E E 8 280 846 294 846 250 869 888 888 844 867 882 C D D D C D E E D E E 4 208 266 280 262 206 84 6 880 880 259 820 298 C C C C C D D D D D D 5 482 288 206 267 476 264 272 272 24 7 274 285 C C C C B C C C C C C Note Values are soft convened trom metne values 8 Oversaturated segment service measure and MOEs Does not apply in this case since the facility is fully undersaturated 9 Directional facility MOE estimation The individual segment performance measures are aggregated for each time interval The exhibit below summarizes these results Note that the average speed is defined as the ratio of vehicle miles to vehicle hours of travel in each time interval and therefore does not consider the effect of any onramp delays On the other hand vehicle hours of delay is the sum of mainline delays and ramp delays Chapter 22 Freeway Facilities Example Problems 2226 Highway Capacity Manual 2000 Mainline delays are computed as the difference between total mainline travel time and freeflow travel time SUMMARY OF FACILITYWIDE PERFORMANCE MEASURES Perform nce Measures Tlrne Vehlcleernl of Vehlcleeh of Vehlcleeh of Average Average Densrty Facrllty Travel Interval Trave Travel Delay Speed mlh vehrnll n Tlrne mm 4 4873 798 84 644 305 334 2 4976 842 80 643 342 333 3 5020 838 400 599 347 340 4 4244 669 45 634 260 322 5 3658 568 30 644 226 347 Overall 22774 3685 336 648 7 329 Results It is evident from the results that the facility provides freeflow conditions Time Intervals 1 through 3 are fairly similar with average speeds varying within a 15mih range and densities slightly below 32 vehmiln Time Intervals 4 and 5 have higher average speeds exceeding 63 mih and average densities equal to and under 26 vehmiln 2227 Chapter 22 Freeway Facilities Example Problems Highway Capacity Manual 2000 EXAMPLE PROBLEM 2 The Facility In this example thefacility described in Example Problem 1 is evaluated under revised traffic demands The Question What is the capacity and Ievelofservice profile for a directional freeway facility using the revised demands The Facts V The facts shown in Example Problem 1 apply V Demand is adjusted upward by 6 percent uniformly The new demand rates are shown in the exhibit below REVISED INPUT DEMANDS OneRarnp O eF arnp Tlrne Entry Malnllne O4 O2 08 D4 D2 EXlt Malnllne Interval O D 4 5084 804 4548 689 695 594 6826 2 5058 4084 4284 674 628 506 6869 8 4982 4062 4845 682 674 850 6966 4 4444 588 4644 64 5 554 644 6062 5 8954 544 4254 54 8 670 475 5084 Outline of Solution Since the base demands and capacities have not changed Steps 1 to 3 of Example Problem 1 are skipped The analysis begins by adjusting demands and then proceeds to determine whether oversaturated conditions will prevail If they do a shorter time step will be used to track the position of the queues the location of the bottlenecks and their effect on both mainline and rampflows speeds and densities Note that speeds densities and queue lengths are soft converted from metric values Steps 1 Demand adjustments The input demands shown in the exhibit above represent increases of 6 percent compared with Example Problem 1 2 HCM capacity estimation and adjustment Normally no adjustments of the capacities computed in Example Problem 1 are needed since the facility geometrics are fixed There is evidence however that when queuing occurs on a segment the discharge flow rate in the queue may be less than the HCMestimated capacity by 3 to 5 percent The HCM capacities assume undersaturated flow conditions To implement a variable segment capacity under queuing the analyst must first identify which if any segments have a queue and then make a second run with a reduced capacity for those segments using the capacity adjustment factor For simplicity in this example the HCM capacity is assumed to apply to queued segments as well 3 Adjusted dc matrix Using the adjusted demands a revised dc matrix shown in the exhibit below is generated Cells having dc gt 10 are underlined ESTIMATED CAPACITY AND dC RATIO MATRIX Segme Nurnbe and Ty e Tlrne 4 2 8 4 5 6 7 8 9 40 44 Interval B ONR B OFR B ONR B OFR B ONR B 4 078 085 085 085 075 097 097 097 088 098 098 2 078 088 088 088 079 096 096 096 089 099 099 8 072 087 087 087 077 w w w 094 w w 4 064 072 072 072 064 088 088 088 078 087 087 5 057 064 064 064 055 078 078 078 066 078 078 Capactty 6946 6946 6946 6946 6946 6946 6946 6946 6946 6946 6946 Note Capamty values are taken from metrlc verston of HCM 2000 Chapter 22 Freeway Facilities Example Problems 2228 Highway Capacity Manual 2000 The dc matrix indicates that fully undersaturated conditions prevail in the first two and the last two time intervals Two sets of bottlenecks occur in Time Interval 3 The first and more severe bottleneck is on Segments 6 through 8 with a dc of 103 The second and less severe bottleneck is on Segments 10 and 11 with a dc of 1003 It is likelythat the second bottleneck will be hidden as a result of the metering effect of the first one Whether the two queues from the bottlenecks will overlap thus violating an important constraint of the methodology remains to be seen 4 Undersaturated segment service measure and MOEs The first two time intervals are undersaturated and therefore all MOEs are derived directly from the procedures in Chapters 23 24 and 25 5 Oversaturated segment service measure and MOEs Starting with Time Interval 3 the analysis is performed in 1min increments and a set of nodes is defined at each ramp terminal First flow rates are determined in each time step Starting from the furthest upstream segment in Time Interval 3 flows across nodes are calculated until the bottleneck Segment 6 is reached On Segment 6 flow is equated to capacity and the residual demand is applied at that bottleneck in Time Interval 4 Upstream of Segment 6 the queue density is calculated and queue length is tracked on Segments 5 4 and so forth Downstream of Segment 6 flows are metered at the segment capacity rate The same process is applied to the bottlenecks on Segments 10 and 11 Since the demands in Time Intervals 4 and 5 drop significantly queues will begin to clear and dissipate by the end of the analysis period The exhibit below shows the actual volumetocapacity ratios estimated on each segment and time interval Note that volumes are averaged over the 15 time steps per interval and reflect the output flow for a segment By definition no vc ratio can exceed 100 As anticipated the bottleneck Segments 6 through 8 are operating at capacity in Time Interval 3 The metering effect of this bottleneck hides the second bottleneck on Segments 10 and 11 which have a vc lt 10 in Time Interval 3 A comparison of the dc and WC matrices indicates that flows exceed demands in Time Interval 4 which indicates that the unserved demand in Time Interval 3 is now being served in Time Interval 4 There are no differences in demand and flows in the last time interval suggesting that thefacility performance has fully recovered by the end of the analysis period ESTIMATED CAPACITY AND vc RATIO MATRIX Segment Number and Type Tlrne 1 2 8 4 5 6 7 8 9 10 11 Imewal B ONR B OFR B ONR B OFR B ONR B 078 085 085 085 075 097 097 097 088 098 098 078 088 088 088 079 096 096 096 089 099 099 072 087 087 087 077 100 100 100 088 097 097 064 072 072 072 064 091 091 091 081 090 090 5 057 064 064 064 055 078 078 078 066 078 078 CapaCIty 6946 6946 6946 6946 6946 6946 6946 6946 6946 6946 6946 Note Capame values are taken from mine versmn of HCIVI 2000 boom The next performance measure investigated is the queue lengths observed on the mainline segments and on the ramps These values represent instantaneous observations at the end of each time interval The results are shown in the exhibit below by segment and time interval Blank entries indicate no queuing The vc matrix above indicates that a queue develops on the onramp roadway on Segment 6 in Time Interval 3 This queue is caused by the heavy onramp demand of 1815 vehh in that time interval Since the mainline entering demand is under 1800 vehhIn no queuing occurs on the freeway mainline The actual onramp flow is estimated at 1576 vehh and the difference 1815 1576 causes a queue to develop and reach a length of 3901 ft at the end of Interval 3 That queue is fully dissipated bythe end of Time Interval 4 Whilethere are no 2229 Chapter 22 Freeway Facilities xample Problems Highway Capacity Manual 2000 queues in Time Interval 5 the excess flows withheld in the previous intervals are served fully and all vehicles are discharged at the end of the analysis period ESTIMATED QUEUE LENGTH fl ON MAINLINE AND RAMPS R AT END OF EACH TIME INTERVAL Segme tNumbera dType Tlme 4 2 3 4 5 7 8 9 40 44 Interval B ONR B OFR B ONR R OFR B ONR B 4 2 3 3904 R 4 5 Note Value IS soft convened from metrlc values To complete the oversaturated segment analysis a summary of the resulting segment speeds segment densities and segment LOS for each time interval is given in thetwo exhibits below ESTIMATED SEGMENT SPEEDS mih Segment Number and Type Tlme 4 2 3 4 5 6 7 8 9 40 44 Interval B ONR B OFR B ONR R OFR B ONR B 4 676 579 640 597 673 542 542 578 620 543 540 2 677 569 624 598 663 533 533 587 645 540 533 3 678 570 632 597 668 470 470 574 624 548 550 4 683 598 678 602 680 520 520 563 654 573 607 5 683 605 682 600 680 589 584 584 663 604 676 Note Values are soft convened from metrlc values ESTIMATED SEGMENT DENSITIES vehmiIn AND LOS Segment Number and Type Tlme 4 2 3 4 5 6 7 8 9 40 44 Interval B ONR B OFR B ONR R OFR B ONR B 4 254 327 306 327 258 369 383 383 330 380 422 C D D D D E E E D E E 2 250 338 325 338 275 369 377 377 337 383 430 C D D D D E E E D E E 3 245 335 320 335 269 378 395 395 329 377 409 C D D D D E E E D E E 4 24 6 280 246 277 24 7 345 367 367 288 353 345 C D C D C D E E D D D 5 493 254 247 248 487 279 288 288 230 285 254 C C C C C D D D C D C Note Values are soft convened from metrlc values 6 Directional facility MOE estimation The individual segment performance measures are aggregated for each time interval An important addition in this example is the inclusion of two VMT measures the first based on demands VMTD and the second based on actual flow rates VMTF These values are used to detect whether vehicle storage when VMTD gt VMTF or queue release VMTD lt VMTF is occurring in each interval Appendix A provides details of the computations needed to obtain the Chapter 22 Freeway Facilities Example Problems 2230 Highway Capacity Manual 2000 facilitywide measures The exhibit below summarizes the facilitywide results by time interval SUMMARY OF FACILITYWIDE PERFORMANCE MEASURES Pe orrnance Mea ures Tlrne Vehlcleernl Vehlcleernl Vehlcleeh of Vehlcleeh of Average Average Facrllty Interval of Travel of Travel Travel Delay Speed nsrty Travel Tlrne Demand Flow Rate mlh vehrnll n mm 4 5466 5466 874 444 593 334 344 2 5275 5275 894 448 590 344 346 3 5322 5240 893 202a 587 336 348 4 4499 4580 744 409a 648 284 330 5 3878 3878 603 33 643 236 34 7 Overall 24440 244 39 4002 573 603 7 337 Note a Vehlcle not delay values are taken from mine versron of HCM 2000 Result It is instructive to compare the above results with those obtained in Example Problem 1 Whereas the total VMT between the two problems increased only by 6 percent the total vehicle hours of travel on the mainline increased by 86 percent The total vehicle delay on the system which includes estimated delay on the onramps went up by 70 percent If one compares the performance in the third time interval the difference is even greater with delays increasing by more than 102 percent On average the system density appears to have increased by 10 percent Interestingly the average speeds do not vary substantially This may be due to boundary segments which contribute significantly to the overall speed value by virtue of their length but typically experience little congestion 2231 Chapter 22 Freeway Facilities Example Problems Highway Capacity Manual 2000 EXAMPLE PROBLEM 3 The Facility In this example the facility analyzed in Example Problem 2 is evaluated with revised geometry The Question What is the capacity and Ievelofservice profile for the directional freeway facility using the revised geometry The Facts v The facts from Example Problem 2 apply v Recurring congestion is observed during the first hour downstream of onramp Segment 6 to the end of the study section An auxiliary lane on the freeway mainline between Segments 6 and 8 over a distance of 2300 ft is proposed Outline of Solution The capacity of the upgraded segment which is now a Type A weave is first estimated Its effects on the segment and facility performance measures are shown For ease of reference this segment is labeled 678 The total number of segments on thefacility is reduced from 11 to 9 Notethat speeds densities and queue lengths are soft converted from metric values Steps 1 The analysis of Weaving Segment 678 requires knowledge of weaving and nonweaving demand volume In this example weaving demands of 1868 1340 2065 1925 and 1326 vehh are assumed to occur in Time Intervals 1 through 5 respectively 2 HCM capacity estimation and adjustments The number of lanes on Segments 6 through 11 is now adjusted to four No changes in segment types or other geometric data are made 3 Adjusted dc matrix The application of the methodology yields the revised dc matrix and segment capacities indicated in the exhibit below The auxiliary lane addition to Segment 678 was sufficient to restore undersaturated conditions on that segment However the second bottleneck on Segments 10 and 11 still exists This implies that the improved facility can for the most part absorb the additional growth rate in traffic demands and still operate at an acceptable level ESTIMATED CAPACITY vehh AND dC RATIO MATRIX Segment Number and Type Tlrne Interval 1 2 3 4 5 678 9 10 11 B ONR B OFR B W B ONR B 1 073 085 085 085 075 080 088 098 098 8410 2 073 088 088 088 079 075 089 099 099 8946 3 072 087 087 087 077 087 091 1003 1003 8272 4 064 072 072 072 064 076 078 087 087 8055 5 057 064 064 064 055 060 066 073 073 8469 Capacrty 6946 6946 6946 6946 6946 capacrty 6946 6946 6946 Note Capame values are taken from metrlc versmn of HCIVI 2000 4 Undersaturated segment service measure and MOEs The segment speeds densities and level of service for the upgraded facility are summarized in the exhibits below In Time Interval 3 the oversaturated analysis is initiated 5 Oversaturated segment service measures and MOEs The nowactive bottleneck on Segments 10 and 11 yields a queue 400 ft long on Segment 9 in Time Interval 3 Note Chapter 22 Freeway Facilities Example Problems 2232 Highway Capacity Manual 2000 that this value is soft converted from the metric value The queue is dissipated at the start of Time Interval 4 More important however is that the geometric improvement on Segment 678 has eliminated the 3901ft queue that was observed on the ramp roadway in the preceding example 6 Directional facility MOE estimation The individual segment performance measures are aggregated for each time interval The results are shown in the three exhibits below Results The upgraded facility performance is compared with that given in Example Problem 2 The mainline travel time has increased slightly by 07 percent because of the nowactive bottleneck on Segments 10 and 11 in Time Interval 3 However the overall system delay including onramp delays dropped by 15 percent There were minor changes in overall facility speeds densities and travel times ESTIMATED SEGMENT SPEEDS mih Segment Number and Type Tlme 1 2 3 4 5 673 9 10 11 New B ONR B OFR B w B ONR B 1 67 6 57 9 64 0 597 673 52 2 62 0 54 2 54 0 2 67 7 56 9 624 593 663 56 6 615 53 9 53 3 3 67 3 57 0 62 3 597 668 50 2 53 5 53 3 521 4 63 3 59 3 67 3 602 630 50 9 66 7 57 6 62 5 5 63 3 60 5 63 2 600 630 56 3 67 6 59 6 67 6 ESTIMATED SEGMENT DENSITIES vehmiIn AND LOS Segment Number and Type Tlme 1 2 3 4 5 673 9 10 11 New B ONR B OFR B w B ONR B 1 251 327 306 327 253 322 330 330 422 C D D D C D D E E 2 250 333 325 333 275 296 337 333 430 C D D D D D D E E 3 245 335 320 335 269 357 393 386 444 C D D D D E E E E 4 216 230 246 277 217 300 274 340 325 C D C D C D D D D 5 193 251 217 243 137 224 225 235 251 C C C C C C C D C SUMMARY OF FACILITYWIDE PERFORMANCE MEASURES Performance Measures Tlm Vehlcleeml Vehlcleeml of Vehlcleeh Vehlcleeh Average Average Facrllty Interval ofTravel Travel Flow of Travel of Delay Speed mlh Densrty Travel T1 me Demand Rate vehmlIn mm 1 5166 5166 874 114 591 324 346 2 5275 5275 891 115 592 331 346 3 5322 5318 928 149a 573 341 357 4 4499 4503 730 71a 617 272 332 5 3878 3878 607 37 639 228 320 Overall 24140 24140 4029 486 599 7 340 Note a Vehlcle not delay values are taken from metrlc versron 01HCM 2000 2233 Chapter 22 Freeway Facilities Example Problems Highway Capacity Manual 2000 EXAMPLE PROBLEM4 The Facility In this example the facility analyzed in Example Problem 1 is evaluated with reduction of capacity on Segment 9 in the first four time intervals due to an accident on the shoulder nonrecurring congestion The Question What is the capacity and Ievelofservice profile for a directional freeway facility with nonrecurring congestion on Segment 9 The Facts v The facts shown in Example Problem 1 apply Outline of Solution The segment capacity adjustment factor is used This factor reduces the subject segment capacity for a limited number of time intervals A revised speedflow curve is also used in this case Because of space limitations the results that follow are confined to the effect of the incident on segment and facility performance The results are compared with those obtained in Example Problem 1 Note that speeds densities and queue lengths are soft converted from metric values Steps 1 Adjustment of HCM capacities in this example the previously computed capacity for Segment 9 6946 vehh is multiplied by the capacity adjustment factor for shoulder accidents This value is taken from Exhibit 226 and is estimated at 083 It yields a revised segment capacity of 5765 vehh The revised capacity is applied in Time Intervals 1 through 4 only 2 Adjusted dc matrix The matrix is shown in the exhibit below As suspected a single bottleneck on Segment 9 appears and is active during the first three time intervals As stated in Example Problem 2 the incident causes oversaturation in the first time interval and therefore it may be desirable for the user to begin the analysis one time interval earlier However because the level of oversaturation is very light Segment 9 dc is 1005 the methodology will still produce correct estimates of performance in this case Note that demand drops significantly in Time Interval 4 and demand flows can still pass through the reduced segment capacity ESTIMATED CAPACITY vehh AND dC RATIO MATRIX Segment Number and Type Tlrne 4 2 3 4 5 6 7 8 9 40 44 Interval B ONR B OFR B ONR R OFR B ONR B 4 069 080 080 080 070 094 094 094 m 093 093 2 069 083 083 083 074 094 094 094 M 093 093 3 068 082 082 082 073 098 098 098 g 095 095 4 060 068 068 068 060 083 083 083 089 082 082 5 054 061 061 061 052 069 069 069 062 069 069 Capacnya 6946 6946 6946 6946 6946 6946 6946 6946 5765b 6946 6946 6946 Note a Capame values are taken from metrlc versmn of HCIVI 2000 b Applles 10 Tlme lntervalsj through 4 only 3 Oversaturated segment service measures and LOS The results of the oversaturated analysis are shown in the exhibit below for queue length position at the end of each interval Chapter 22 Freeway Facilities Example Problems 2234 Highway Capacity Manual 2000 ESTIMATED QUEUE LENGTH II AT END OF EACH TIME INTERVAL Segment Number and Type Tlme 4 2 3 4 5 6 7 3 9 4o 44 Interval B ONR B OFR B ONR R OFR B ONR B 4 594 2 430 3 328R 656 320 669 4 4692 R 656 320 5 1411R Note Values are soft convened from metnc values The exhibits below illustrate segment speeds densities and levels of service ESTIMATED SEGMENT SPEEDS mih Segment Number and Type Tlme 4 2 3 4 5 6 7 3 9 4o 44 Imewal B ONR B OFR B ONR R OFR B ONR B 4 634 537 660 599 679 540 467 467 433 567 592 2 634 530 649 600 674 552 407 353 433 563 594 3 682 530 654 599 669 492 463 409 437 570 601 4 683 602 682 603 680 636 650 630 486 534 632 5 683 609 682 601 680 593 534 534 662 601 679 Note Values are soft convened from metnc values ESTIMATED SEGMENT DENSITIES vehmiln AND LOS Segment Number and Typ 1 2 3 4 5 6 7 8 9 10 11 Tlme Interval B ONR B OFR B ONR R OFR B ONR B 235 309 280 308 240 348 361 361 300 361 364 C D D D C D F F E E E 2 233 319 295 319 254 348 356 356 303 362 369 C D D D C F F F E E E 3 230 316 291 316 250 369 388 388 314 367 382 C D D D C F F F E E D 4 203 266 230 262 206 316 330 330 259 320 293 C C C C C D D D E E D 5 182 238 206 235 176 264 272 272 217 271 235 C C C C B C D D C D C Note Values are soft convened from metnc values The above results indicate that the incident causes queues to develop on both the freeway mainline and the onramp at Segment 6 in Time Intervals 1 through 3 Since traffic demand drops sharply in Interval 4 the mainline queues dissipate by the end of that interval A residual queue 1411 ft long remains on the onramp roadway proper at the end of Time Interval 4 Poor level of service is observed in Segments 6 through 8 upstream of the bottleneck during the first three time intervals However all queues are cleared and undersaturated operations are restored during Time Interval 5 4 Directional facility MOE estimation The individual segment performance measures are aggregated for each time interval Both VMT measures based on demands VMTDemand and the actual flow rates VMTFIow Rate are computed The following exhibit summarizes the facilitywide results by time interval 2235 Chapter 22 Freeway Facilities Example Problems Highway Capacity Manual 2000 SUMMARY OF FACILITYWIDE PERFORMANCE MEASURES Performance Measures Trrne Vehrcleernr Vehrcleernr Vehrcleeh Vehrcleeh Average Average Facrlrty Interval of Travel of Travel of Travel of Delay Speed rnrh Densrty Travel Trrne Demand Flow Rate vehrnrln rnrn 4 4873 4872 833 4 4 9H 585 305 349 2 4976 4972 874 454a 569 34 2 359 3 5020 5009 874 245a 575 34 7 355 4 4244 4264 680 484 a 627 260 325 5 3658 3658 568 345a 644 223 34 7 Overall 22774 22772 3824 7335 595 7 344 Note a Vehrcle not delay values are taken from rnetnc versron of HCM 2000 Results It is instructive to compare the results of this example problem with those obtained in Example Problem 1 While serving the same VMT the total vehicle hours of travel on the mainline due to the incident increases by 38 percent The total vehicle delay on the system which includes estimated delay on the onramps increases by 118 percent In the fourth time interval the differences are even greater with delays increasing by 302 percent On average the system density under incident conditions appears to have increased by 10 percent and the average speed has dropped by about 36 percent Chapter 22 Freeway Facilities Example Problems 22 36 Highway Capacity Manual 2000 EXAMPLE PROBLEM 5 The Facility In this example problem the facility analyzed in Example Problem 4 is evaluated with incident management to mitigate the effect of the incident The Question For normal conditions a 60min incident and a 30min incident compare qualityofservice and performance measures The Facts v The facts of Example Problem 1 apply except that the incident effect on the capacity of Segment 9 is limited to the first two time intervals Ste s 1 A summary of the results is given in the exhibit below EFFECT OF REDUCED INCIDENT DURATION 0N SELECTED FACILITY PERFORMANCE MEASURES Factllty Performance Measure Normal Condltlons 607mm Ineldent 307mm Ineldent mplet Example 4 Example 5 Vehlcleeml malnllne travel 2277t 2277t 2277t Vehlcleeh malnllne travel 3685 3824 3782 Vehlcleeh malnllne delay h 336 487 442 Vehlcleeh oneramp delay h 00 245 87 Vehlcleeh total delay h 336 732 529 Overall maxtmum dc ratlo segment 098 6 7 8 t04 9 t0t 9 Average malnllnefactllty speed mlh 6L8 595 603 Average malnllnetravel tlme mm 329 34t 340 Maxlmum malnllne queuea ft 0 2t46 L657 Tlme Interval WlIIl max malnllne queue NA 3 2 Maxlmum ramp queue ft 0 4692 2762 Tlme Interval WlIIl max ramp queue NA 3 3 Note a Measured from the downstream end of Segment 8 ust upstream of Segment 9 NA not applleable Values are soft convened from metrle values Results As expected the reduced incident duration improves both mainline and ramp traffic performance Overall mainline delays drop by a modest 92 percent while ramp delays are reduced by 65 percent Similarly the maximum queue length on the mainline drops by 23 percent compared with a 41 percent drop in ramp queues The maximum on ramp demand occurs at the start of Interval 3 by which time the incident has been cleared under the 30min incident scenario 2237 Chapter 22 Freeway Facilities Example Problems Highway Capacity Manual 2000 EXAMPLE PROBLEMS The Facility In this example problem the facility analyzed in Example Problem 5 is evaluated with ramp metering for the onramp flow on Segment 6 The Question What are the performance measures of normal 60min incident and rampmetering conditions The Facts v The facts shown in Example Problem 4 apply v Metering rates of 900 vehh and 1200 vehh are selected Outline of Solution This strategy is intended to minimize the queues on the freeway at the expense of ramp queues and delays The effect on the adjacent surface operation is not considered in this analysis and therefore the results should be viewed with caution The metering rate selected was 900 vehh which is the maximum rate recommended for singlelane onramps 15 Ramp metering is applied only tothe first three time intervals since the onramp demand drops significantly in Time Interval 4 A second metering strategy is also evaluated This strategy uses a twolane rampmetering rate of 1200 vehh in which vehicle departures alternate at the higher rate As in Example Problem 5 only facilitywide measures are reported Note that speeds densities and queue lengths are soft converted from metric values Steps 1 A summary of the facility performance measures is given in the exhibit below As expected the singlelane ramp metering causes severe congestion and queuing on the onramp at Segment 6 while eliminating the mainline queue In fact the onramp queues on Segment 6 are not cleared by the end of the analysis period resulting in fewer vehicle miles of travel production However it is virtually impossible that the observed maximum ramp queue of 32113 ft could ever materialize in the field without spilling back onto the surface street system or causing ramp drivers at Segment 6 to divert elsewhere EFFECT OF RAMPMETERING STRATEGIES 0N SELECTED FACILITY PERFORMANCE MEASURES Factllty Performance Measure Normal 607mm Ineldent Meterlng Rate Meterlng Rate Condltlons Example 4 N0 900 vehh t200 vehh Example t Meterlng Slngle Lane Two Lanes Vehlcleeml malnllne travel 2277t 2277t 22720 2277t Vehlcleeh malnllne travel 3685 3824 3709 380t Vehlcleeh malnllne delay h 336 487 377 460 Vehlcleeh oneramp delay h 00 245 2605 949 Vehlcleeh total delay h 336 732 2982 t409 Overall maxtmum dc ratlo segment 098 6 7 8 t04 9 t04 9 t04 9 Average malnllne faculty speed mlh 6t 8 595 6t 4 60t Average malnllnetravel tlme mm 329 34t 330 340 Maxlmum malnllne queuea ft 0 2t46 0 M09 Tlme Interval wtth max malnllne queue NA 3 NA 2 Maxlmum ramp queue ft 0 4692 32tt3 9846 Tlme Interval wtth max ramp queue NA 3 4 2 Note a Measured from the downstream end of Segment 8 NA not applleable Values are set convened from metrle values With twolane metering the onramp queue is reduced to 9846 ft which is still quite high Furthermore there is now queuing on the mainline Thus it appears that thetwo Chapter 22 Freeway Facilities Example Problems 2238 Highway Capacity Manual 2000 rampmetering strategies presented in this example are not as effective in improving system performance as the reduction in incident responsetime performed in Example Problem 5 The user may test additional strategies that can be handled by the methodology They include for example a combination of reduced incident response and ramp metering and systemwide ramp metering in which metering rates on Segments 3 and 6 are jointly determined Diversion strategies in which the excess demand on Segment 6 is rerouted to the surface street system and back onto the freeway downstream of the incident location can also be evaluated Results An overall comparison of the freeway facility performance measures is shown in the exhibit below Scenarios 1 through 5 represent the conditions described in Examples Problems 1 through 5 respectively Scenarios 6 and 7 represent the effects of the two rampmetering strategies described in Example Problem 6 The purpose of this chart is to demonstrate the sensitivity of various facility performance measures to key geometric and traffic management improvement strategies The results suggest that mainline speed total vehicle miles of travel and total vehicle hours of travel are not very sensitive to the various strategies On the other hand total system delay VHD appears to vary considerably across scenarios VHD is defined as the difference between the actual mainline travel time and travel time at the freeflow speed the sum of all ramp delays Since this is the only performance measure that incorporates ramp delays in its calculations it should be considered a key measure in evaluating the operational performance of freeway facilities 2239 Chapter 22 Freeway Facilities Example Problems Highway Capacity Manual 2000 SUMMARY COMPARISON OF FACILITY PERFORMANCE MEASURES 4500 3500 7 quot quotquot 4000 1 39 7 3000 R 3500 I I I 7 2500 3000 VHTeMarnIrne II g VHDeSyslem I E s d M l I gt i pee 7 am me I 7 2000 3 2500 VMTrMarnIrne 0005 I E I z I E 2000 i I g I 7 1500 g I o E I E 1500 i I gt I l 7 1000 I I I000 i I I A I 50 0 L 39 39 39 39 39 39 39 39 39 39 39 quotquot39I i 39 500 i OUII2I3I4I5I6I7O39O Scenarlo Number Notes Seenarlo I base seenano ExampleI Seenarlo 2 base 6 demand growth Seenarlo 3 Seenarlo 2 aUXIllan lane on Seetlon 4 Seenarlo 4 base 60 mln lneldent on Seetlon 5 Seenarlo 5 base 30 mln lneldent on Seetlon 5 Seenarlo 6 base 60 mln lneldent 900 venn slngle lane meter second on ramp Seenarlo 7 base 60 mln lneldent I200 venn two lane meter second on ramp Chapter 22 Freeway Facilities 2240 Example Problem VHD n and Speed m n i Q Equot P 5 quot 0 gt1 so gt9 i O i E0 Equot a P 5 quot Highway Capacity Manual 2000 V REFERENCES May A D et al Capacity and Level ofService Analysisfor Freeway Facilities Fourth Interim Report SAlC Corp March 1999 Manual on Uniform Traffic Control Devices Federal Highway Administration US Department of Transportation 1986 Krammes R A and G O Lopez Updated Capacity Values for ShortTerm Freeway Work Zone Lane Closures ln Transportation Research Record I 442 TRB National Research Council Washington DC 1994 pp 49756 Dudek C L Notes on Work Zone Capacity and Level ofService Texas Transportation Institute Texas AampM University College Station Tex 1984 Dudek C L S H Richards and J L Buffington Improvements and New Concepts for Traf c Control in Work Zones Volume I FourLane Divided Highways Report FHWARD85034 Federal Highway Administration US Department of Transportation 1985 Burns E N C L Dudek and O J Pendleton Construction Costs and Safety Impacts of Work Zone Traffic Control Strategies Volume I Final Report Report FHWARD89209 Federal Highway Administration US Department of Transportation 1989 Ressel W Traffic Flow and Capacity at Work Sites on Freeways Highway Capacity and Level of Service Proc International Symposium on Highway Capacity Karlsruhe Germany Balkema Rotterdam Netherlands 1991 pp 3217 328 Lamm R E M Choueiri and T Mailaender Comparison of Operating Speeds on Dry and Wet Pavements of TwoLane Rural Highways ln Transportation Research Record 1280 TRB National Research Council Washington DC 1990 pp 1997207 Ibrahim A T and F L Hall Effect of Adverse Weather Conditions on Speed FlowOccupancy Relationships ln Transportation Research Record 1457 TRB National Research Council Washington DC 1994 pp 1847191 Hogema J H A R A Vanderhorst and P J Bakker Evaluation ofthe I6Fog Signaling System with Respect to Driving Behaviour Evaluatie Van Het a 16 Mistsignaleringssysteem in Termen Van Het Rijgedrag Report TNOTM 1994 C48 TNO Technische Menskunde Soesterberg Netherlands 1994 Aron M M Ellenberg P Fabre and P Veyre Weather Related Traffic Management In Towards an Intelligent Transport System Proc First World Congress on Applications of Transport Telematics and Intelligent Vehicle Highway Systems Paris Vol 3 Ertico Brussels Belgium 1994 pp 108971096 Brilon W and M Ponzlet Auswirkungen on Zeitlich Veraenderlichen Leistungsfaehigkeiten Schlussbericht Lehrsti39ihl fur Verkehrswesen Ruhr Universitat Bochum Germany 1995 Giuliano G Incident Characteristics Frequency and Duration on a High Volume Urban Freeway Transportation Research Vol 23A No 5 1989 pp 3877396 Reiss R A and W M Dunn Jr Freeway Incident Management Handbook Report FHWASA91056 Federal Highway Administration US Department of Transportation 1991 Gordon R L R A Reiss H Haenel E R Case R L French A Mohaddes and R Wolcott Traf c Control Systems Handbook Report FHWASA95032 Federal Highway Administration US Department of Transportation 1996 2241 Chapter 22 Freeway Facilities References Highway Capacity Manual 2000 APPENDIX A DETAILED COMPUTATIONAL MODULES FOR FREEWAY FACILITIES A1 SCOPE OF APPENDIX MATERIAL The freeway facility analytical methodology is described in the main body of this chapter The computations contained within the methodology are detailed in this appendix In Section II of the main body the characteristics of freeway flow that are computed in the methodology are discussed The computational steps are given in Section III In Section A1 of this appendix the limitations of the methodology are outlined and a glossary of all relevant variables is presented The overall procedure presented in Section III of the main body is described in more detail in Section A2 The computations for the undersaturated portion of the methodology are detailed in Section A The 1 39 of the are detailed in Section A4 Section A5 contains the directional facility computations A11 Limitations The procedure described herein becomes extremely complex when the queue from a downstream bottleneck extends into an upstream bottleneck causing a queue collision When such cases arise the reliability of the methodology is questionable and the user is cautioned about the validity of the results However noninteracting bottlenecks are accommodated by the methodology he completeness of the analysis will be limited if freeway segment cells in the first time interval the last time interval and the first freeway segment do not all have demand tocapacity ratios less than 100 The methodology can handle congestion in the first interval properly although it will not quantify any congestion that could have occurred before the analysis To ensure complete quantification of the effects of congestion it is recommended that the analysis contain an initial undersaturated time interval If all freeway segments in the last time interval do not exhibit demandtocapacity ratios less than 100 congestion continues beyond the last time interval and additional time intervals should be added This fact will be noted as a difference between the vehicle miles of travel demand desired at the end of the analysis and the corresponding vehicle miles of travel flow generated If queues extend upstream of the first segment the analysis will not account for the congestion oumide the freeway facility but will store the vehicles vertically until the congestion clears the first segment The same process is followed for queues on onramp roadways The analyst could given enough time analyze a completely undersaturated time space domain manually although this is highly unlikely It is not expected that an analyst will ever manually analyze a timespace domain that includes oversaturation For heavily congested directional freeway facilities with interacting bottleneck queues a simulation model might be more applicable A12 Glossary In this glossary internal variables used exclusively in the freeway facilities methodology are defined The glossary of variables covers six parts global variables segment variables node variables onramp variables offramp variables and facilitywide variables Segment variables represent conditions on segments Node variables denote flows across a node connecting two segments Facilitywide variables pertain to aggregate traffic performance over the entire facility Onramp and offramp variables are variables that correspond to flow on ramps In addition to these spatial categories there are temporal divisions that represent characteristics over either a time step or a time interval The first dimension associated with each variable specifies whether the variable refers to segment or node characteristics The labeling scheme for nodes and segmenm is such that Segment i is immediately downstream of Node i Chapter 22 Freeway Facilities Appendix A 2242 Highway Capacity Manual 2000 Thus there is always one more node than the number of segments on a facility The second and third dimensions denote a time step t and a time interval p Facility variables are estimates of the average performance over the entire length of the facility The unis of flow are in vehicles per time step The selection of the time step size is discussed later in this appendix Global Variables KCiDensity at capacity the ideal density at capacity vehmiln The density at capacity is 45 pcmiln which must be converted to vehmiln using the heavyvehicle factor fHV described in Chapter 23 KJiJam density the facilitywide jam density vehmiln NSiNumber of segments the number of segments on the facility iilndex to segment or node number i l 2 NS for segments andi l NS l for nodes PiNumber of time intervals number of time intervals in the analysis period P piTime interval number p l 2 P SiTime steps per interval number of time steps in a time interval integer tiNumber of time steps in a single interval t l 2 S TiTime steps per hour number of time steps in l h integer Segment Variables EDi piExpected demand the demand that would arrive at Segment i on the basis of upstream conditions over Time Interval p The upstream queuing effects include the metering of traffic from an upstream queue but not the spillback of vehicles from a downstream queue Ki piAverage segment density the average traffic density of Segment i over Time Interval p as estimated by the oversaturated procedure KB i piB ackground density Segment i density vehmiln over Time Interval p assuming there is no queuing on the segment This density is calculated using the expected demand on the segment in the corresponding undersaturated procedure in Chapters 23 through 25 KQi t p4Queue density vehicle density in the queue on Segment i during Time Step t in Time Interval p The queue density is calculated on the basis of a linear densityflow relationship in the congested regime see Exhibit A22 5 LiiLength the length of Segment i mi Ni piNumber of lanes the number of lanes on Segment i in Time Interval p Could vary by time interval if a temporary lane closure is in effect NVi t p7Number of vehicles the number of vehicles present on Segment i at the end of Time Step t during Time Interval p The number of vehicles is initially based on the calculations of Chapters 23 through 25 but as queues grow and dissipate inputoutput analysis updates these values in each time step Qi t p4Queue length total queue length on Segment i at the end of Time Step t in Time Interval p ft SCi piSegment capacity maximum number of vehicles that can pass through Segment i in Time Interval p based strictly on traffic and geometric properties These capacities are calculated using Chapters 23 through 25 SDi piS egment demand the desired flow rate through Segment i including on and offramp demands in Time Interval p veh This segment demand is calculated without any capacity constraints SFi t piSegment flow the segment flow out of Segment i during Time Step t in Time Interval p veh WS i piWave speed the speed at which a frontclearing queue shock wave travels through Segment i during Time Interval p fts 2243 Chapter 22 Freeway Facilities ppendix A Highway Capacity Manual 2000 WTTi piWave travel time the time taken by the shock wave traveling at the wave speed WS to travel from the downstream end of Segment i to the upstream end of the segment during Time Interval p in time steps Ui piAverage segment speed the average spacemean speed over the length of Segment i during Time Interval p mih UVi t piUnserved vehicles the additional number of vehicles stored on Segment i at the end of Time Step t in Time Interval p due to a downstream bottleneck Node Variables MIi t piMaximum mainline input the maximum flow desiring to enter Node i during Time Step t in Time Interval p based on flows from all upstream segments taking into account all geometric and traffic constraints upstream of the node including queues accumulated from previous time intervals MFi t piMainline flow the actual mainline flow rate that can cross Node i during Time Step t in Time Interval p MOli t piMaximum Mainline Output 1 the maximum allowable mainline flow rate across Node i during Time Step t in Time Interval p limited by the flow from an onramp at Node i M02i t piMaximum Mainline Output 2 the maximum allowable mainline flow rate across Node i during Time Step t in Time Interval p limited by the available storage on Segment i due to a downstream queue M03i t piMaximum Mainline Output 3 the maximum allowable mainline flow rate across Node i during Time Step t in Time Interval p limited by the presence of queued vehicles at the upstream end of Segment i while the queue clears from the downstream end of Segment i OnRamp Variables ONRIi t piOnramp input ramp flow rate desiring to enter the merge point at OnRamp i during Time Step t in Time Interval p based on current ramp demand and ramp queues accumulated from previous time intervals ONRDi p4n ramp demand desired entry flow rate for onramp at Node i in Time Interval p ONRCi piOnramp capacity geometric carrying capacity of onramp at Node i roadway during Time Interval p ONRFi t p4n ramp flow actual ramp flow rate that can cross OnRamp Node i during Time Step t in Time Interval p takes into account control constraints eg ramp meters ONRQLi t piOnramp queue length queue length on OnRamp i at the end of Time Step t in Time Interval p ONROi t piOnramp output maximum flow rate that can enter the merge point from OnRamp i during Time Step t in Time Interval p constrained by Lane 1 shoulder lane flow on Segment i and the Segment i capacity or by a queue spillback filling the mainline segment from a bottleneck further downstream whichever govenis ONRQi t piOnramp queue the unmet demand that is stored on the onramp roadway at Node i during Time Step t in Time Interval p veh RMi piRampmetering rate the maximum allowable rate of an onramp meter at onramp at Node i during Time Interval p vehh OffRamp Variables DEFi t piDeficit the unmet demand from a previous Time Interval p that flows past Node i during Time Step t used in offramp flow calculations downstream of a bottleneck Chapter 22 Freeway Facilities Appendix A 22 44 Highway Capacity Manual 2000 OFRDi piOfframp demand the desired flow exiting at OffRamp i during Time Interval p OFRFi t piOfframp flow the actual flow that can exit at OffRamp i during Time Step t in Time Interval p Facilitywide Variables SMSNS piAverage time interval facility speed the average spacemean speed over the entire facility during Time Interval p KNS piAverage time interval facility density the average vehicle density over the entire facility during Time Interval SMSNS P7Average analysis period facility speed the average spacemean speed over the entire facility during the entire analysis period P KNS P7Average analysis period facility density the average vehicle density over the entire facility during the entire analysis period P A2 OVERALL PROCEDURE DESCRIPTION The procedure is described according to the ninestep process shown in Exhibit A22l A21 Input Module The first step in the methodology is to gather all geometric and traffic data The most basic data are required for sizing the analysis These basic data are listed below Number of time intervals the number of time intervals is input to size the analysis with the correct time dimension There is no practical limit on the number of time intervals although the current computer implementation is limited to 12 intervals ime interval duration the time interval duration can vary to allow for finer or broader analysis of freeway facilities Caution should be used when using other than the recommended 15min time interval First the capacities that are calculated are based on the maximum hourly flow rate that can travel through a segment during a 15min analysis interval As the interval duration decreases the capacity may actually increase and vice versa The methodology assumes that there is instantaneous travel time between segments when demands are computed on segments In other words there is no demand shock wave at any point where the demand changes ie when a new time interval begins For this assumption to be reasonable the uncongested travel time of the freeway facility being analyzed which is directly related to its length should not be longer than the duration of the time intervals being used Time step duration once oversaturation begins the procedure moves to time steps The duration of the time steps should be determined on the basis of the segment lengths as shown later in Exhibit A224 There must be an integer number of time steps in a time interval Number of segments the number of segmenm must be determined from the freeway facility chapter Refer to Exhibit 223 for a suggested process to divide a facility into sections and segments Jam density the systemwide jam density is required for oversaturated analysis The default value is 190 pcmiln The geometric traffic and demand data required for a freeway facility analysis are shown in Exhibit 2212 A22 Demand Estimation Module The demand estimation module is invoked when the methodology uses actual freeway counts If demand flows are known or can be projected those values can be used directly The demand estimation module is designed to convert the input set of freeway exit 15min traffic counts into a set of freeway exit 15min traffic demands Freeway exit demand is defined as the number of vehicles that desire to exit the freeway in a given 15 2245 Chapter 22 Freeway Facilities ppendix A Highway Capacity Manual 2000 min time interval This demand may not be represented by the 15min exit count because of upstream freeway congestion within the freeway facility EXHIBIT A224 OVERALL PROCEDURE LAYOUT i Coiiect input data Exhibit 22 i2 Y 2 Demand estimation needed N 3 Establish spatial and time units 4 Demand adjustments Convert counts to demand AdJUSL demands 5 HCM segment capamty estimation Ch 23 24 or 25 5 Adjust HCM capamties AdJUSL capamties 7 Undersaturated segmentSM and MOEs AH segment dc s S LO Notes dc demand to capamty ratio SM senice measure MOE measure of effectiveness The procedure followed is to sum the freeway entrance demands along the entire freeway facility including the freeway mainline entrance and to compare it with the sum of the freeway exit counts along the entire freeway facility including the freeway mainline exit for each time interval The ratio of the freeway entrance demands to the freeway exit counts is calculated for each time interval and will be referred to as the time interval scale factor Theoretically the scale factor should approach 100 when the freeway exit counts are in fact1 freeway exit demands Chapter 22 Freeway Facilities 2246 Appendix A Highway Capacity Manual 2000 Scale factors greater than 100 indicate increasing levels of congestion within the freeway facility and the storing of vehicles on the freeway Here the exit traffic counts underestimate the actual freeway exit demands Scale factors less than 100 indicate decreasing levels of congestion within the freeway facility and the release of stored vehicles on the freeway Here the exit traffic counts overestimate actual freeway exit demands To provide an estimate of freeway exit demand each freeway exit count in the time interval is multiplied by the time interval scale factor The accuracy of this procedure primarily depends on the quality of the set of freeway traffic counts and to a lesser extent on the length of the freeway facility With the use of 15min time intervals freeway facility lengths up to 9 to 12 mi should not introduce significant errors into the procedure The calculated scale factor patteni over the study period duration offers a means of checking the quality of the traffic count data For example if there is no congestion over the entire timespace domain then there should be no patteni in the calculated 15min scale factors and they all should be within the range of 095 to 105 If there is congestion within the timespace domain then there should be a pattern in the calculated 15min scale factors During the early time intervals with no congestion the scale factors are expected to approach 100 and be within the range of 095 to 105 As congestion begins to occur and increase over time the scale factors are expected to increase over 100 and be within the range of 100 to 110 When the extent of congestion reaches its highest level the scale factor is expected to approach 100 and be within the range of 095 to 105 As the level of congestion recedes the scale factor is expected to be less than 100 and be within the range of 090 to 100 If the final time intervals exhibit no congestion over the complete timespace domain then there should be no patteni in the calculated 15min scale factors and they all should be within the range of 095 to 105 Once the freeway entrance and exit demands are estimated using the scale factors the traffic demands for each freeway section in each time interval can be determined A23 Establish Spatial and Time Units The procedure analyzes a freeway in spatial units called segments which are defined in Chapters 23 through 25 The division of a freeway facility into segments is described in Section II of this chapter Time units are described in Section A21 A24 Demand Adjustment Module Driver responses such as spatial temporal or modal shifts caused by traffic management strategies are not 39 39 1 in the On viewing the facility traffic performance results the analyst can modify the demand input manually to simulate the effect of user demand responses or traffic growth effects The accuracy of the results depends on the accuracy of the estimation of the user demand responses Rampmetering strategies are evaluated through adjusting the ramp roadway capacity and this application is described in the segment capacity adjustment module A25 Segment Capacity Estimation and Adjustment Module Segment capacity estimates are determined from Chapters 23 through 25 for basic segments weaving segments and ramp segments respectively All capacities are expressed in vehicles per hour All estimates of segment capacity should be carefully reviewed and compared with local knowledge and available traffic information for the study site The capacity value used for bottleneck segments has the greatest effect on the predicted freeway traffic performance Actual fieldobserved capacities at bottlenecks should be obtained whenever practical and substituted for estimated capacities Onramp and offramp roadway capacities are also determined in this capacity module Onramp demands may exceed onramp capacities and limit the traffic demand entering the freeway Offramp demands may exceed offramp capacities and cause congestion on the freeway although this particular effect is not accounted for in the 2247 Chapter 22 Freeway Facilities ppendix A Highway Capacity Manual 2000 methodology The relationships of demand and capacity for each onramp and offramp as well as for each freeway segment will be addressed later in the demandtocapacity ratio module Again unlike the analyses in the basic freeway freeway weaving and ramp chapters all analyses in this chapter are on a vehiclebased capacity and not in passenger car units The effect of a predetermined rampmetering plan can be evaluated in this methodology by modifying the ramp roadway capacities The capacity of each entrance ramp in each time interval is changed to the desired metering rate specified This feature not only permits the evaluation of the prespecified rampmetering plan but also permits the user to experiment to obtain an improved rampmetering plan Freeway design improvements can be evaluated within this methodology by modifying the design features of any segment or segmenm of the freeway facility as described in Section II of this chapter Reducedcapacity situations can also be investigated The capacity in any cell of the timespace domain can be reduced to represent incident situations such as construction and maintenance activities adverse weather and traffic accidentsvehicular breakdowns Similarly capacity can be increased to match field measurements When analyzing adjusted capacity situations it is important to use an alternative speed ow relationship The following relationship assures a constant ideal density of 45 pcmiln at capacity as indicated in Chapter 23 of the manual Exhibit A222 shows speedflow plots for capacity adjustment factors CAFS of 100 95 90 and 85 percent of the original capacity The predicted speed for the alternative speed ow model can be computed by using Equation A22l In FFSHrC 4ch VgAF SFFS 179 A224 where S 2 segment speed mih FFS 2 segment freeflow speed mih C 2 original segment capacity pchln CAF 2 capacity adjustment factor CAF 10 use Chapters 23 through 25 speed estimation procedures and vp 2 segment flow rate pchln Note that when vp z 0 in Equation A22l S approaches FFS Similarly when vp z C CAF S approaches speed at capacity A26 DemandtoCapacity Ratio Module Once all freeway segment cells have been analyzed demandtocapacity ratios are modified into volumetocapacity ratios for later use in calculating freeway traffic performance measures As stated earlier if all freeway segment cells are undersaturated demands less than capacities the volumetocapacity ratios are identical to the demand tocapacity ratios and the analysis is simple However if demand is greater than capacity in one or more of the freeway segment cells oversaturated flow conditions will occur and the time step analysis procedure is invoked Until oversaturated conditions are encountered segmenm are analyzed using the undersaturated segment MOE module All subsequent time intervals however are analyzed using the oversaturated segment MOE module Chapter 22 Freeway Facilities Appendix A 2248 Highway Capacity Manual 2000 EXHIBIT A222 ALTERNATIVE SPEEDFLOW CURVES FOR INDICATED CAPACITY ADJUSTMENT FACTORS SEE FOOTNOTE FOR ASSUMED VALUES Speed in h 5 I 30 A5 My CAF i 00 2o 7 am W3 107 CAP 085 n I I I I I 0 400 800 I200 I600 2000 2400 Fiow Rate pchIn Notes Assumptions FFS 75 mih capame adjustmentiactor CAF 0M 0 095 090 and O 85 A3 UNDERSATURATED SEGMENT MOE MODULE This module begins with the first segment in the first time interval For each cell the flow or volume is equal to demand the volumetocapacity ratio is equal to the demand tocapacity ratio and undersaturated flow conditions prevail Performance measures for the first segment during the first time interval are calculated using the procedures for the corresponding segment type in Chapters 23 through 25 The analysis continues to the next downstream freeway segment in the same time interval and the performance measures are calculated The process is continued until the last downstream freeway segment cell in this time interval has been analyzed For each cell the volumetocapacity ratio and performance measures are calculated for each freeway segment in the first time interval The analysis continues in the second time interval beginning at the furthest upstream freeway segment and moving downstream until all freeway segments in that time interval have been analyzed This pattern continues for the third time interval fourth time interval and so on until the methodology encounters a time interval that contains one or more segments with a demandtocapacity ratio greater than 100 or when the last segment in the last time interval is analyzed If none is encountered the segment performance measures are taken directly from Chapters 23 through 25 and the facility performance measures are calculated as in Section A4 When the analysis moves from isolated segments to a facility an additional constraint is necessary To limit the speeds downstream of a segment experiencing a low average speed a maximum achievable speed is imposed on each segment average speed This maximum speed is based on acceleration characteristics reported by the American Association of State Highway and Transportation Officials and is shown in Equation A222 1 vmax FFS 7 FFS 7 vpeve 0 6 A222 where Vmax 2 maximum achievable segment speed mih FFS 2 segment freeflow speed mih VFW average speed on immediate upstream segment mih and L 2 distance from midpoints of the upstream segment and the subject segment ft 2249 Chapter 22 Freeway Facilities ppendix A Highway Capacity Manual 2000 A4 OVERSATURATED SEGMENT MOE MODULE Oversaturated flow conditions occur when the demand on one or more freeway segment cells exceeds its capacity Once oversaturation is encountered the methodology changes its temporal and spatial units of analysis The spatial units become nodes and segments and the temporal unit moves from a time interval to smaller time steps A node is defined as the junction of two segments There is always one more node than segment1 with nodes added at the beginning and end of each segment The numbering of nodes and segments begins at the upstream end and moves to the downstream end with the segment upstream of Node i numbered Segment i 7 l and the downstream segment numbered i as shown in Exhibit A223 The intermediate segmenm and node numbers represent the division of the section between Ramps l and 2 into three segmenm numbered 2 ONR 3 BASIC and 4 OFR The oversaturated analysis moves from the first node to each downstream node in the same time step After the completion of a time step the same nodal analysis is performed for the subsequent time steps EXHIBIT A223 NODESEGMENT REPRESENTATION OF A DIRECTIONAL FREEWAY FACILITY Sag I Sag 2 Sag 3 Sag 4 Sag 5 Sag 6 RampZ Ramp I The oversaturated analysis focuses on the computation of segment average flows and densities in each time interval These parameters are later aggregated to produce facilitywide estimates Two key inputs into the flow estimation procedures are the time step duration for flow updates and a owdensity function They are described in the next sections A41 Procedure Parameters Segment flows are calculated in each time step and are used to calculate the number of vehicles on each segment at the end of every time step The number of vehicles on each segment is used to track queue accumulation and discharge and to calculate the average segment density To provide accurate estimates of flows in oversaturated conditions the time intervals are divided into smaller time steps The conversion from time intervals to time steps occurs during the first oversaturated time interval and remains until the end of the analysis The transition to time steps is essential because at certain points in the methodology future performance estimates are made on the basis of the past value of a variable The time steps correspond to the following lengths in Exhibit A224 These values are vital in two major situations EXHIBIT A224 RECOMMENDED TIME STEP DURATION FOR OVERSATURATED ANALYSIS SheriasisagmaniIangih 300 600 i000 L300 2I500 TimasiapduraiioMs I5 25 40 60 60 The first situation is when segments are short and the rate of queue growth is rapid Under these conditions a short segment may be completely undersaturated in one time step and completely queued in another The methodology may store more vehicles in this segment during a time step than there is allowable space Fortunately this error is compensated for in the next time step and the procedure continues to accurately track queues and store vehicles after this correction Chapter 22 Freeway Facilities Appendix 2250 Highway Capacity Manual 2000 The second situation in which small time steps are important is when two queues interact There is a temporary inaccuracy due to the maximum output of a segment changing thus causing the estimation of available storage to be slightly in error This results in the storage of too many vehicles on a particular segment This supersaturation is temporary and is compensated for in the next time step Inadequate time step size will result in erroneous estimation of queue lengths and may affect other performance measures as well Regardless if interacting queues occur the results should be viewed with extreme caution Analysis of freeway segments depends on the relationships between segment speed flow and density Chapter 23 of this manual defines a relationship between these variables and the calculation of performance measures in the undersaturated regime The methodology presented here uses the same relationships for undersaturated segments Calculations for oversaturated segmenm use a simplified linear flowdensity diagram in the congested region Exhibit A225 shows this owdensity diagram for a segment having a freeflow speed of 75 mih For other freeflow speeds the corresponding capacities in Chapters 23 through 25 should be used EXHIBIT A225 SEGMENT FLOWDENSITY FUNCTION SEE FOOTNOTE FOR ASSUMED VALUE Capame 2400 pchIn 2000 7 I5007 Fow pch n I000 7 U ndersaturated Oversaturated Regime Regime I I I I I I I I I I I I I I I 500 i I I L DenSIty at capame 45 pcmIIn I I I I I I I I 20 4O 60 80 I 00 I20 I40 I60 I80 2 O DenSIIy pcmIIn Note Assumption FPS 75 mIh A42 Flow Estimation The oversaturated portion of the methodology is detailed in a flowchart as Exhibit A226 The owchart is divided into nine parts which are discussed in this section Within each subsection computations are detailed and labeled according to each step of the flowchart The procedure first calculates a number of flow variables starting at the first node during the first time step of oversaturation followed by each downstream node and segment in that same time step After all computations in the first time step are completed calculations are performed at each node and segment during subsequent time steps for all remaining time intervals until the analysis is completed 2251 Chapter 22 Freeway Facilities ppendix A Highway Capacity Manual 2000 EXHIBIT A22 6 OVERSATURATED ANALYSIS PROCEDURE t CaIcuIate background densttytor each segment In thIs traveI ttme tntervaI 2 IntttaItzethetreewaytacthty Segment IntttaItzatton 3 Move to rst node 4 FOI39IIIIS node and ttme step OtteRamp FIow 7 CaIcuIate otteramp ow 8 CaIcuIate otteramp ow usIng deIICII method wtthout ustng deIICII method 9 CaIcuIate matnhne Input MaInItne Input Exhibit A22 6 is continued on next page Chapter 22 Freeway Facilities 2252 Appendix Highway Capacity Manual 2000 EXHIBIT AZZ G CONTINUED OVERSATURATED ANALYSIS PROCEDURE IO Onerarnp at node 5 o E a 5 I4 Onerarnp ow oneramp output 7 7 transfer unmet ramp demand I5 on ramp on mm mm I6 CaIcuIate MaInIIne Output I MOI S g I7 Queue presen on segment Exhibit A22 6 is continued on next page 2253 Chapter 22 Freeway Facilities ppendix A Highway Capacity Manual 2000 EXHIBIT AZZ G CONTINUED OVERSATURATED ANALYSIS PROCEDURE t8 Istnereatronte cIeanng gueue In ms ttme IntervaI7 Ma n ne Output t9 CaIcuIate MatnIIne Output 3 M03 20 CaIcuIate denstty 0t queue on segment 21 CaIcuIate MaInIIne Output 2 M02 22 CaIcuIate matnIInetIow Man neFow 23 FII39SI node 24 CaIcuIate segment ow Segment Fow 25 Update number of venIcIes 0n segment Exhibit A22 6 is continued on next page Chapter 22 Freeway Facilities 2254 Appendix A Highway Capacity Manual 2000 EXHIBIT AZZ G CONTINUED OVERSATURATED ANALYSIS PROCEDURE 27 Move to the next downstream node 28 Last time step in current time intervaI 29 Move to nexttime step 30 CaIcuIate segment performance measures Segment and Fac ty Performance Measures 3t Last time intervaI in anaIysis 32 Move to the first time step in the nexttime intervaI 33 CaIcu Iate background density for this time intervaI 36 CaIcuIatefaciIitywrde performance measures 34 stnere a frontecIearing queueintnistime intervaI 35 CaIcuIate wave speed A42 1 Segment Initialization Exhibit A22 6 Steps 1 Through 4 Steps 1 through 4 of the oversaturated procedure prepare the flow calculations for the first time step and specify return points for subsequent time steps To calculate the number of vehicles on each segment at the various time steps the segments must contain 2255 Chapter 22 Freeway Facilities ppendix A Highway Capacity Manual 2000 the proper number of vehicles before the queuing analysis places unserved vehicles on segments The initialization of each segment is described below A simplified queuing analysis is initially performed to account for the effecm of upstream bottlenecks These bottlenecks meter traffic downstream of their location The storage of unserved vehicles those unable to enter the bottleneck on upstream segments is performed in a later module To obtain the proper number of vehicles on each segment the expected demand ED is calculated ED is based on demands for and capacities of the segment and includes the effects of all upstream segments The expected demand is the flow of traffic expected to arrive at each segment if all queues were stacked vertically ie no upstream effects of queues In other words all segments upstream of a bottleneck have expected demands equal to their actual demand expected demand of the bottleneck segment and all further downstream segmenm are calculated assuming a capacity constraint at the bottleneck which meters traffic to downstream segments The expected demand is calculated for each segment using Equation A223 EDi p minSCi p EDi7 1 p ONRDi p 7 OFRDi p A22 3 Note that the segment capacity SC applies to the entire length of the segment With the expected demand calculated the background density KB can be obtained for each segment using the appropriate segment density estimation procedures in Chapters 23 through 25 The background density is used to calculate the number of vehicles on each segment NV using Equation A224 If there are unserved vehicles at the end of the preceding time interval the unserved vehicles UV are transferred to the current time interval Here S refers to the last time step in the preceding time interval The 0 term in NV represents the start of the first time step in Time Interval p The corresponding term at the end of the time step is NVi l p NVi 0 p KBi p Li UVi S p 7 1 A22 4 The number of vehicles calculated from the background density is the minimum number of vehicles that can be on the segment at any time This is a powerful check on the methodology because the existence of queues downstream cannot reduce this minimum Rather the segment can only store additional vehicles The storage of unserved vehicles will be determined in the segment flow calculation module later in this appendix A422 Mainline Flow Calculations Exhibit A22 6 Steps 9 and 16 Through 23 The description of ramp flows will follow the description of mainline flows Thus Steps 5 through 8 and 10 through 15 are skipped at this time to focus first on mainline flow computations Because of the skipping of steps in the descriptions some computations may include variables that have not been described but that have been previously calculated within the flowchart Flows analyzed in oversaturated conditions are calculated every time step and are expressed in terms of vehicles per time step The procedure separately analyzes the flow across a node on the basis of the origin and destination of the flow across the node The mainline flow is defined as the flow passing from upstream Segment i 7 l to downstream Segment i It does not include the onramp flow The flow to an offramp is the offramp flow The flow from an onramp is the onramp flow Each of these flows is shown in Exhibit A227 with their origin destination and relationship to Segment i and Node i The segment flow is the total output of a segment as shown in Exhibit A227 Segment flows are calculated by determining the mainline and ramp flows The mainline flow is calculated as the minimum of six constraints the mainline input Mainline Output 1 MOl Mainline Output 2 MOZ Mainline Output 3 M03 the upstream Segment i 7 1 capacity and the downstream Segment i capacity as explained next Chapter 22 Freeway Facilities Appendix A 2256 Highway Capacity Manual 2000 EXHIBIT A22 7 DEFINITIONS OF MAINLINE AND SEGMENT FLOWS Sag 7 1 Node I Sag U Sag U 7 1 Node I Sag U ONRF OFRFI SFI 7 IVIFI SFI 7 IVIFI OFRFI SFI IVIFI ONRFh SFI IVIFI A4221 Mainline Input Exhibit A226 Step 9 The mainline input MI is the number of vehicles that wish to travel through a node during the time step The calculation includes a the effects of bottlenecks upstream of the analysis node b the metering of traffic during queue accumulation and c the presence of additional traffic during upstream queue discharge The mainline input is calculated by taking the number of vehicles entering the node upstream of the analysis node adding onramp flows or subtracting offramp flows and adding the number of unserved vehicles on the upstream segment This is the maximum number of vehicles that wish to enter a node during a time step The mainline input is calculated using Equation A225 where all values have units of vehicles per time step Mli t p MFi7 1 t p ONRFi7 1 t p 7 OFRFi t p UVi7 1 t7 1 p A225 A4222 Mainline Output Exhibit A22 6 Steps 16 Through 21 The mainline output is the maximum number of vehicles that can exit a node constrained by downstream bottlenecks or by merging onramp traffic Different constraints on the output of a node result in three separate types of mainline outputs MOL M02 and M03 A42221 Mainline Output 1 Hamp Flows Exhibit A22 6 Step 16 M01 is the constraint caused by the flow of vehicles from an onramp The capacity of an onramp segment is shared by two competing flows This onramp flow limits the flow from the mainline through this node The total flow that can pass the node is estimated as the minimum of the Segment i capacity and the mainline outputs from the preceding time step The sharing of Lane 1 shoulder lane capacity is determined in the calculation of the onramp flow and is described in Section A423 M01 is calculated using Equation A226 MO1i t p minSCi t p7 ONRFi t p M02i t7 1 p MO3i t7 1 p A226 A42222 Mainline Output 2 Segment Storage Exhibit A22 6 Steps 20 and 21 The second constraint on the output of mainline flow through a node is caused by the growth of queues on a downstream segment As a queue grows on a segment it may eventually limit the flow into the current segment once the boundary of the queue reaches the upstream end of the segment The boundary of the queue is treated as a shock wave M02 is a limit on the flow exiting a node due to the presence of a queue on the downstream segment The M02 limitation is determined first by calculating the maximum number of vehicles allowed on a segment at a given queue density The maximum flow that can enter a queued segment is the number of vehicles that leave the segment plus the 2257 Chapter 22 Freeway Facilities ppendix A Highway Capacity Manual 2000 difference between the maximum number of vehicles allowed on the segment and the number of vehicles already on the segment The density of the queue is calculated using Equation A227 for the linear densityflow relationship shown in Exhibit A225 earlier KJi KC SFi 71 p mu 1 p KJi so p A22 7 Once the queue density is computed M02 can be computed using Equation A228 M0203 t P SFUE 1quot 1 P ONRFU t P K002 t P quot L39 NW 1quot 1 P A2243 The performance of the downstream node is estimated by taking the performance during the preceding time step This estimation remains valid when there are no interacting queues When queues do interact and the time steps are small enough the error in the estimations is corrected in the next time step A42223 Mainline Output 3 Front Clearing Queues Exhibit A226 Steps 17 Through 19 The final constraint on exiting mainline flows at a node is caused by downstream queues clearing from their downstream end These frontclearing queues are typically caused by incidents where there is a temporary reduction in capacity A queue will clear from the front if two conditions are satisfied First the segment capacity minus the on ramp demand if present for this time interval must be greater than the segment capacity minus the ramp demand if present in the preceding time interval The second condition is that the segment capacity minus the ramp demand for this time interval be greater than the segment demand for this time interval A queue will clear from the front if both conditions in the following inequality Equation A22 9 are met If 3003 P ONRDU P gt 3003 P i 1 ONRDU P i 1 and SCi p 7 ONRDi p gt SDi p A22 9 A segment with a frontclearing queue will have the number of vehicles stored decrease during recovery while the back of queue position is unaffected Thus clearing does not affect the segment throughput until the recovery wave has reached the upstream end of the segment In the flowdensity graph shown in Exhibit A22 8 the wave speed is estimated by the slope of the dashed line connecting the bottleneck throughput and the segment capacity points The assumption of a linear flowdensity function greatly simplifies the calculated wave speed The bottleneck throughput value is not required to estimate the speed of the shock wave that travels along a known line All that is required is the slope of the line which is calculated using Equation A2210 SCUY P Ni p KJi KC The wave speed is used to calculate the time it takes the front queueclearing shock wave to traverse this segment called the wave travel time WTT Dividing the wave speed WS by the segment length in miles gives the wave travel time The recovery wave travel time is the time required for the conditions at the downstream end of the current segment to reach the upstream end of the current segment To place a limit on the current node the conditions at the downstream node are observed at a time in the past This time is the wave travel time This constraint on the current node is called the Mainline Output 3 or M03 The calculation of M03 is performed by using Equations A22ll and A2212 If the wave travel time is not an integer number of time steps then the weighted average performance of each variable is taken for the time steps nearest to the wave travel time This method is based on a process described elsewhere 24 WSi p A221 0 TLi A2241 W30 P Chapter 22 Freeway Facilities Appendix A 2258 Highway Capacity Manual 2000 M03i t p minMO1i 1 t7 WTT p M02i 1 t7 WTT p OFRFi 1 t7 WTT p M03i 1 t7 WTT p OFRFi 1 t7 WTT p SCi t7 WTT p SCi 1 t7 WTT p OFRFi 1 t7 WTT p 7 ONRFi t p A2212 EXHIBIT A22 8 FLOWDENSITY FUNCTION WITH A SHOCK WAVE SEE FOOTNOTE FOR ASSUMED VALUE 500 apamty 2400 pchI I Shock wave 7 I 2000 I I E 15007 I oBo Ieneck throughput g Undersaturated I Oversaturated I 1000 I I I I 500 I I DenSIty alcapamty 45 pcmIIn I I 1 I I I I I I I 20 40 60 80 100 120 T40 160 T80 2 0 DenSIiy pcmIIn Note AssumptIon FPS 75 mIh A4223 Mainline Flow Exhibit A22 6 Steps 22 and 23 The flow across a node is called the mainline flow and is the minimum of the following variables mainline input M01 M02 M03 upstream Segment i 7 1 capacity and downstream Segment i capacity MFUZ t P min MIZ t P M0103 t P M0203 t P M030 1 p 300 L P 30039 i 1 t 3 A221 3 In addition to mainline flows ramp flows must be analyzed The presence of mainline queues also affects ramp flows A423 OnRamp Calculations Exhibit A22 6 Steps 10 Through 15 A423 1 OnRamp input Exhibit A22 6 Steps 10 and 1 1 The maximum onramp input is calculated by adding the onramp demand and the number of vehicles queued on the ramp The queued vehicles are treated as unmet ram demand that was not served in previous time steps The onramp input is calculated using Equation A22l4 ONRIi t p ONRDi t p ONRQ i t7 1 p A221 4 A4232 OnRamp Output Exhibit A226 Step 12 The maximum onramp output is calculated on the basis of the mainline traffic through the node where the onramp is located The onramp output is the minimum of two values The first is Segment i capacity minus the mainline input in the absence of 2259 Chapter 22 Freeway Facilities ppendix A Highway Capacity Manual 2000 Chapter 22 Freeway Facilities Appendix A downstream queues Otherwise the segment capacity is replaced by the throughput of the queue This estimation implies that vehicles entering an onramp segment will fill lanes 2 to N where N is the number of lanes on the current segment to capacity before entering Lane 1 This assumption appears to be consistent with the estimation of V12 from Chapter 25 of this manual The second case is when the Lane 1 flow on Segment i is greater than onehalf of the Lane 1 capacity At this point the onramp maximum output is set to onehalf of Lane 1 capacity This implies that when the demands from the freeway and the onramp are very high there will be forced merging in a oneto one fashion on the freeway from the freeway mainline and the onramp in Lane 1 An important characteristic of traffic behavior is that in a forced merging situation ramp and rightlane freeway vehicles will generally merge one on one sharing the capacity of the rightmost freeway lane 5 In all cases the onramp maximum output is also limited to the physical ramp road capacity and the rampmetering rate if present The maximum onramp output is an important limitation on the ramp flow Queuing occurs when the combined demand from the upstream segment and the demand on the onramp exceed the throughput of the ramp segment The queue can be located on the upstream segment on the ramp or on both and is dependent on the onramp maximum output Equation A2215 determines the value of the maximum onramp output ONROUZ t P miniRMll P ONRCUZ P m vDltmir7SCIl P M02i t7 1 p ONRFi t7 1 p MO3i t7 1 p ONRFi t7 1 p 7 Mli t p minSCi p M02i t7 p ONRFi t7 1 p M030 t7 1 p ONRFi t7 1 p2Ni p A2215 Note that this model incorporates the maximum mainline output constraints from downstream queues not just the segment capacity This is significant because as a queue spills over an onramp segment the flow through Lane 1 is constrained This in tuni limim the flow that can enter Lane 1 from the onramp The values of M02 and M03 for this time step are not yet known so they are estimated from the preceding time step This estimation is one rationale for using small time steps If there is forced merging during the time step where the queue spills back over the current node the onramp will discharge more than its share of vehicles ie more than 50 percent of the Lane 1 flow This will cause the mainline flow past Node i to be underestimated But during the next time step the onramp flow will be at its correct flow rate and a onetoone sharing of Lane 1 will occur A4233 OnRamp Flows Queues and Delays Exhibit A22 6 Steps 13 Through 15 Finally the onramp flow is calculated on the basis of the onramp input and output values computed above If the onramp input is less than the onramp output then the on ramp demand can be fully served in this time step and Equation A2216 is used ONRFi t p ONRIi t p A2216 Otherwise the ramp flow is constrained by the maximum onramp output and Equation A22l7 is used ONRFi t p ONROi t p A2217 In the latter case the number of vehicles in the ramp queue is updated using Equation A2218 ONRQU t p ONRQU t7 1 p ONRIi t p 7 ONROU t p A2218 The total delay for onramp vehicles can be estimated by integrating the value of onramp queues over time The methodology uses the discrete queue lengths estimated at the end of each interval ONRQi S p to produce overall ramp delays by time interval 2260 Highway Capacity Manual 2000 A424 OffRamp Flow Calculation Exhibit A226 Steps 5 Through 8 The offramp flow is determined by calculating a diverge percentage on the basis of the segment and offramp demands The diverge percentage varies only by time interval and remains constant for vehicles that are associated with a particular time interval If there is an upstream queue traffic may be metered to this offramp This will cause a decrease in the offramp flow When the vehicles that were metered arrive in the next time interval they use the diverge percentage associated with the preceding time interval A deficit in flow caused by traffic from an upstream queue meter creates delays for vehicles destined to this offramp and other downstream destinations The upstream segment flow is used because the procedure assumes that a vehicle destined for an off ramp is able to exit at the offramp once it enters the offramp segment The calculation of this deficit is performed using Equation A22 l9 DEFi t p Max0 pi 3017 1X7 pf ElMFU 7 1 t X ONRFi71 t X X1 X1 t PipH171 t p ONRFi71 t p A224 9 r If there is a deficit then the offramp flow is calculated using the deficit method The deficit method is used differently in two different situations If the upstream mainline flow plus the flow from an onramp at the upstream node if present is less than the deficit for this time step then the offramp flow is equal to the mainline and onramp flows times the offramp turning percentage in the preceding time interval as indicated below OFRFIZ t P MFI39 1 t P ONRFI39 1 t P OFRDi p 7 1SDi7 1 p 7 1 A2220 If the deficit is less than the upstream mainline flow plus the onramp flow from an onramp at the upstream node if present then Equation A2221 is used This equation separates the flow into the remaining deficit flow and the balance of the arriving flow OFRFIZ t P DEFUZ t P quot OFRDi P 1SDI39 1P i 1 MFI39 1 t P ONRFi7 1 t p 7 DEFi t p OFRDi pSDi7 1 p A2221 If there is no deficit then the offramp flow is equal to the sum of upstream mainline flow plus the onramp flow from an onramp at the upstream node if present multiplied by the offramp turning percentage for this time interval according to Equation A2222 OFRFi t p MFi7 1 t p ONRFi7 1 t p OFRDi pSDi7 1 p A2222 Note that the procedure does not currently incorporate any delay or queue length computations for offramps A425 Segment Flow Calculation Exhibit A226 Steps 24 and 25 The segment flow is the number of vehicles that flow out of a segment during the current time step These vehicles enter the current segment either to the mainline or to an offramp at the current node The vehicles that entered the upstream segment may or may not have become queued within the segment The segment flow is calculated using Equation A2223 SFi7 1 t p MFi t p OFRFi t p A2223 The number of vehicles on each segment is calculated on the basis of the number of vehicles that were on the segment in the preceding time step the number of vehicles that entered the segment in this time step and the number of vehicles that leave the segment in this time step Because the number of vehicles that leave a segment must be known 2261 Chapter 22 Freeway Facilities ppendix A Highway Capacity Manual 2000 the number of vehicles on the current segment cannot be determined until the upstream segment is analyzed The number of vehicles on each segment is calculated using Equation A2224 NVi7 1 t p NVi7 1 t7 1 p MFii 1 t p ONRFi7 1 t p 7 MFi t p 7 OFRFi t p A2224 The number of unserved vehicles stored on a segment is calculated as the difference between the number of vehicles on the segment and the number of vehicles that would be on the segment at the background density The number of unserved vehicles stored on a segment is calculated using Equation A2225 UVi7 1 t p NVi7 1 t p7 KBi7 1 p Li7 1 A2225 A43 Segment and Ramp Performance Measures Exhibit A226 Steps 26 Through 30 In the last time step of a time interval the segment flows are averaged over the time interval and the measures of effectiveness for each segment are calculated If there was no queue on a particular segment during the entire time interval then the performance measures are calculated from the corresponding HCM 2000 method for that segment in Chapters 23 through 25 Since there are T time steps in an hour the average segment flow rate in vehicles per hour in Time Interval p is calculated using Equation A22 26 SFltL p gaspsm t p A2226 Note that ifT 60 lmin time step and S 15 interval 15 min then TS 4 If there was a queue on the current segment in any time step during the time interval then the segment performance measures are calculated in three steps First the average number of vehicles over a time interval is calculated for each segment using Equation A2227 NVi1P er1VVIE t1P A2227 Next the average segment density is calculated by taking the average number of vehicles NV for all time steps in the time interval and dividing it by the segment length using Equation A2228 NVi p K 1 P LU Next the average speed on the current segment i during the current time interval p is calculated using Equation A2229 A2228 SFi p K i p Additional segment performance measures can be derived from the basic measures shown in Equations A2226 through A2228 Most prominent is segment delay which can be computed as the difference in segment travel time at speed Ui p and at the segment freeflow speed The final segment performance measure is the length of the queue at the end of the time interval ie Step S in Time Interval p The length of a queue in feet on the segment is calculated using Equation A2230 uvis p Koi s p7 KBi p Ui p A2229 0i S p 5 280 A2230 Queue length on onramps can also be calculated A queue will form on the onramp roadway only if the flow is limited by a metering rate or by the merge area capacity If Chapter 22 Freeway Facilities Appendix A 2262 Highway Capacity Manual 2000 the flow is limited by the ramp capacity then unserved vehicles will be stored upstream of the ramp roadway most likely a surface street The methodology does not account for this delay since vehicles cannot enter the ramp roadway However the unserved vehicles in this case are transferred as added demand in subsequent time intervals If the queue is on the ramp roadway the queue length is calculated by using the difference in background density and queue density For an onramp the background density is assumed to be the density at capacity and the queue density is calculated within Equation A223l For onramp queue length Equation A2231 is used omen s p minHMi p ONHOU s p KJ 7 KC A2261 omen p ONHQLU s p KJ A5 DIRECTIONAL FACILITY MODULE EXHIBIT A226 STEP 36 The previously discussed traffic performance measures can be aggregated over the length of the directional freeway facility over the time duration of the study interval or over the entire timespace domain Each will be discussed in the following paragraphs Aggregating the estimated traffic performance measures over the entire length of the freeway facility provides facilitywide estimates for each time interval Facilitywide travel times vehicle and person distance of travel and vehicle and person hours of travel and delay can be computed and pattenis of their variation over the connected time intervals can be assessed The current computer implementation of the methodology is limited to 15min time intervals and lmin time steps Aggregating the estimated traffic performance measures over the time duration of the study interval provides an assessment of the performance of each segment along the freeway facility Average and cumulative distributions of speed and density for each segment can be determined and pattenis of the variation over connected freeway segments can be compared Average trip times vehicle and person distance of travel and vehicle and person hours of travel are easily assessed for each segment and compare Aggregating the estimated traffic performance measures over the entire timespace domain provides an overall assessment over the study interval time duration Overall average speeds average trip times total vehicle and person distance traveled and total vehicle and person hours of travel and delay are the most obvious overall traffic performance measures Equations A2232 through A2235 show how some of the facilitywide MOEs are calculated Facility spacemean speed in Time Interval p ZESFU PLi SMSNS p LU A2232 251SFiipgt U I P Average facility density in Time Interval p NS i KiNS p A2233 21LINIi P Overall spacemean speed across all intervals P quot13 SF i L i SMSNS P 2p 2quot mg A2234 2P Z ZSSFU p P Uiz p Overall average density across all intervals P is K i L i KUVSY P M A2235 2212131Linwiip 2263 Chapter 22 Freeway Facilities ppendix A Highway Capacity Manual 2000 i E0 Equot P 5 quot REFERENCES A Policy on Geometric Design of Highways and Streets American Association of State Highway and Transportation Officials Washington DC 1994 Newell G F A Simplified Theory of Kinematic Waves in Highway Traffic Part I General Theory Transportation Research Vol 27B No 4 1993 pp 2817287 Newell G F A Simplified Theory of Kinematic Waves in Highway Traffic Part II Queuing at Freeway Bottlenecks Transportation Research Vol 27B No 4 1993 pp 2897303 Newell G F A Simplified Theory of Kinematic Waves in Highway Traffic Part III Multidestination Flows Transportation Research Vol 27B No 4 1993 pp 3057313 Newman L Freeway Operations Analysis University of Califoniia Institute of Transportation Studies University Extension Course Notes 1986 Chapter 22 Freeway Facilities Appendix A

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I made $350 in just two days after posting my first study guide."

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.