Traffic Flow Theory
Traffic Flow Theory CE 571
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This 42 page Class Notes was uploaded by Savanna Cruickshank on Friday October 23, 2015. The Class Notes belongs to CE 571 at University of Idaho taught by Ahmed Abdel-Rahim in Fall. Since its upload, it has received 13 views. For similar materials see /class/227776/ce-571-university-of-idaho in Civil Engineering at University of Idaho.
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Date Created: 10/23/15
CE571 Traf c Flow Theory Spring 2009 Microscopic Flow Characteristics Time Headway Distribution Week 2 rModeling Headway Distribution Time Headway De nition Time Headway versus Gap ed Abdeera im h Civil Engineering Depatment University of Idaho Headway Characteristics Headway Characteristics S me Applications S me Applications Uninterrupted Traf c Interrupted Traf c DriverBehavior Studies minimum headway Saturation Flow Studies Gap Acceptance Unsigualized intersection capacity Samration Flow Studies Freeway Simulation models FreewayMerging Characteristics Traf c Signal Control Microscopic Flow Characteristics Microscopic Flow Characteristics Time Headway Distribution rTime Headway Distribution quotMm Inm mm ii Headway Distribution Headway Distribution Northbound Traf c E astb ound Traf c Microscopic Flow Characteristics Time Headway Classification lt6gtRandom Headway State Negative ExponentialPoisson count Distribution OConstant Headway State Normal Distribution Intermediate Headway State Pearson type II Gam shifted Negative Exponential ma Enlarg Negative Exponential Microscopic Flow Characteristics Random Headway StatePoisson Distribution mxem P T Px Probability that exactly x number of v n 5 occur during time interval t m Average number of events during time interval t e Napierian base of logarithms e271828 Population mean population variance Examples of using Poisson Distribution On an intersection approach with a left turn volume of 120 lw isson what is the probability ofskipping the green phase for the left turn traf c The intersection is controlled by am actuated signal with an average cycle length of 90 seconds m Average number oileitturu vehicles per Cycle number oi cyclesper hour 360090 40 m 120 vph 40 3 vehiclescycle Px mxe m x Probability of x 0 P0 0049737 49 quotn 196 cycleshours Examples of using Poisson Distribution A parking study was conducted for a pak39ng lot that has 60 e arkin ac The study used 5 m39nutes hmrvals ova a 2 hour during the mml time period is 200 Assuming a Poisson disthutionwhat is the probability that a parking space will be available at my time m Average number oi empty spaces per time period total number oitime periods 24 x 5 120 m 200 vph 120 167 spacetime period mxe m Px 77x Probability of x gt 0 lsP0 P0 013 Px gt 0 17 013 032 32 Probability oi linding an empty parking space Examples of using Poisson DistIibutiorl An intersection is controlled by a fixed time signal having a cycle length of55 seconds From the northbound there is a WEB ER tum movement of175 vph Iftwo vehicles can turn each cycle without causing delay on what percent ofthe cycles will delay occur m Average number or leit turn vehicles per Cycle number of cyclesper hollr 360055 6546 m 175 Vph 39 6546 267 LT Vehiclescycle x 7m 7 m e Probability of x gt 2 1309 7 x P xgt2 1 7 more P1P 2 1 7 0069 0135 0247 499 3267 Cycleshour Examples of using Poisson Distribution 39 39 quot 39 39 A 39L determine L m tgwait 12 or 3 gaps before entering the tragic stream the minimum gap acceptance is 4 0 seconds Gap size Observed g P h x freq P 0quotquot ency 1 576 677 778 8 3 Total ol 70 Observations Examples of using Poisson Distribution Using the following data to construct a distribution curve determine 1 2 or 3 the P h lt 40 034 Ph2401 70344164 Proh ability of first gap 2 40 064 64 Probability that 2 vehicle on the side street will wait gm gap r Probability that a vehiais on the side street in wait ng gaps Prob ability at iirst gap lt 40m setund gab lt4 AND third gab 2 4 034 x 034xo64 41074 74 Random Headway StatePoisson Distribution Px7mx7m P 0 e 39m If no vehiclesarrive in time interval t then the time headway must be equal to or greater than t Therefore P h 2 t P0 e If V hourly ow rate then m V3600 t vehtime interval And PalEtermeth36UU Random Headway StatePoisson Distribution Mean Time Headway t7 3600v And Ph 2 t e quotmmquot Therefore P h 2 t e 7W Pthlt tAt Ph2t7Pht At To obtain the frequency of headways r tSh lt tAt N Pt h lt tAt Where N is total number of observed headway traf c volume Ph2terttiert5er lt F t h lt HAL Constant Headway StateNormal Distribution tMeantimehsaadutay h ML Normal distribution with mean GI and smndard deviation s 95 39 inthe range lzi 2s Minimum headway at 11 2s or t7 7 2s Then sh 7 U2 Constant Headway StateNormal Distribution i Normal Distribution To get the probability P As X lt B Z B 7 A From the table using the value 25 We are interested in the probability P t s h lt t Constant Headway StateNormal Distribution 47 Example V 2000 vph Mean time hadway 36002000 18 seconds Assuming a minimum headway of06 seconds 5 18 7 052 05 To obtain the probability P 10 s h lt t7 2 18 r 10 08 or Zs 0805 1333 P 10 s h lt 18 0408 408 ofthe headway between the man headway and 10 second Intermediate Headway State W Generalized Mathematical Model Approach 9 Composite Model Approach lt9 Other Approaches Intermediate Headway State eneralized Mathematical Model Approach Pearson Type 1 D Gamma Erlang 7 Negative Exponentiap Shifted Negative Exponential Intermediate Headway State Generalized Mathematical Model Approach 7 earson Type III 39 ft Probability density innction K and a User selectparameters that aiiecttbe shape and the shirt oithe distribution mete 39 39 oithemean 39 thetwo user speci ed parameters K and a t Time headway being investigated 139 K Gamma innction equivalent to K71 Ge P lr rt rlirllrt i enerallzed Mathematlca Moe Approach EWType 1 0andKgt0 Gamma Distribution A ft FKlltl e a lfl3931FiIIL ll lv V Generalized Mathematical Model Approach Piearson Type III 0andK1 7 Negative Exponential A 5 Distribution lrr39f rrrrf h39 r 39 Generalized M thematical Mel Aproach Pearson Type I TgtOandK1 awn ShiftedNegative f 01 e Exponential Distribution Intermediate Headway State Generalized Mathematical Model Approach For any Model P h 2 t ftdt Intermediate Headway State Composite Model Approach of tth PP tNP PNP PP Proportion of vehicles in Platoon snirtetl Negative Exponential Distribution PM Proportion ol39vehicles NOT in Platoon Normal Distribution rrr Hfr39er Generalized Mathematical M 7 earson Type II gt n anrl K 1 j MHZ shimdNegative Exponential Distribution 40 quot d K 1 ft 2e 97 Negative ExponentialDistribution 1 0 andKgt0 fti t 2 GanunaDistrioution UK 1 u0 andK 1 2 3 ft UMP 2 Erlang Distribution FurznyMudel prhztgtI rgtm CORSIM Headway distribution Q This entry speci s a code 012 which determines if vehicle entry headways should be generated uniformly 0 or by a normal 1 or Erlang 2 distribution RSIM can generate vehicle ent headwa non stochasticay Entry 7 0 or stochastically using either a normal Entry 7 1 or an Erlang distribution Entry 7 2 See the discussion ofEntIy 4 for the random number seed used when Entry 7 When Entry 7 0 all vehicle entry headways are set equal to the uniform hadway de ned as 3600 secN vehiclshourIane CORSIM Headway distribution W lt9 This entry speci s the value of quotaquot dscribing the type of Erlang distribution to be used to generate vehicle entry headways a 1 2 Z fa K7 e 712 ad 7 Va XW e MTWD 29 aK and A qK where t is hadway and q is the average traf c volume e CORSIM Headway distribution R 08 O The parameter quotaquot describes the level of randomnss ofthe distribution ranging from a 1 most ran omness o a D complete uniformity The case w ere a 1 is considered a special form ofthe Erlang distribution known as the negative exponential 39s ribution When the Erlang distribution is selected ie Entw 7 2 then Entry 8 is use to e ne the value of quotaquot for the distribution The negative exponential distribution can be selected by setting Entw 8 1 CORSIM can generate hmdways from Erlang distributions ranging from a 1 to a 4 Thus acceptable values of Entw 8 range from 1 to 4 This entiy must be blank or Zero if Entry 7 is blank or Zero Assignment 3 Usin Poisson distribution develop frequency hea way distribution for a traffic volume of 320 vph use 10 second interva Q Usin Normal distribution develop frequency hea way distribution plot for a traffic volume of 2050 vph use 01 second interva lt gt Code Pearson type 111 family of models into MathCad Be ready to integrate them to obtain frequency headway distribution for different volumes In Monday39s 222009 Class CE571 Traf c Flow Theory Spring 2009 Week 5 rMicroscopic Density characteristics Ahmed Abdeerahim Civil Engineering Department University of Idaho Distance Headway Characteristics 1 Lima L 5 m0 dm t Distance headway of vehilce n 1 at time t feet Ln Length of Vehilce n feet gm t gap length between vehicles n and n 1 at time t feet dwr ham 1 1M time headway of vehilce n1 at point p sec vh average speed of vehicle n during the time period hm ftsec ATraf c Density k density vehilces per mile per lane N Number of observed distance headways d average distance headway feet per vehicle 4 Pipe s Theory v I dMlN xx 1 xn1tM1N Lquot miLn 1W 136Vn1ti 20 0 h 136 7 MIN VMU 7 Forbe s Theory Tlme Headway L a h At quot MIN v I E 20 s h 15 2 M1 v t E M 15vnt20 Speed mph Distance Headway 4 GM Models Minimum Headway Speed mph Response d sensitivity relative speed GM Model 1 mt N am VHlttgt GM Model 2 GM Model 3 an1ltzAzalom2 ammo HA2 ammo an new I GM Model 4 GM Model 5 a39 mean xn t xn1t V A an lttArgt mm mo amamrMmymm Traffic Stability The Human Factors Driver Attempts to Keep up with the vehicle ahead of him speed and adequate spacing SC mm Drive control acceleration rather than speed or distance Avoid collision Traffic Stability Mathematical Representation amt 1 N 4V 0 44h 0 Mn t At Axquot t 7 xm 13 se 0 3 Solution ofthe differential equation Where Jo ao ibo Traffic Stability C 11At Local Stability Asymptotic Stability Nunoscillatory Damped Oscillatory DamPEd OSCillalUl39y Increased Oscillatory Increased Oscillatory SteadyState Flow Models 4 Initial State Platoon of vehicles traveling with speed Vi and interivehicle spacing of Si Leading vehicle changes its speed from Vi to V during time period t t n At All following vehicles will reach speed ofVi in time t 11 At Damped Oscillatorxl Interivehicle spacing transition from Si to Sfby the end of t n At SteadyState Flow Models linear accelera onresponse independent oi vehicle spacing E ample G M model 1 an1tAt oIn1f7Vn1 1 onilin ear acceleration response dependent of vehicle spacing Ekamples GM model 3 MANN Karma my EUFXMU GM MW 5 wt A2 1 x lm mm mo 7 fry SteadyState Flow Models linear Models GM model 1 an1rmamrimt v1k Qkva 1 SteadyState Flow Models flinear Models GM model 3 amtAt Vanivwml a0 XMUFXMU V k v a linE j gt Q ask liquot a k SteadyState Flow Models Nondinea Iodels GM model 5 a m Mal am A2 a WM 0 mm mm vvfekm vkvfe Density Measurements Single PresenceType Detector Two Detectors Sinule PresenceType Detector Measured tnnn tnnn1 tn n tn n1 Measured LD Length of detection Zone Assumed LH and Lu Calculated tmn tmn1 V n VWI Single Presence Tyge Detector Time Headway and Occupancy hnl 11101 tnnn Inclquot tn n lun l n1 tnnn1 tnnnl tot Single PresenceType Detector Speed VL LD tmm Vn1L1 Loy two1 VnKl tmn VnlKlt n1 or Distance Headway d hn1Vn Single PresenceType Detector 47 Macroscopic Traffic Flow Characteristics 3600 M T Number of changes in detector signal from not occupied to occupied occupancy T Data collection period Single PresenceTvpe Detector awfil NK 7 2 Mgmt k7q V avzmge Macroscopic Traffic Flow Characteristics 1 Single PresenceTxpe Detector Percent Occupancy iconquot OccquotlT100 7 Measurements with Two Detector 17 Fundamental Equation k density vpm lane mile d average distance feetvehicle k 75280 d Estimating Speed from Occupancv Individual Speed V 7 Ld Lv 7 Z a p individual vehicle occupancy time ftsec vi speed of individual vehicle ftsec Ld detection zone length ft L39 length of individual vehicle ft Estimating Speed from Occupancx Average Speed d A mmga my to Wga v 3600 La lvlwmga 39 r average speed g 39 W 5280 WWW I 3600 Ld LV 1ng a my 280 v awmgtz 7 Total occupancy time Tn To in hours 3600 g N Id iv nge o 5280 V awmga and Percent occupancy Occ 1005 time TD in hours T Omg N100 Ldkavayagz T5280 v mmga N 100 Occ i T 5280 mega L Occq1 1 Amy Vawmga L L mg mm 528 tim39ation of Total Travel Time ZN n H T also have N Zk ltnlt i1 TT Total Travel Time number of subsections in the system 1 number of vehicles in the system at time t it density in 5Ub599 0n i at timet m number of observation periods Li length of subsecuoquot l n number of lanes in subsection i CE571 Traf c Flow Theory Spring 2009 Week 4 ispeed Characmristics Ahmed Abdeerahim Civil Engineering Department University of Idaho Equation of Motion b 51147 bz0733mZ 1 Hi Speed mph at the beginning of the acceleration or deceleration quot1 Speed mph at the end of the acceleration or deceleration AccelerationDeceleration rate V Normal Average Maximum Em ergencyPanic Factors Type of Vehicle Pavement Conditions Tire Condition Grade Others 2 Histupping Distance 3 M 30f i g Th Speed mph at the beginning ofthe deceleration f Coef cient of friction between tires and pavement g grade expressed as a decimal Speed Trajectories at an intersection NonStopped Vehicles p1 on Delayed Vehicles 0lt pilt uquot Stopped Vehicles pi 0 By the end of the green p p VUninterrupted Flow Sample Mean Speed and SD N N 7 7 24 204402 i1 S2 1 N N71 pi Speed of individual vehicle i N number of observations Uninterrupted Flow Sample Mean Speed and SD 47 Grouped observations 5 g 2 1 g 2 1 gm S2 7 Ef e 7m T T pi Midipoint Speed of group i N Number of Observations g Number of Speed Groups 1 number of observations in speed group i Mathematical Distribution Normal Distribution Large Samples Ngt30 T Distribution Small Samples Nlt30 ppopulation mean speed and SD 6827 of the observations 11126 9545 of the observations piJo39 9973 of the observations 41 P prob ability of an observation between speed p1 and the mean sp eed 11 X absolute di erencebetween pump 6 S D ol the population Speed Data Analysis CE571 Traf c Flow Theory Spring 2009 Week 9 e Queuing Theory Ahmed Abdeerahim Civil Engineering Department University of Idaho Queuing Theory rate ofpassa e I Input storage area queue restriction output I Custo mers arrivals arrival process server service mechanism departures Restriction I Airplanetakeoff toll gate wait to at a port water storage in a res rvoir grocery store telecommunications ci cui s I Interested in maximum queue length typical queueing times Queuing Theory Introduction What Should we know OArrival Distribution IService Distribution Queuing Theory is either 0 Deterministic Either or Both Arrival and Service Distributions are Deterministic 0 Stochastic Both Arrival and Service Distributions are Determin stic Queuing Theory I Customers don t disappear I Arrival times of customers completely characterizes arrival process I Timdaccumulation axes Nxt Time x I Objects passingthrough point with restriction on maximum r elevator taxi stand ships e Queuing Theory I jAt increases by 1 at each t I Observer can record arrival times I Inverse tA li is timejth object arrives integers I lflarge numbers can draw curve through midpoints of stair steps continuous curves differentiable N090 Anon Time x t t2 t3 t4 Queuing Theory I Observer records times of departure for corresponding objects to construct Dt N090 At 4 3 Dt 2 1 Time x t t2 t3 m4 t2 t3 t4 Queuing Theory I lfsystem empty at t0 I Vertical distance is queue length at timet QtAtDt I At and Dt can never cros I For FIFO horizontal distance is waiting time for jth customer 391 Nxt Time x t t2 t3 tlt4 t t4 t5 Queuing Theory I Horizontal strip ofunit height wid h W Nxt Time x t t2 t3 tit t 2 tg t Queuing Theory I Add up horizontal strips total delay I Total time spent in system by some number ofvehicles horizontal strips Nxt Total DelayArea quot 4 Time x t t2 t3 m4 t2 t3 n Queuing Theory I Add up horizontal strips total delay I Total time spent in system by some number ofvehicles horizontal strips I Total time spent by all objects during some speci c ime period vertical strips N090 Total Del ayArea gt Time x t t2 t3 m4 t 2 t t Queuing Th ory I Total delay W I Average time in queueW Wn I Average number in queue Q WIT I W T Wn I Q WnT 9 say nT arrival rate A I Q AW Average queue length avg wait time x avg arrival rate rt Time x t t2 t3 t t t3 t5 Combination I Time space diagram looks at one or more objects many points I Queueing theory looks at one point many objects I ombining the two results in a threedimensional surface I Use care when distinguishing between queuing diagrams and tlme space diagrams Combination Combination ake vertical slices at t1 and t2 I Constructvehicle counting functions Nxt1 and Nxt2 I Can observe distances traveled and numbers passing a particular polnt I Take vertical slices at t1 and t2 I Construct vehicle counting functions Nxt1 and Nxt2 I Can observe distances traveled and numbers passing a particular point Combination I I e I Take horizontal slices at x and x t 1 I 7 I functions Ntx1 and N099 T 5 I Can observe accumulations and trip I I times between points 7 7 Combination A I I e I Take horizontal slices at T T Xi and a functions Ntx1 and N099 l T I Can observe accumulations and trip I times between points 7 4 t N s 4 a V mmmma I Manx n 1 Queuing theory applications 553 en39rso 39 d 7 cun xnuiav1ive2y at on Queuing theory applications Pict sensor data cuameialfveiy at am palm N t A TravelDlreamn 4 1 l Ilnterval Count Equal Time Intervals 1 min mmor QQQYT ZTImeJ Jx 00000 Queuing theory applicat39 PMS 1 err 53 d8 Ions a cumuiaiively ai one L965 a NOW TrawlDlredmn 4 0quot Queuing theory applications l3 m sensor Elam curmniati xlely ITravel Diredmn 4 0quot x Nxt ll Slope numbertime FLOW DQOF QQTET ZTImex 0000 Queuing theory applications 553 GHEO39 39 7 cun miativeiy at on Queuing theory applications Pict sensor data cuameialfveiy at am palm N t N t NOW ITmelDlredmn 4 x NOW ITraveleedmn 4 x x x Flow Decrease Slope numbertime FLOW Slope numbertime FLOW Flow Increase Flow Increase Ov NMVVJONDQOF Ov NMVVJONDQOF QQQQQQQQQQT ZT ZTWEJQ X QQQQQQQQQQEETImeIX 000000000000 000000000000 ory applications Queueing diagram mus plots in series is see aqua Use two eljiim 39 s sway Nan NOW vaelDlredmn 4 NOW X1 Time I X1 Time I Ref Veh Trip Time Queueing diagram Lise two obiique p o s in seziee to see queueing and resuiting delay 9 mm Mm X1 Time I Ref Veh Trip Time Queueing diagram Use iwo oblique piste in series to see queueing and we Lli ng delay N m A Travei X1 Time I Ref Veh Trip Time Queueing diagram upsh eam cu ITmei Diredmn 4 j 0quot0 L7 X1 X3 NOW Time I Queueing diagram hii l upg iream cu accumuie cm 17 ITravei Diredmn w x1 9 Excess Accumulation gt to reveal EXCESS 6quot 5 NW New gt t2 Time I Queueing diagram 3 stimuli at eveai mucosa EN 0 r 1 NX1 t Now we Diredmn u x1 x3 cess Accumulation wayL3 TravelTi neDelay t2 Time I Queuing Theory Equations Definitions A Arrival Rate u Service Rate P 7 l1 C Number of Service Channels M Random ArrivalService rate Poisson D Deterministic Service Rate Constant rate Queuing Theory Equations J llDI arise mndamArrimi Deterministic service and onesa39vice channe Expected average queue length Eon 29 92V 2 1 9 Expected average total time EV2 92 11139 9 Expected average Waiting time Wp21u 19 Queuing Theory Equations IMAMC case RundomArrivaL RandomService and C service channel Nate QC mustbe lt 10 Theprubability ufhaving zero vehicles in the systems p T Theprubability ufhaving n vehicles in the systems Queuing Theory Equations MM case Random Arrival Random Service and one service channe0 The probability of having zero vehicles in the The probability of having rt vehicles in the systems Eritpected aoverage queue length Em p2 1 p Expected average total time Ev p A 1 p Expected average Waiting time EW Ev 7 1 u Example Atruchng cornpanv has two choices in designing a newwarehouse The tirstisto use dockvvorkers to ioad This takes on averagei hour per trucx random distribution and costs 50 per hour tor each crew distribution The cost or the containers is i00 per dav andthe cost otthe who oper te it is i0 per hour Trucxs arrive at a rate or 2hour crew a gPoisson distribution tor i0 hourperdav The cost ottrucxwaiting is iAhour Use queuing theoiv to cornpare the cost or a svstern using 4 crews container Aiternative 1dockworkers A 2h u ih c4 MMC svstern p2 pc0 5 The prooaoiiitv or having zero vehicies in the svsterns P0 01035 E pected average queue ength E m 013 Expected average number otvehicies in the svstern E n 2 i38 Expected averagetotai tirne E v i 009 Expected average waiting tirne E w 0 009 Totai daiiv Cost 20 x 0 009 x15 4 x 50 x i0 2020 Aiternative 2 container A 2m u 2m c2 MMC svstern pi pc 0 The prooaoiiitv or having zero vehicies in the svsterns P0 0 33 Expected average queue ength E m 3 Expected average number otvehicies in the svstern E n 2 33 Expected average totai tirne E v i iss Expected average waiting tirne E w 0 005 Totai daiiv Cost20x0005x i5 i00 2x i0x i0490 Example m e at the entrance ofa State park at a rate 0f60 Veh c es the Mme the of ceratthe tngate 5 free to Work on other actwmeS Queuing Theory Equations M llCN case RandumArI39ival Random Service C service channel and Nsramgz 1i i Traffic Studies and Traffic Flow c5571 Traf c Flow Theory Spring 2009 Characteristics 7 li aystudies Data Analysis Week 5 rMicroscopic Density Characteristics 7 Problem 1 High I Car Crash Rate 7 Ahmed Abdeerahim Identify Possible Reasons Civil Engineering Department University of Idaho Propose 1m provement Measures Traffic Studies and Traffic Flow Traffic Studies and Traffic Flow Characteristics Characteristics imdy Ques on 1 eeway studies Data Analysis CarCar Headway Distribution vs CarTruck 39 39 39 v ruckCar Headway Distribution Piroblem 2 High Truck SingleCrash rates Study Question 2 arCar Speed Distribution vs CarTruck Speed Distribution vs TruckCar Speed Distribution Identify Possible Rea son 5 Propose Improvement Measures Methodology Test whether there are signi cant differences in mean speed and headway among the three groups Traffic Studies and Traffic Flow Characteristics A39Wion 1 Site Speci c Geometric and Vehicle Speci c Characteristics Operational Sal e Speed for Trucks Study Question 2 ed ol Trucks are Signi cantly higher than the Safe Operational Speed Methodology Test the signi cance of difference Traffic Studies and Traffic Flow Characteristics V17 Study Question 1 De nition of Congestion WVhen and Where Methodology Set Congestion Severity Index CSI SpeedDensity thresholds Congestion Index per Location and Time of Day Traffic Studies and Traffic Flow Characteristics eeway studies Data Analysis roblem 3 Increased Congestion Identify Problem area and time Propose lm provement Measures Traffic Studies and Traffic Flow Characteristics Xamples ol CSI CS T Total Vehicle Mlle of Travel CSI Z eongested lane mile Congestion Duration H 1 Traffic Studies and Traffic Flow Characteristics Characteristics Am nljjmDislrihution Bias GPSProbo voliclo Link Travel Time and Dalay A rivals During Green Estimates Sources of Bias Sampling NonAStoopmg Vehicles N1 and npl Does the ProbeVehicles Represent a random Ddayed V9hid95 N2 md 112 sample ofa vehicles 1 A rivals During Red St 1 V h39cl N d Bias in individual speed distribution 0 e 1 es 3 an 93 Bias in arrival time distribution Traffic Studies and Traffic Flow V Characteristics 1 N1 nquot N2 quotP2 Nxth er quotpquot2n N1N2N quotthny np i NO ARRIVAL TIME DI STRI BUTION BIAS CE571 Traf c Flow Theory Spring 2009 Week 4 ispeed Characmristics d Abdeera him Ahme Civil Engineering Department University of Idaho iKevin 300 ft 4 kmzi mm gig Apiaiijsributi f 351 E ii 7 2 77 3 Zn a 39 in in martArte39Ial 9510quot mi new l236557xim VJorge 200 ft new Dixlnbulmn nr speed um rm Pawnxv Snell 2n swims 3quot quotquot quuentleslnbulmn nr spend m Mmz Mubassera mummumma Nommwmm Vslmon q geedS1udiesz Sample Size Estimates Sx Standard error of the mean mph S x S Standard Deviation ofthe Sample EV N Sample Size 3000 J gggg tudies Samgle Size Estimates n 7 E 2500 g 2000 1500 11 Required Sample Size 1000 t Coef cient ol the standard error a User Speci ed allowable error 500 0 Mathematical Distributions Seiection of a Distribution ENormai Distribution 139 Standard Deviation Normal Distribution m m Log normal distribution similar to the M normal distribution except the 6 distribution is skewed with a larger tail Q Coef cientofskewness Normal Distribution of the distribution extending to the right WM mOde Composite distribution Composite 5 traf c Size ofspeed interval for Chisquare test I Mmet n 1 332210g N J Speed Calibration Corsim Q The decile value assigned to each driver speci ed in recor e 147 in simulation lie The record has default values ranging tween 75 and 127 of the mean free ow s gt In order to transform the normal distribution of the free ow s e into a decile distribution eac peroentile of the normal distri ution curve is replaced with the oenter ofgravity of the percentile area Speed Calibration Corsim Free Flow Speed Percentages E E 2 5 s urivenype I Delaultvalues u sts Calibraled Values nussi Calibrated Values me me Cycle seal Tum mlo Cyde sacl 3 g mm mm cm secl rune lnlo Cycle sec Speed Calibration VISSIM fl39Desired Speed Distribution The speed a vehicle desires to travel if it is not hindered by other vehicles with small oscillations Any Driver with a hi her desired s eed than hisher current trave s eed will c eck for the opportunity to pass wit out endangering other ve ic es Minimum and Maximum values can be en ered Number of observed preceding vehicles will affect the speed performance Assignment 6 AFor the Freeway data you have Execute the following tasks a 1 Test the hypothesis that the average speed of vehicles traveling in lane 2 is higher than the average speed of vehicles traveling in lane 1 tIaveling in lane 2 is different than the speed distTibution of vehicles traveling in lane 1 Tas 3 Test e goodness of fit of the speed distrbutions in lane 1 against the normal and log normal distributions Task 4 Repeat task A33lexc1ding trucks for the data comment s on the output of this m Task 5 Determine the sample size required m determine the average speed of tIucks with accuracy of i 2 m h Task 6 Develop calibrate and validate CORSIM or VISSIM microscopic simulation model for a freeway section using the freeway data you have Task 2 Test the It othesis that the speed distIibution of vehicles Flow Level SpeedF low relationship Vehicle Mix Vehicle Interaction Driver Population Familiarity Driver Characteristics Profiling Speed limit Enforcement Time Mean Speed and Space Mean Speed 7 1 2y Mm lint 7 ms n n H t Travel time rate hours per mile or feet per seconds 7 7 S 2 IuTMS 1 SMS l SMS u EMS Testing Significant Difference Between Means 717 Standard Deviation of the difference ofthe mean 1 and 52 Standard Deviation of Study 1 and 2 respectively nl and n2 Sample size of Study 1 and 2 respectively ul 7 1 numerical differencein the means Compare p1 7 p1 with g udy Hypothesis Differencebetween means is due to chance Example l Difference within l 1s 682 confidence 1 11 702 mph 1600 5143 mph Difference within l 2s 955 confidence T1721 mph quot2700 5256 mph Difference within l 3s 997 confidence 0275 1 113 970o confidence that the differenceis NOT due to chance Speed Studies t cf Issues Speed vs Travel Time Operational Difference vs Statistical Difference Accuracy of Speed Measurements TraVEI Time VS39 Dalay Identical Studies M0133 Sample Size Considerations Freeway speed distribution bias Arterials stopped no stopped Intersection stopped no stopped LSpeedTravel Time Data Collection Techniques Automated Traffic Detection Freeway SingleStation Measurements Radar Laser etc Floating CarProbe vehicle Speed and Volume TimeLog InOut Stations License Plate Matching Vehicle Matching Digital Image Processing Matching j39esting difference in mean values ANUVAlee Fll mu I I Summ Squavs m mansquave SPKD39AGGM BetweenGvaS ammo Swan 1 Swan mam Wm Gmqu 1m 2 9322 mm w 2527m5 gm c5571 Traf c Flow TheorySpring 2009 Traffic Stream Models 391 2 2 Vehicular Followuig s Vg szVLxa Week 7 iTraffic Stream Models v initial speed ofthe two vehicles d1 deceleration of the leading vehicle dr 7 deceleration of the following vehicle med Abdeerahim Civil Engineering Department University of Idaho 5 Percep onnreamon time xquot 7 safety margin after stop length of vehicle Traffic Stream Models Traffic Stream Models Strea m Varia b les Safety Consideration Spacing and Concentration 5 1 dn Comfortable normal deceleration Headway and Flow h d3 Emergency deceleration Average Mean Speed 00 Instantaneous or stone wall stop Traffic Stream Models Traffic Stream Models The case of Uniform flow k l s The Fundamental Equation of a Vehicular Stream QVK k fv f V6ZKTIZV71LxD The three variables Q V and K qfv vary simultaneously V5 L XD I 1 Traffic Stream Models Traffic Stream Models 17 17 Car following Models Individual Models Describes the relationship between the driver s SingleRegime Models Same model for desired speed acceleration and the distance uncongested and congested headway from a preceding Vehicle Multiregime Models Different model for Describe steadystate ow uncongested and congested Microscopic in nature Traffic stream models Famlly 0f Madels Describes the steadystate behavior of a traf c stream Multiregime Models SingleRegime Models Traffic Stream Models SingleRegime Models Greenshields Greenberg Underwood N orthwestern Pip es Van Aerde Traffic Stream Models 1 Greenshields SingleRegime Models Based on GM3 car Following Model Assume Linear DensitySpeed Relationship Traffic Stream Models 47 Greenberg SingleRegime Models Nonlinear model based on equation of motion and continuity for onedimensional compressible flow v volinikiji W J Vn optimal speed Traffic Stream Models LUnderwood SingleRegime Models K v vfe kn Optimal Density Traffic Stream Models ijNorthwestern SingleRegime Models 2 0 M V V We f kn Optimal Density Traffic Stream Models Pipes SingleRegime Models The carlength for each 10 mph rule Assume Linear DensitySpeed Relationship 1 1 1 dCC2v Cilia Traffic Stream Models I Van Aerde SingleRegime Models Introduced new parameter that can be calibrated using filed data C dCJC2v vfiv Traffic Stream Models mgillle Models More than one model to cover different density regions Driver behavior might be different in the two regions Edie proposed y 1650 V5498 1639 1250 v286
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