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## Final Study Guide

by: Lauren Notetaker

43

1

6

# Final Study Guide COSC 459-101

Lauren Notetaker
Towson
GPA 3.3

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This study guide goes over some of the homework questions and vocabulary that may be on the final exam.
COURSE
Computer Simulation & Modeling
PROF.
Darush Davani
TYPE
Study Guide
PAGES
6
WORDS
CONCEPTS
Computer Science, simulations
KARMA
50 ?

## Popular in ComputerScienence

This 6 page Study Guide was uploaded by Lauren Notetaker on Tuesday May 17, 2016. The Study Guide belongs to COSC 459-101 at Towson University taught by Darush Davani in Spring 2016. Since its upload, it has received 43 views. For similar materials see Computer Simulation & Modeling in ComputerScienence at Towson University.

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Date Created: 05/17/16
Final Study Guide Before Midterm Topics Simulation – art & science of creating a representation of a process or system for the purpose of experimentation & evaluation A simulation model can be: static or dynamic, deterministic or stochastic, & discrete or continuous. Static – does not change over time Dynamic – changes over time Deterministic – independent of random variables Stochastic – contains processes controlled by random variables Discrete - finite Continuous – variables in the system change, deals with a time rate of change Steps in a simulation study: 1. Problem formulation 2. Setting of objectives & overall project plan 3. Model conceptualization 4. Data collection/ input data 5. Model translation 6. Model verification 7. Validation checks 8. Experiment design 9. Production runs & analysis 10. Running checks 11. Documentation & reporting 12. Implementation There are 3 types of models:  Opinion – composed of assumptions, they test egos rather than solution feasibility  Static mathematical – mathematical approach  Simulation – mathematical event driven approach Model Type Ability to Analyze Stochastic/ Dynamic Systems Opinion Low Static Mathematical Medium Simulation High Synergism – simultaneous actions of separate elements within a system which together have a greater total effect on system performance than the sum of their individual effects Monte Carlo simulation – scheme for employing random numbers in order to solve certain stochastic/ deterministic problems where passage of time plays no substantive role ???? ???? ????(???? ???? ???????????????? = ∫ ???? ???? ???????? = ???? − ???? ∑ ) ???? ????=1 ???? Model verification – is the model operating in its intended manner Model validation – making sure that the results generated by a model coincide with the results produced by the system being represented by the model Random number stream – sequence of random numbers where each succeeding number is calculated from the previous number derived Random number seed – the initial number in the stream Homework #2 ∑ ???????? ???????????????? = ???? ∑(???? ???? ???? ????????????) 2 ???????????????????????????????? ???????????????????????????????????? = √ ???? − 1 ∑(???? ???? ???? ????????????) 3 ???????????????????????????????????????? ???????? ???????????????????????????????? = 3 (???? − 1 ???????????? Where Std stands for standard deviation ∑ (????????− ???? ????????????) 4 ???????????????????????????????????????? ???????? ???????????????????????????????? = (???? − 1 ???????????? 4 Where Std stands for standard deviation ???????????????????????????????????????? ???????? ???????????????????????? ???????????????????????????????? = ???????????????????????????????????????? ???????? ???????????????????????????????? − ???????????????????????????????????????? ???????? ???????????????????????????????? Some characteristics of good computer simulation are:  Mathematical operations  Properties  Attributes  Statistical analysis  Built-in functions  Display output Simscript program for distribution Let mean = 2 Let s = 3 For I = 1 to 1000 Let Xn(i) = normal.f(1,2,…,mean) Let Xsn(i) = cxn(i) – mean/s Loop Let xchi(1) = xsn(15) + xsn(50) + xsn(500) Let xchi(2) = xsn(10) + xsn(100) + xsn(1000) . . . Let xchi(5) = xsn(6) + xsn(333) + xsn(666) End Know how to calculate Chi-Square using the % Factor equation After Midterm Topics There are 3 types of queues:  Single queue single server  Single queue multiple servers  Multiple independent queues multiple servers Example of single queue single server is a one lane car toll booth Example of single queue multiple servers is the airport luggage check-in Example of multiple queues multiple servers is check-out lanes at a grocery store Homework #5 a) Probability that the check in clerk is busy ⋋ = 20 ???????????? = 24 Assuming there is only 1 check-in clerk ???? = ⋋ = 20 = 5 (Μ ∗ mew ) (1 ∗ 24 6 5 Meaning the check-in clerk is6busy of the time. b) Average passenger waiting time for check in ???? 5 ???????????????????????????? ???????????????????????????? ???????????????? = = 6 (1 − ???? ∗ ???????????? (1 − ) ∗ 24 6 5 5 6 6 5 ???????????????????????????? ???????????????????????????? ???????????????? = 1 = 4 = 24 ???????? 0.208 (6) ∗ 24 c) Probability that the passenger queue length will be greater than 4 ∞ 5 ∑ ???? ????+1 = ???? 6 = ( ) 6 ????=????+1 d) Probability that passengers have to wait for more than 15 minutes to check in ???? = 15 ⋋ = 20 ???????????? = 24 ???????????????????????????????????????????? ???????? ???????????????????????????? ???????????????? ???????????????????????????? ????ℎ???????? ???? = ????????−????(????????????− ⋋) 5 5 ????15 = ???????? −????(????????????− ⋋)= ( )???? −15(24−20)= ( )???? −15(4) 6 6 5 −15(24−20) 5 −15(4) 5 −60 −27 ????15 = ( )???? = ( )???? = ( )???? = 7.297 ∗ 10 6 6 6 The probability that passengers have to wait for more than 15 minutes to check-in is 7.297 ∗ 10−27. e) Proportion of time the check in clerk is idle 5 1 ???? 0 1 − ???? = 1 − = ???????? 0.333 6 6 1 The proportion of time that the check-in clerk is of the time. 6 f) What must the average check in time be in order to reduce the average waiting to 10 minutes 2 10 ∗ ???????????? − 10 ∗ ???????????? ∗ ⋋ − ⋋ = 0 ⋋ = 1/3 ???????????? = 0.4139 1 = 2.416 ???????????????????????????? ???????????? Central Limit Theorem – distribution function of the arithmetic average of a large number of independent, identically distributed random variables is approximately equal to the standard normal distribution function ???????????????? ???? − ???????????? ???? = ???? √???? /???? The equation for calculating # of model replications 2 ????????−1,1−????(????) ???? = ( 2 ) ???? Where e is amount of error and S(n) is the point estimate of σ Transient period – when the state of the simulation is changing

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