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MA231 Operations Research Methods
创建日期：2024-04-07 14:56:19
所属分类：数学mathematics
标签： MA231
Operations Research Methods

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MA231 Operations Research Methods

Exercises:
1. (Homework) Consider the model of the single server queueing system that we studied in
lecture. Suppose we also wanted to obtain information about the amount of idle time a server
would experience in a time horizon of length T. Explain how this could be accomplished by
editing the variables, event list, output variables and the pseudocode that we presented in
lecture.
2. Consider a single server queueing model in which customers arrive according to a NPP. Upon
arriving they either enter service if the server is free or else they join the queue. Suppose,
however, that each customer will only wait a random amount of time, having distribution F,
in the queue before leaving the system. Suppose we are interested in estimating the average
number of lost customers by time T, where a customer that departs before entering service is
considered lost. We also want the average time that lost customers spent in the system but
we are not interested in the time in the system of the remaining customers. Define variables
and events so as to analyse this model and give the updating procedures.
3. Exercise on “Two servers in parallel” queueing model
(a) In lecture we looked at the queueing model with two servers in parallel. We wrote the
pseudocode for two updating procedures cases 1 and 2. Write the pseudocode of the
updating procedure for case 3.
(b) Using your answer for case 3 in (a) above and pseudocode for the updating procedures
1 and 2 write the R code for the queueing system with two servers in parallel. In lecture
we did not specify how to end the simulation: run the model for a specified time T after
which no customers are allowed in the system. But allow the servers to finish serving
all customers that are present in the system at time T. Further, for the state variable
store ST = (n, i1, i2, t) every time the state (n, i1, i2) changes; with this information you
should be able to reproduce the entire process. You will run this code with data from
part (c) below, so read part (c) before writing the R script.
(c) Use T = 4, a NPP with rate λ(t) = 3 + 4
t+1
. For λ > 0 such that λ(t) ≤ λ for all
0 ≤ t ≤ T, pick λ = 7. For the servers distribution use exponential with rate µ = 5. Run
the R script from 3(b) with the above data to output Tp, the average time customers
spend in the system, and the number of customers served by S1 and S2. Start with
“set.seed(1)”.
(d) Use the state variable ST to calculate time spent in each state n = 0, 1, ... during
[0, T + Tp], where n is the total number of customers in the system. Use this to find the
average number of customers in the system.

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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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