Advanced Waiting Line Theory and Simulation Modeling Chapter 6 - Supplement

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 2 Chapter Objectives Be able to:  Describe different types of waiting line systems.  Use statistics-based formulas to estimate waiting line lengths and waiting times for three different types of waiting line systems.  Explain the purpose, advantages and disadvantages, and steps of simulation modeling.  Develop a simple Monte Carlo simulation using Microsoft Excel.  Develop and analyze a system using SimQuick.

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 3 Alternative Waiting Lines  Single-Channel, Single-Phase  Ticket window at theater  Multiple-Channel, Single-Phase  Tellers at the bank, windows at post office  Single-Channel, Multiple-Phase  Line at the Laundromat, DMV

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 4 Single-Channel, Single-Phase Figure 6S.1

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 5 Multiple-Channel, Single-Phase Figure 6S.2

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 6 Single-Channel, Multiple-Phase Figure 6S.3

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 7 Common Assumptions  Arrivals  At random (Poisson distribution)  Service times  Variable (exponential, normal distributions)  Fixed (constant service time)  Other  Size of arrival population, order, balking, reneging, first- come, first-served, urgency, speed, desirability of different customer types

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 8 P 0 = Probability of 0 Units in Multiple-Channel System

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 9 Waiting Lines for Different Environments Table 6S.1

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 10 Single-Channel, Single-Phase Manual Car Wash Example Arrival rate = 7.5 cars per hour Service rate  = an average of 10 cars per hour Utilization  = /  = 75%

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 11 Single-Channel, Single-Phase Automated Car Wash Example Arrival rate = 7.5 cars per hour Service rate  = a constant rate of 10 cars per hour Utilization  = /  = 75%

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 12 Adding a Second Crew

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 13 Adding a Second Crew

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 14 Comparisons

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 15 Simulation Modeling Advantages  Off-line evaluation of new processes or process changes  Time compression  “What-if” analyses Disadvantages  They are not realistic.  The more realistic a simulation model, the more costly it will be to develop and the more difficult it will be to interpret.  Simulation models do not provide an “optimal” solution

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 16 Monte Carlo Simulation  Maps random numbers to cumulative probability distributions of variables.  Probability distributions can be either discrete (coin flip, roll of a die) or continuous (exponential service time or time between arrivals).

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 17 Building a Simulation Model with SimQuick Four basic steps  Develop a picture of system to be modeled (process mapping).  Identify objects, elements, and probability distributions that define the system.  Objects – People or products moving through system  Elements - Pieces of the system  Determine experimental conditions (constraints) and required output information  Build and test model, capture and evaluate the data.

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 18 Building a Simulation Model with SimQuick An Excel-based application for simulating processes that allows use of constraints (see text example 6S.4) Figure 6S.6

Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall6S - 19 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.