Advanced Waiting Line Theory and Simulation Modeling Chapter - Supplement 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 Hall 6S - 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 Hall 6S - Single-Channel, Single-Phase Figure 6S.1 Copyright © 2013 Pearson Education, Inc publishing as Prentice Hall 6S - Multiple-Channel, Single-Phase Figure 6S.2 Copyright © 2013 Pearson Education, Inc publishing as Prentice Hall 6S - Single-Channel, Multiple-Phase Figure 6S.3 Copyright © 2013 Pearson Education, Inc publishing as Prentice Hall 6S - 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, firstcome, first-served, urgency, speed, desirability of different customer types Copyright © 2013 Pearson Education, Inc publishing as Prentice Hall 6S - P0 = Probability of Units in Multiple-Channel System Copyright © 2013 Pearson Education, Inc publishing as Prentice Hall 6S - Waiting Lines for Different Environments Table 6S.1 Copyright © 2013 Pearson Education, Inc publishing as Prentice Hall 6S - 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 Hall 6S - 10 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 Hall 6S - 11 Adding a Second Crew Copyright © 2013 Pearson Education, Inc publishing as Prentice Hall 6S - 12 Adding a Second Crew Copyright © 2013 Pearson Education, Inc publishing as Prentice Hall 6S - 13 Comparisons Copyright © 2013 Pearson Education, Inc publishing as Prentice Hall 6S - 14 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 not provide an “optimal” solution Copyright © 2013 Pearson Education, Inc publishing as Prentice Hall 6S - 15 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 Hall 6S - 16 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 Hall 6S - 17 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 Hall 6S - 18 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 Copyright © 2013 Pearson Education, Inc publishing as Prentice Hall 6S - 19 .. .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... 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... 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 not provide an “optimal” solution Copyright