Advanced Waiting Line Theory and Simulation Modeling Chapter

Advanced Waiting Line Theory and Simulation Modeling Chapter 6 - Supplement

6 S 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 Sim. Quick. Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6 S - 2

6 S 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 6 S - 3

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

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

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

6 S 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 6 S - 7

6 S P 0 = Probability of 0 Units in Multiple-Channel System Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6 S - 8

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

6 S 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 6 S - 10

6 S 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 6 S - 11

6 S Adding a Second Crew Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6 S - 12

6 S Adding a Second Crew Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6 S - 13

6 S Comparisons Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6 S - 14

6 S Simulation Modeling Advantages Disadvantages § Off-line evaluation of new processes or process changes § Time compression § “What-if” analyses § 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 Hall 6 S - 15

6 S 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 6 S - 16

6 S Building a Simulation Model with Sim. Quick 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 6 S - 17

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

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