Advanced Waiting Line Theory and Simulation Modeling Chapter 6 - Supplement

Advanced Waiting Line Theory and Simulation Modeling

Chapter 6 - Supplement

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

6S 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.


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


6S Single-Channel, Single-Phase

Figure 6S.1


6S Multiple-Channel, Single-Phase

Figure 6S.2


6S Single-Channel, Multiple-Phase

Figure 6S.3


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, first-

come, first-served, urgency, speed, desirability of different customer types


6S P0 = Probability of 0 Units in Multiple-Channel System


6S Waiting Lines for Different Environments

Table 6S.1


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%


6S 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%


6S Adding a Second Crew


6S Adding a Second Crew


6S Comparisons


6S 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


6S 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).


6S 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.


6S 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


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Advanced Waiting Line Theory and Simulation Modeling Chapter 6 - Supplement