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Advanced Waiting Line Theory and Simulation Modeling Chapter 6 - Supplement... Chapter ObjectivesBe able to:  Describe different types of waiting line systems..  Use statistics-based f

Advanced Waiting Line Theory and

Simulation Modeling

Chapter 6 - 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

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

Single-Channel, Single-Phase

Figure 6S.1

Multiple-Channel, Single-Phase

Figure 6S.2

Single-Channel, Multiple-Phase

Figure 6S.3

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

P 0 = Probability of 0 Units

in Multiple-Channel System

Waiting Lines for Different Environments

Table 6S.1

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%

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%

Adding a Second Crew

Adding a Second Crew

Comparisons

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

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).

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.

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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