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I . — . . . .- Session 3565

--– Why Do I Always Get in the Slow Line? Lynn Kiaer Rose-Hulman Institute of Technology

Abstract

Queueing Theory is one of the most elegant application areas in applied probability, but queueing is also an -mea in which many interesting, practical problems are mathematically intractable. By developing a practical introduction to discrete event simulation, using a spreadsheet, the author has been able to incorporate treatment of some of these intractable problems within an upper division course, Stochastic Models in Operations Research. The presentation includes an overview of the introduction to simulation, sample spreadsheet simulations and a sampling of student projects.

Introduction

Queueing is a phenomenon with universal appeal. Students may lack experience in many application areas, but they have invariably experienced waiting in line. The mathematics of queueing is particularly elegant, with many apparently complex interactions being rendered understandable. But queueing can become a frustrating topic when students want to analyze the line at McDonald’s drive-through window, or the check-out line at the grocery store, because the typical distributions that prevail in these situations do not lead to mathematically tractable models.

The mathematically intractable cases can be analyzed, and frequently are, using simulation. Buts teaching a simulation language for a two-week module on simulation is not practical. However, today’s spreadsheets have random number generators and permit quite complicated if-then-else statements, and most science, engineering and mathematics students already know how to use them. It seems natural, therefore, to use spreadsheets to introduce students to simulation. The author has done this in an upper division course, MA 445, Stochastic Models in Operations Research.

From a practical standpoint, spreadsheets are fairly awful simulation engines, being clumsy, often slow, and very large. From a pedagogical point of view, however, they are not so bad. Students have to think about what they are doing, and have a great deal of flexibility. Whereas a simulation language makes it easy to create and run the simulation, the spreadsheet forces students to understand every step.

An Overview of the Simulation Module

The simulation module begins with generating random variables. In particular, we begin by generating random variables from an exponential distribution, so that we can compare our simulation results to the

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Kiaer, L. (1996, June), Why Do I Always Get In The Slow Line? Paper presented at 1996 Annual Conference, Washington, District of Columbia. 10.18260/1-2--6400