C Queueing Theory

Learning Objectives

• To be able understand basic queueing theory notation

• To be able to compute queueing results for single queue situations

• To be able to identify and apply standard queueing models

Many real-life situations involve the possible waiting of entities (e.g. customers, parts, etc.) for resources (e.g. bank tellers, machines, etc.). Systems that involve waiting lines are called queuing systems. This appendix introduces analytical (formula-based) approaches to modeling the performance of these systems.

Once the performance of the system is modeled, the design of the system to meet operational requirements becomes an important issue. For example, in the simple situation of modeling a drive through pharmacy, you might want to determine the number of waiting spaces that should be available so that arriving customers can have a high chance of entering the line. In these situations, having more of the resource (pharmacist) available at any time will assist in meeting the design criteria; however, an increase in a resource typically comes at some cost. Thus, design questions within queuing systems involve a fundamental trade-off between customer service and the cost of providing that service.

To begin the analysis of these systems, a brief analytical treatment of the key modeling issues is presented. Analytical results are available only for simplified situations; however, the analytical treatment will serve two purposes. First, it will provide an introduction to the key modeling issues, and second, it can provide approximate models for more complicated situations. The purpose of this appendix is not to provide a comprehensive treatment of queueing theory for which there are many excellent books already. The purpose of this appendix is to provide an introduction to this topic for persons new to simulation so that they can better understand their modeling and analysis of queueing systems. This appendix also serves as a reference for the formulas associated with these models to facilitate their use in verifying and validating simulation models.