Chapter 9 - Queueing Systems

Abstract

This chapter reviews queueing processes. A queueing theory is the mathematical study of waiting lines or queues. A queueing system consists of customers arriving at random times to some facility where they receive service of some kind and depart; the term customer is used generically. Queueing systems are classified according to the input process, the service distribution, and the queue discipline. The most common queue discipline is first come, first served where customers are served in the same order in which they arrive. Queueing models aid the design process by predicting system performance. Also, a standard short-hand is used in much of the queueing literature for identifying simple queueing models. The simplest and most extensively studied queueing models are those having a Poisson arrival process and exponentially distributed service times. Variations on the simple queueing models can be seen. Often queueing networks, comprised of groups of service stations, with the departures of some stations forming the arrivals of others, arise computer and information processing systems, manufacturing job shops, service industries such as hospitals and airport terminals, and in many other contexts; these complex systems can be analyzed component by component as departures from a queue with Poisson arrivals and exponentially distributed service times, in statistical equilibrium, also form a Poisson process. As corollary to the above, general open networks may also be analyzed.