Basic Queueing Theory

Abstract

As shown in the simple example of the previous chapter, the basic approach to the analysis of simple queueing models would begin by defining an appropriate system state for the queue. The analysis of the queue would then essentially be the study of the way this system state would evolve. The transient solution would be the solution obtained for this system state, given the various input parameters, and the initial conditions with which the queue starts operation. In this text, we are however interested in the performance analysis of the queue once equilibrium conditions have been reached. Analyses of some basic queues where the arrivals come from a Poisson process and the service times are exponentially distributed will be considered in this chapter. Before we consider such analysis, it would be useful to review some of the basics of the theory of Markov Chains and Birth-Death Processes. These are considered next. Further details on this may be found in [Fel65], [Kle75] or [Wol89].