ABSTRACT
In Chapters 2 and 3, we studied queues for which both the interarrival times and service times were exponentially distributed. This enabled us to use CTMCs to model and analyze such queues. In this chapter, we study how to analyze queues with other distributions for interarrival times or service times or both. Of course, if the distributions are mixtures of exponentials (such as exponential, Erlang, hyperexponential, hypoexponential, and phase-type), we could still analyze using CTMCs. Otherwise, wewould need other techniques and approximations to model and analyze these queues. The objective of this chapter is to present a breadth of methods to analyze queues with general distributions for either interarrival times or service times or both. We present techniques that would result in closed-form algebraic expressions, numerical values, or approximations for various measures of performance such as distributions and moments of queue length as well as sojourn times. We begin by considering discrete time Markov chains to model some queueing systems to obtain closed-form algebraic expressions with the understanding that such Markov models can be widely used for many other settings. We also end the chapter with closed-form algebraic expressions; however, the techniques presented are somewhat specialized for those settings. The middle of the chapter describes techniques that can be used for obtaining performance measures numerically or through approximations.
