ABSTRACT
This chapter discusses the important role that exponential distribution has played and continues to play in the development of queueing theory. It demonstrates the use of exponential distributions by considering, as an example, a single server queueing system and illustrating ways in which the queueing theory has evolved as a result of it. The embedded discrete time Markovian nature of the process can be extended to queueing systems even when the inter-arrival time distribution is of the phase type. Because of the simplicity in analysis that arise with the assumption of Poisson arrival process (that is, exponentially distributed inter-arrival times), there has been several hundreds of variants of M/GI/1 queues that have been proposed (and continue to be proposed) in the queueing literature.
