Exact Transient Solutions of Nonempty Markovian Queues

It has been shown by Sharma and Tarabia [1] that a power series technique can be successfully applied to derive the transient solution for an empty M/M/1/N queueing system. In this paper, we further illustrate how this technique can be used to extend [1] solution to allow for an arbitrary number of initial customers in the system. Moreover, from this, other more commonly sought results such as the transient solution of a nonempty M/M/1/~ queue can be computed easily. The emphasis in this paper is theoretical but numerical assessment of operational consequences is also given.