A Queuing-Type Birth-and-Death Process Defined on a Continuous-Time Markov Chain

Abstract

This paper considers an n-phase generalization of the typical M/M/1 queuing model, where the queuing-type birth-and-death process is defined on a continuous-time n-state Marker chain. It shows that many models analyzed in the literature can be considered special cases of this framework. The paper focuses on the steady-state regime, and observes that, in general, closed-form results for the limiting probabilities are difficult to obtain, if at all possible. Hence, numerical methods should be employed. For an interesting special case, explicit results are obtained that are analogous to the classical solutions for the simple M/M/1 queue.