Bounding stationary results of Tandem networks with MAP input and PH service time distributions

Abstract

In this paper, we propose a new approach to compute bounds on stationary measures of queueing systems with an input process described by a Markovian Arrival Process (MAP) and a sequence of stations with Phase Type (PH) service time distributions. Such queueing systems cannot be solved exactly since they have an infinite state space in several natural dimensions. Based on earlier work on the computation of bounds for specific classes of infinite Markov chains, the paper presents a new approach specifically tailored to the analysis of the mentioned class of queueing networks. By increasing the size of the state space of the aggregated Markov chain to be solved for bound computation, bounds can be made arbitrarily tight, but practical limits come up due to the computational complexity. However, we show by means of several examples that tight bounds can be derived with low effort for a large set of queueing systems in the mentioned class.