On Decomposition Methods for Tandem Queueing Networks with Blocking

Abstract

Queueing networks with blocking are useful for modeling and analyzing discrete event systems, especially manufacturing systems. Most analysis methods for queueing networks with blocking are approximation methods that involve a decomposition of the network into a set of subsystems. This paper presents some insight into these decomposition methods as well as new results. Attention is mainly restricted to the case of tandem queueing networks with exponential service times and blocking-after-service. This type of blocking is especially encountered in manufacturing systems. The first aim of this paper is to improve the understanding and present a unified view of the decomposition methods. We show that decomposition methods can be classified according to three main approaches. One of these approaches is of special interest because it offers a symmetrical view of the decomposition. The second aim of the paper is to provide properties pertaining to these decomposition methods in the case of exponential characterizations of subsystems. We prove the existence and uniqueness of the solution. Moreover, we prove the convergence of the computational algorithm associated with the symmetrical approach.