Mean value analysis of mixed, multiple class BCMP networks with load dependent service stations

Abstract

In this paper we describe a mean value analysis algorithm to solve product form queueing network models of the Baskett, Chandy, Muntz, and Palacios type (BCMP) [5]. These networks can accommodate multiple job classes and load dependent service stations. The networks can be closed (i.e., jobs neither enter nor leave the network), open (i.e., jobs can enter and leave the network), or mixed (i.e., closed with respect to some job classes and open with respect to others). Two major aspects of this paper are: 1. (1)to present a unified approach to the solution of this class of BCMP queueing networks [5], and 2. (2)to thereby extend and consolidate the results of the work of several authors (Balbo, Bruell and Schwetman (1977), Bruell and Balbo (1980), Chandy and Sauer (1980), Krzesinki, Teunissen and Kritzinger (1981), Resier and Kobayashi (1975), Reiser and Lavenberg (1980), Reiser (1981), Sauer (1983), Schwetman (1980), Tucci and MacNair (1982) and Zahorjan and Wong (1981)). The paper concludes by collecting together all the results into an explicit algorithm, MVALDMX (for mean value analysis load dependent mixed) that is a generalization of the original MVA algorithm of Reiser and Lavenberg (1978, 1980).