The Factorization of Queueing Equations and Their Interpretation

Abstract

There are many queueing systems, including the Mx/My/c queue, the GIx/M/c queue and the M/D/c queue, in which the distribution of the queue length at certain epochs is determined by a Markov chain with the following structure. Except for a number of boundary states, all columns of the transition matrix are identical except for a shift which assures that there is always the same element occupying the main diagonal. This paper describes how one can find the equilibrium distribution for such Markov chains. Typically, this problem is solved by factorizing of a certain expression characterizing the repeated columns. In this paper, we show that this factorization has a probabilistic significance and we use this result to develop new approaches for finding the equilibrium distribution in question.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 30 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.