Author:
Gelenbe Erol,Schassberger Rolf
Abstract
We prove necessary and sufficient conditions for the existence and uniqueness of the stationary solution of the queueing networks (G-networks) with negative and positive customers introduced in Gelenbe [3], which have been shown to have product form. First, the existence of the solution of the nonlinear customer flow equations is established using Brouwer's fixed-point theorem; this result is valid for stable and unstable systems, as well as for certain networks that may not have product form. Then, the result is used to establish general stability related to the usual “load factor less than 1” criterion of queueing systems for G-networks with product form.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
Reference6 articles.
1. Queues with negative arrivals
2. Gelenbe E. & Mitrani I. (1980). Analysis and synthesis of computer systems. London and New York: Academic Press.
3. Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
4. Fourneau J.M. & Gelenbe E. (1992). Multiple class G-networks. EHEI Technical Report.
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