Stability of Product Form G-Networks
- 27 July 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in Probability in the Engineering and Informational Sciences
- Vol. 6 (3), 271-276
- https://doi.org/10.1017/s0269964800002539
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.Keywords
This publication has 3 references indexed in Scilit:
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- Queues with negative arrivalsJournal of Applied Probability, 1991
- Open, Closed, and Mixed Networks of Queues with Different Classes of CustomersJournal of the ACM, 1975