G-networks with resets

    Authors

    E. Gelenbe;J. M. Fourneau

    Abbreviated Journal Title

    Perform. Eval.

    Keywords

    queuing networks; product forms; Gelenbe networks; negative customers; triggers; resets; existence; uniqueness; POSITIVE CUSTOMERS; QUEUING-NETWORKS; MULTIPLE CLASSES; QUEUES; Computer Science, Hardware & Architecture; Computer Science, Theory &; Methods

    Abstract

    Gelenbe networks (G-networks) are product form queuing networks which, in addition to ordinary customers, contain unusual entities such as "negative customers" which eliminate normal customers and "triggers" which move other customers from some queue to another. These models have generated much interest in the literature since the early 1990s. The present paper discusses a novel model for a reliable system composed of N unreliable systems, which can hinder or enhance each other's reliability. Each of the N systems also tests other systems at random; it is able to reset another system if it is itself in working condition and discovers that the other system has failed, so that the global reliability of the system is enhanced. This paper shows how an extension of G-networks that includes novel "reset" customers can be used to model this behavior. We then show that a general G-network model with resets has product form, and prove existence and uniqueness of its solution. (C) 2002 Elsevier Science B.V. All rights reserved.

    Journal Title

    Performance Evaluation

    Volume

    49

    Issue/Number

    1-4

    Publication Date

    1-1-2002

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    179

    Last Page

    191

    WOS Identifier

    WOS:000178165600013

    ISSN

    0166-5316

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