Max-plus algebra models of queueing networks

Research outputpeer-review

Abstract

A class of queueing networks which may have an arbitrary topology, and consist of single-server fork-join nodes with both infinite and finite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic state equation which relates the departure epochs of customers from the network nodes in an explicit vector form determined by a state transition matrix. It is shown how the matrices inherent in particular networks may be calculated from the service times of customers. Since, in general, an explicit dynamic equation may not exist for a network, related existence conditions are established in terms of the network topology.
Original languageEnglish
Title of host publicationInternational Workshop on Discrete Event Systems WODES'96, University of Edinburgh, UK, Aug. 19-21, 1996
PublisherInstitution of Electrical Engineers (IEE)
Pages76-81
ISBN (Print)0-85296-664-4
Publication statusPublished - 1996

Scopus subject areas

  • Management Science and Operations Research
  • Algebra and Number Theory

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