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Networks of queues in discrete time

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Abstract

We study a new class of networks of queues whose nodes operate in round-robin fashion and other ways of interest to computer science. We compute a stationary law of product form for the Markov process describing the state of the network. Moreover, we obtain the conditional expected travel time of a job given the job's requested processing times at particular nodes along its route.

Zusammenfassung

Die Arbeit untersucht ein Netzwerk von Bedienern, die nach der round-robinoder anderen Regeln arbeiten, wie sie etwa bei Rechenanlagen benutzt werden. Es wird ein Markovscher Zustandsprozeß für das Netzwerk definiert und dessen invariantes Gesetz angegeben. Ferner wird die bedingte mittlere Aufenthaltszeit eines Kunden im Netzwerk berechnet, gegeben des Kunden Route und seine Bedienungszeitforderungen entlang der Route.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Berlin, Straße des 17. Juni 135, D-1000, Berlin 12

    H. Daduna &  R. Schaßberger

Authors
  1. H. Daduna
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  2. R. Schaßberger
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Daduna, H., Schaßberger, R. Networks of queues in discrete time. Zeitschrift für Operations Research 27, 159–175 (1983). https://doi.org/10.1007/BF01916912

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  • DOI: https://doi.org/10.1007/BF01916912

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