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Product form solution for exponential G-networks with dependent service and completion of service of killed customers

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Abstract

Queueing networks with negative customers (G-networks), Poisson flow of positive customers, multi-server exponential nodes, and dependent service at the different nodes are studied. Every customer arriving at the network is defined by a set of random parameters: customer route, the length of customer route, customer volume and his service time at each route stage as well. A killed positive customer is removed at the last place in the queue and quits the network just after his remaining service time will be elaborated. For such G-networks, the multidimensional stationary distribution of the network state probabilities is shown to be representable in product form.

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Authors and Affiliations

  1. Department of Probability Theory and Mathematical Statistics, Peoples’ Friendship University of Russia, Moscow, Russia

    Pavel Bocharov

  2. Department of Information Engineering and Applied Mathematics, University of Salerno, Salerno, Italy

    Ciro D’Apice

  3. Institute of Informatics Problem, Russian Academy of Sciences, Moscow, Russia

    Alexandre Pechinkin

Authors
  1. Pavel Bocharov
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  2. Ciro D’Apice
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  3. Alexandre Pechinkin
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Correspondence to Pavel Bocharov.

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Bocharov, P., D’Apice, C. & Pechinkin, A. Product form solution for exponential G-networks with dependent service and completion of service of killed customers. CMS 3, 177–192 (2006). https://doi.org/10.1007/s10287-006-0013-0

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  • DOI: https://doi.org/10.1007/s10287-006-0013-0

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