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Transient behavior ofM/M ij/1 queues

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Abstract

We obtain the time dependent probabilities for the joint distribution of the number of arrivals and departures in [0,t] for theM/M ij/1 queue. This queue has the exponential service with parametersμ ij, depending on the types of the successive customers attended. We provide an intuitive interpretation of the solution and also present some numerical results, including time dependent event probabilities and queue length.

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Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, 24061, Blacksburg, VA, USA

    John N. Daigle

  2. IME - Departamento de Estatística, Universidade de São Paulo, Caixa Postal 20570, 01498, São Paulo, SP, Brasil

    Marcos N. Magalhães

Authors
  1. John N. Daigle
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  2. Marcos N. Magalhães
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Daigle, J.N., Magalhães, M.N. Transient behavior ofM/M ij/1 queues. Queueing Syst 8, 357–377 (1991). https://doi.org/10.1007/BF02412260

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  • DOI: https://doi.org/10.1007/BF02412260

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