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Two phases queue systems with dependent phases service times via copula

Author

Listed:
  • Hossein Foroutan

    (Allameh Tabataba’i University)

  • Mohammad Reza Salehi Rad

    (Allameh Tabataba’i University)

Abstract

A single server $${M/G_{1},G_{2}/1}$$ M / G 1 , G 2 / 1 queue with Poisson arrivals, two phases of general heterogeneous services that both phases are essential, with Bernoulli feedback and Bernoulli vacation is assumed. In the common queue models the service times of the phases are assumed to be independent. However, in this paper we assume that they are dependent random variables, considering that this dependency is one-way. It means that the second-phase service time does not affect the first-phase service time. Whereas, the first-phase service time affects the second-phase service time. For this model, the steady-state probability generating function of the queue size distribution is obtained. The Laplace–Stieltjes transform of the service times’ distributions and some important performance measures such as the mean of the queue size and the waiting time of a customer in the queue are obtained. Finally, numerical results via the Farlie–Gumbel–Morgenstern copula function are presented.

Suggested Citation

  • Hossein Foroutan & Mohammad Reza Salehi Rad, 2024. "Two phases queue systems with dependent phases service times via copula," OPSEARCH, Springer;Operational Research Society of India, vol. 61(1), pages 189-204, March.
    • Handle: RePEc:spr:opsear:v:61:y:2024:i:1:d:10.1007_s12597-023-00702-8
    DOI: 10.1007/s12597-023-00702-8
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    References listed on IDEAS

    as
    1. M. Vadivukarasi & K. Kalidass, 2022. "Discussion on the transient solution of single server Markovian multiple variant vacation queues with disasters," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1352-1376, December.
    2. Ramin Behzad & Mohammad Reza Salehi Rad & Nader Nematollahi, 2019. "Queues with Simultaneous Arrival of Customers and the Dependence Structure of the Waiting Times," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1045-1056, December.
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