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On a fractional queueing model with catastrophes

Author

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  • Souza, Matheus de Oliveira
  • Rodriguez, Pablo M.

Abstract

A M/M/1 queue with catastrophes is a modified M/M/1 queue model for which, according to the times of a Poisson process, catastrophes occur leaving the system empty. In this work, we study a fractional M/M/1 queue with catastrophes, which is formulated by considering fractional derivatives in the Kolmogorov’s Forward Equations of the original Markov process. For the resulting fractional process, we obtain the state probabilities, the mean and the variance for the number of customers at any time. In addition, we discuss the estimation of parameters.

Suggested Citation

  • Souza, Matheus de Oliveira & Rodriguez, Pablo M., 2021. "On a fractional queueing model with catastrophes," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005579
    DOI: 10.1016/j.amc.2021.126468
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    References listed on IDEAS

    as
    1. Dexter O. Cahoy & Federico Polito & Vir Phoha, 2015. "Transient Behavior of Fractional Queues and Related Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 739-759, September.
    2. Dexter O. Cahoy & Federico Polito, 2012. "Simulation and Estimation for the Fractional Yule Process," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 383-403, June.
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