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Analysis of Instantaneous Feedback Queue with Heterogeneous Servers

Author

Listed:
  • Agassi Melikov

    (Institute of Control Systems, Department of Teletraffic Theory, National Academy of Science, Baku AZ 1148, Azerbaijan)

  • Sevinj Aliyeva

    (Faculty of Applied Mathematics and Cybernetics, Baku State University, Baku AZ 1148, Azerbaijan)

  • János Sztrik

    (Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary)

Abstract

A system with heterogeneous servers, Markov Modulated Poisson flow and instantaneous feedback is studied. The primary call is serviced on a high-speed server, and after it is serviced, each call, according to the Bernoulli scheme, either leaves the system or requires re-servicing. After the completion of servicing of a call in a slow server, according to the Bernoulli scheme, it also either leaves the system or requires re-servicing. If upon arrival of a primary call the queue length of such calls exceeds a certain threshold value and the slow server is free, then the incoming primary call, according to the Bernoulli scheme, is either sent to the slow server or joins its own queue. A mathematical model of the studied system is constructed in the form of a three-dimensional Markov chain. Approximate algorithms for calculating the steady-state probabilities of the models with finite and infinite queues are proposed and their high accuracy is shown. The results of numerical experiments are presented.

Suggested Citation

  • Agassi Melikov & Sevinj Aliyeva & János Sztrik, 2020. "Analysis of Instantaneous Feedback Queue with Heterogeneous Servers," Mathematics, MDPI, vol. 8(12), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2186-:d:458755
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    References listed on IDEAS

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    1. Rakesh Kumar & Narendra Kumar Jain & Bhupernder Kumar Som, 2014. "Optimization of an M/M/1/N feedback queue with retention of reneged customers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(3), pages 45-58.
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