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Analysis of Queueing System MMPP/M/K/K with Delayed Feedback

Author

Listed:
  • Agassi Melikov

    (Institute of Control Systems, National Academy of Science, Baku AZ1141, Azerbaijan)

  • Sevinj Aliyeva

    (Information Technology and Programming, Applied Mathematics and Cybernetics, Baku State University, Baku AZ1141, Azerbaijan)

  • Janos Sztrik

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

Abstract

The model of multi-channel queuing system with Markov modulated Poisson process (MMPP) flow and delayed feedback is considered. After the customer is served completely, they will decide either to join the retrial group again for another service (feedback) with some state-dependent probability or to leave the system forever with complimentary probability. Feedback calls organize an orbit of repeated calls ( r -calls). If upon arrival of an r -call all the channels of the system are busy, then it either leaves the system with some state-dependent probability or with a complementary probability returns to orbit. Methods to calculate the steady-state probabilities of the appropriate three-dimensional Markov chain as well as performance measures of investigated system are developed. Results of numerical experiments are demonstrated.

Suggested Citation

  • Agassi Melikov & Sevinj Aliyeva & Janos Sztrik, 2019. "Analysis of Queueing System MMPP/M/K/K with Delayed Feedback," Mathematics, MDPI, vol. 7(11), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1128-:d:288113
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