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

Agassi Melikov, Sevinj Aliyeva and Janos Sztrik
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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

Mathematics, 2019, vol. 7, issue 11, 1-14

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.

Keywords: multi-channel queuing system; delayed feedback; finite and infinite orbit; calculation methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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