Retrial Queues with Unreliable Servers and Delayed Feedback

Agassi Melikov, Sevinj Aliyeva and Janos Sztrik
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Agassi Melikov: Institute of Control Systems, National Academy of Science, Baku AZ 1141, Azerbaijan
Sevinj Aliyeva: Faculty of Applied Mathematics and Cybernetics, Baku State University, Baku AZ 1148, Azerbaijan
Janos Sztrik: Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary

Mathematics, 2021, vol. 9, issue 19, 1-23

Abstract: In this paper, models of unreliable multi-server retrial queues with delayed feedback are examined. The Bernoulli retrial is allowed upon the arrival of both primary (from outside) and feedback customers (from orbit), as well as the Bernoulli feedback that may occur after each service in this system. Servers can break down both during the service of customers and when they are idle. If a server breaks down during the service of a customer, then the interrupted customer, in accordance with the Bernoulli scheme, decides either to leave the system or join a common orbit of retrial and feedback customers. An approximate method, based on the space merging approach of three-dimensional Markov chains, is proposed for the calculation of the steady-state probabilities, as well as performance measures of the system. The results of the numerical experiments are demonstrated.

Keywords: multi-server queue; unreliable servers; retrial customers; delayed feedback; finite and infinite orbits; balking from orbit; calculation method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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