Retrial Queues with Unreliable Servers and Delayed Feedback

Mathematics

Janos Sztrik¹  Sevinj Aliyeva²  Agassi Melikov³ 

[1] Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary;Faculty of Applied Mathematics and Cybernetics, Baku State University, Baku AZ 1148, Azerbaijan;Institute of Control Systems, National Academy of Science, Baku AZ 1141, Azerbaijan;

关键词: multi-server queue;    unreliable servers;    retrial customers;    delayed feedback;    finite and infinite orbits;    balking from orbit;   

DOI  :  10.3390/math9192415

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown