Optimization of retrial queue with unreliable servers subject to imperfect coverage and reboot delay

• Published in: Quality technology & quantitative management Vol. 19; no. 4; pp. 428 - 453
• Main Authors: Liu, Tzu-Hsin, Chang, Fu-Min, Ke, Jau-Chuan, Sheu, Shey-Huei
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 04.07.2022
• Subjects: Bi-objective optimization; delay reboot; imperfect coverage; Pareto front; retrial queue
• ISSN: 1684-3703; 1684-3703
• DOI: 10.1080/16843703.2021.2020952

A retrial queue with constant retrial policy, unreliable servers and the failed servers may not be detected is investigated in this paper. Upon arrival, a customer either is attended to one of the available servers or enters a retrial orbit and retries in a random time as all servers are not available. The unreliable server can be breakdown when he is working. The breakdown server may not be detected due to some fault matters. Under such a situation, the repair facility will issue a reboot operation to locate the non-detected breakdown server. Once the breakdown server is detected and located, he will be sent for repair. After utilizing the general theory of matrix-geometric approach to determine the stationary distribution, some performance measures are proposed. A single-objective model aiming at minimizing the average cost is constructed. We apply particle swarm optimization algorithm and genetic algorithm to find the optimum combination of parameters. We also formulate a bi-objective model aiming at minimizing the expect cost and the mean waiting time of customers in orbit. Two multi-objective algorithms are developed to solve it.