Performance analysis and optimization of a retrial queue with working vacations and starting failures

• Published in: Mathematical and computer modelling of dynamical systems Vol. 25; no. 5; pp. 463 - 481
• Main Authors: Yang, Dong-Yuh, Wu, Chia-Huang
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.09.2019; Taylor & Francis Ltd
• Subjects: Algorithms; Failure analysis; Mathematical models; Matrix-geometric method; Optimization; Particle swarm optimization; Queues; Queuing theory; starting failure; Systems stability; working vacation
• ISSN: 1387-3954; 1744-5051
• DOI: 10.1080/13873954.2019.1660378

This paper presents a steady-state analysis of an M/M/1 retrial queue with working vacations, in which the server is subject to starting failures. The proposed queueing model is described in terms of the quasi-birth-death (QBD) process. We first derive the system stability condition. We then use the matrix-geometric method to compute the stationary probability distribution of the orbit size. Some performance measures for the system are developed. We construct a cost model, and our objective is to determine the optimal service rates during normal and vacation periods that minimize the expected cost per unit time. The canonical particle swarm optimization (CPSO) algorithm is employed to deal with the cost optimization problem. Numerical results are provided to illustrate the effects of system parameters on the performance measures and the optimal service rates. These results depict the system behaviour and show how the CPSO algorithm can be used to find numerical solutions for optimal service rates.