Bi-objective optimization and reliability analysis in unreliable M/G/1 retrial queues with rational customers, reserved idle times and setup times

ABSTRACT

Energy consumption arising from no-loads and failures is a common and challenging problem in the design of service systems. To analyze the impact of no-load consumption and failure consumption on the energy consumption simultaneously, this paper considers an M/G/1 retrial queue with reserved idle times, setup times and server breakdowns. First, the steady-state condition and performance measures of the system are obtained by the embedded Markov chain and the supplementary variable method. Then, the reliability indicators of the system are analyzed, and an algorithm for solving the system reliability $\mathit{R}(\mathit{t})$ is constructed based on the Monte Carlo method. In order to better optimize the system, the customer’s equilibrium joining strategy is derived, and the socially optimal joining strategy is obtained by the particle swarm optimization (PSO) algorithm. From the decision-maker viewpoint, a bi-objective optimization model is constructed to minimize the expected energy consumption and the expected waiting time of retrial customers, and solved by the non-dominated ranking genetic algorithm II (NSGA-II). Finally, we illustrate an application of the proposed analytical approach in the cloud computing data center, which makes it possible to achieve an appropriate balance between energy consumption and quality of service (QoS).

KEYWORDS:

• Retrial queue equilibrium strategy
• reliability analysis
• bi-objective optimization
• reserved idle times

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grant (Nos. 71971189, 72071175).

Notes on contributors

Fan Xu

Fan Xu is a postgraduate student at the School of Science at Yanshan University in China. His main research interests are stochastic modeling and queueing theory.

Ruiling Tian

Ruiling Tian is a professor in the School of Science at Yanshan University in China. Her research interests are stochastic modeling and queueing theory.

Linmin Hu

Linmin Hu is a professor in the School of Science at Yanshan University in China. His research interests include stochastic system reliability modeling and performance evaluation.

Qi Shao

Qi Shao is a postgraduate student at the School of Science at Yanshan University in China. Her research interests include stochastic system reliability modeling and performance evaluation.