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

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 $R(t)$R(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).