Optimal Pricing Strategy in an Unreliable M/M/1 Retrial Queue with Delayed Repair and Breakdown Deterioration

Abstract

This paper focuses on an unreliable M/M/1 retrial queue with delayed repair, in which a novel breakdown mechanism is considered, i.e., a normal breakdown may deteriorate into a major breakdown. Arriving customers are not provided with the system’s information, but must decide whether or not to join it. First, the steady state of the system is analyzed. Then, based on the practical requirements of the cloud computing system, we construct an optimization model to minimize the response time of requesting information with proportions of detection, and repair of the normal and major breakdown as the decision variable. Furthermore, equilibrium joining strategies and the socially optimal pricing strategy are studied from the perspectives of the customer and the social planner, respectively. Finally, numerical examples are used to illustrate the impact of different parameters on strategies.