Strategic Analysis of Retrial Queues with Setup Times, Breakdown and Repairs

This paper considers a repairable M/M/1 retrial queueing model with setup times. Once the system is empty, the server will be closed down to reduce operating costs. And the system will be activated only when a new customer arrives. The customer who activates the server will enter the retrial orbit waiting to reapply for service. The server may break down during the busy period. First, the steady-state probability of the model is obtained by using the probability generating function method. And we derive performance measures of the system such as the queue length of the orbit, the numerical examples are given to show the sensitivity of the performance measures. Second, the cost function is established to find the minimum cost of the system, and we study the effects of some parameters on the cost by numerical examples. Finally, from the perspective of the customer and social planner, we construct the individual utility function and the social welfare function in the almost and fully unobservable cases, and then the optimal strategy of the customers is analyzed.