Optimal joining strategies in a repairable retrial queue with reserved time and N-policy

We consider the retrial queue with a repairable server (who suffers from breakdowns and repairs) as well as reserved times and setup times under N-policy, and analyze the customers’ strategic behavior and social optimization in the almost unobservable and fully unobservable cases. The linear reward-cost structure is adopted to decide whether the arriving customers enter the orbit or balk when the server is busy or dormant. Firstly, the stationary probabilities are obtained by the probability generating function. The equilibrium strategies for two cases are analyzed. In particular, for the almost unobservable queue, the concrete expression of equilibrium strategy is deduced. Then the social welfare functions for two cases are established and the socially optimal arrival rates are calculated by genetic algorithm. Finally, the sensitivity of optimal arrival rates and social welfare to some system parameters is discussed by numerical experiments.