Equilibrium analysis of the observable queues with balking and delayed repairs

The equilibrium threshold balking strategies are investigated for the fully observable and partially observable single-server queues with server breakdowns and delayed repairs. Upon arriving, the customers decide whether to join or balk the queue based on observation of the queue length and status of the server, along with the consideration of waiting cost and the reward after finishing their service. By using Markov chain approach and system cost analysis, we obtain the stationary distribution of queue size of the queueing systems and provide algorithms in order to identify the equilibrium strategies for the fully and partially observable models. Finally, the equilibrium threshold balking strategies and the equilibrium social benefit for all customers are derived for the fully and partially observable system respectively, both with server breakdowns and delayed repairs.

► Equilibrium threshold strategies for fully and partially observable queues with balking and delayed repairs are obtained. ► It is the first time that server's delayed repair is taken into account to study customers' strategic behaviors. ► The thresholds for partially observable system take intermediate values between two extremes. ► Follow-The-Crowd (FTC) property has been observed. ► The qualitative new property in this model is that the repair time has two stages and hence it is not memoryless.