Equilibrium Joining Strategies in the M/M/1 Queues with Setup Times under N-Policy

This paper carries out a game-theoretic analysis of a single-server queueing system with setup times under N-policy by considering both the partially observable and the partially unobservable information scenarios. The server switches off whenever the system becomes empty, and is resumed when the number of customers reaches a certain threshold value. Customers decide whether to join or to balk the system upon arrival based on their available information. The equilibrium joining strategy of customers as well as the system's performance measures are derived under different information levels. We find that both Follow-the-Crowd (FTC) and Avoid-the-Crowd (ATC) behaviors exist in our system. Numerical results show that the social welfare is unimodal in the threshold, and is decreasing in the waiting cost.