Equilibrium Customer Strategies in the Queue with Threshold Policy and Setup Times

We consider the equilibrium behavior of customers in the M / M / 1 queue with N policy and setup times. The server is shut down once the system is empty and begins an exponential setup time to start service again when the number of customers in the system accumulates the threshold N ( N ≥ 1 ) . We consider the equilibrium threshold strategies for fully observable case and mixed strategies for fully unobservable case, respectively. We get various performance measures of the system and investigate some numerical examples of system size, social benefit, and expected cost function per unit time for the two different cases under equilibrium customer strategies.