Equilibrium Analysis of the M/M/1 Unreliable Queue with Two-phase Vacations and Vacation Interruption

This paper considers the equilibrium behavior of M/M/l unreliable queue which has two-phase vacations and vacation interruption. It enters buffer period, when the system becomes empty. If customers arrive within this time, the server transitions into the working state; otherwise, the server enters the working vacation, their service rates become slower. In addition, the working vacation can be end because of the vacation interruption. We discuss two information cases: the fully visible queue and the fully invisible queue. The strategy of equilibrium threshold and social benefit are considered in the first case. In the other case, we get the probability of the servers by using generating function. Then we calculate some performance measures and research the individual equilibrium strategy of customers and equilibrium social benefit. Moreover, we use numerical examples to demonstrate how information levels and system parameters impact equilibrium strategy and social benefit.