Equilibrium balking strategies of customers in Markovian queues with two-stage working vacations

This paper studies the customers’ equilibrium balking behavior in some single-server Markovian queues with two-stage working vacations. That is, the server starts taking two successive working vacations when the system becomes empty, during which he provides low-rate service but maintains different service rates in the two-stage vacations. Based on different precision levels of system information, we discuss observable queues, partially observable queues and unobservable queues, respectively. For each type of queues, we get the customers’ equilibrium balking strategy and equilibrium social welfare per time unit, and numerically observe that their positive equilibrium strategy is unique. Especially, for partially observable queues, the customers’ equilibrium joining probabilities in vacation states are not necessarily smaller than that in busy state.