Strategic behavior in a Markovian ticket queue with non-negligible clearance times

In this work, we study an M/M/1 ticket queue with a clearance time for balking customers that follows the exponential distribution. The customers’ join/balk decisions depend on the total queue length that they observe upon arrival. The latter leads to a queue with two types of customers, with the type being decided according to the queue length upon arrival. We obtain the steady-state distribution applying when customers use a threshold strategy. We show that the conditional distributions of the tail of the queue given its head can be constructed as mixtures and sums of geometric distributions. We analyze the individual best response and check whether a threshold strategy is an equilibrium, for given values of the clearance rate.