Stationary distribution of a multi-server vacation queue with constant impatient times

This paper analyzes a multi-server queueing system with multiple vacations in which the vacation duration of each server is exponentially distributed. When all the servers are on vacation, customers are impatient if their waiting times exceed a constant value. To derive the stationary distribution of the system, we employ the matrix analytic method. Specifically, our queueing model is represented as an M/G/1-type Markov chain, and the stationary distribution is simply obtained by using its transition structures. Furthermore, we explicitly derive the tail decay rate of the stationary distribution, and demonstrate that the decay rate is not always equal to that for the queueing model without vacations.