Analysis of Two-server Queues with a Variant Vacation Policy

We study an M/M/2 queueing system with two heterogeneous servers under a variant vacation policy, where the two servers may take together at most J vacations when the system is empty. A quasi-birth-and-death process is formulated to analyze the system. We obtain the explicit expressions of the stationary distribution of the system size and the mean system size. We also show that the number of vacations that the servers take continuously under the condition that the servers are in vacation follows a truncated geometric distribution. The conditional stochastic decomposition properties of the queue length and the waiting time are established for such a system.