Analysis of multi-server queue with a single vacation (e, d)-policy

In this paper, we consider a Markovian multi-server queue with a single vacation (e, d)-policy. In an M/M/c system with such a policy, when d (¡c) servers become idle at a service completion (or a customer departure) instant, e   (≤≤d) idle servers take a single vacation. After the vacation is completed, these servers return to attend the queue (either serve or stay idle) until the vacation condition is satisfied again. This model is more appropriate for the service or manufacturing systems with servers’ maintenance performed during their idle time. We formulate the system as a quasi-birth-and-death (QBD) process and develop the various stationary performance measures for this system. In addition, we also prove several conditional stochastic decomposition properties.