A batchSPP/G/1 queue with multiple vacations and exhaustive service discipline

This paper considers a batch-arrival single-server queueing system with multiple vacations and exhaustive service discipline. Customers arrive to the system in accordance with a batch switched Poisson process (batchSPP). Using the supplementary variable technique, we analyze the stationary queue length distribution and derive various formulas for queue lengths and waiting times. In particular, we analytically show the decomposition property for the waiting time distributions. Therefore, the waiting time formulas developed in this paper can also be applied to a batchSPP/G/1 queue without vacations.