Analysis of MX/G/1 and GeoX/G/1 queues with random number of vacations

By using the arrival time approach of Chae et al., we derive various performance measures including the queue length distribution (in probability generating functions (PGF)) and the waiting time distributions (in latest start time and PGF) for both M^X/G/1 and Geo^X/G/1 queueing systems, both under the assumption that the server, when it becomes idle, takes multiple vacations up to a random maximum number. This is an extension of both Choudhury, and Zhang and Tian. A few mistakes in Zhang and Tian are corrected and meaningful interpretations are supplemented.