Exact computational analysis of waiting-time distributions of single-server bulk-arrival queues: M’X/G/1

This paper presents a closed-form analysis and computationally efficient method to study the waiting-time distributions of the first and random customer of an arrival group in the M’X/G/1 queue. Though computational analysis has been carried out for a variety of service-time distributions such as Erlang, generalized Erland, mixed generalized Erland, hyperexponential, and deterministic, only representative results have been included in the form of tables and graphs. For a fixed arrival-batch size, M’X/D/1 queue is analyzed independently as well as through M’X/EÅk/1 by taking k large. A recurrence relation for high order moments is also obtained.