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

Abstract 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 Erlang, mixed generalized Erlang, 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 /E k /1 by taking k large. A recurrence relation for higher order moments is also obtained.