Performance Analysis of a Versatile Correlated Batch-arrival and Batch-service Queue

Abstract

In this paper, we investigate the BMAP/BMSP/1 queueing system. Analysis of this queueing system is carried out using the zeros of the associated characteristic function of the vector-generating function of system-length distribution at random epoch. A comparative study is also carried out to compare the roots method with that of the matrix-geometric method. We then obtain the steady-state system-length distributions at pre-arrival and postdeparture epochs. The sojourn-time distribution of an arbitrary customer in an arriving batch is also derived. Various performance measures such as mean system-length and mean sojourntime are determined. We generate adequate numerical results based on the diversified inputs but only a few of them are appended in the forms of tables and graphs.