Analytic and Computational Analysis of GI/Ma,b/c Queueing System

Bulk-service queueing systems have been widely applied in many areas real life. While single-server work some cases, multi-servers can efficiently handle most complex applications. Bulk-service, multi-server (compared to well-developed systems) are more and harder deal with, especially when the inter-arrival time distributions arbitrary. This paper deals with analytic computational analyses of queue-length for a bulk-service, system GI/Ma,b/c, wherein times follow an arbitrary distribution, is quorum, b capacity each server; service exponential distributions. The introduction quorum further increases complexity model. In view this, two-dimensional Markov chain has be involved. Currently, it appears that this not addressed so far. An elegant closed-form solution efficient algorithm obtain at three different epochs, i.e., pre-arrival epoch (p.a.e.), random (r.e.), post-departure (p.d.e.) presented, servers busy idle states, respectively.