Waiting Times in the Queueing System GI/Ma, b/c

Abstract

In this paper, we present analytical techniques for determining the waiting times for a complex bulk-service, multi-server queueing system GI/M^a,b/c, where inter-arrival times follow an arbitrary distribution. The introduction of quorum ′′a′′ increases the complexity of the model, and as of now, it remains unaddressed for this specific system. We derive a closed-form formula for computing the mean waiting-time. Numerical results are presented for the queueing systems with inter-arrival time distributions of Erlang, deterministic, and uniform. Additionally, We verify Little’s Formula for these systems.