A Novel Computational Procedure for the Waiting-Time Distribution (In the Queue) for Bulk-Service Finite-Buffer Queues with Poisson Input

In this paper, we discuss the waiting-time distribution for a finite-space, single-server queueing system, in which customers arrive singly following Poisson process and server operates under (a,b)-bulk service rule. The system has finite-buffer capacity ‘N’ excluding batch service. service-time of batches follows general distribution, is independent arrival process. We first develop an alternative approach obtaining probability queue length at post-departure epoch and, subsequently, random using embedded Markov chain, renewal theory semi-Markov (in queue) customer derived functional relation between generating function (pgf) queue-length Laplace–Stieltjes transform (LST) queueing-time customer. Using LSTs, derivation density customer’s waiting time its numerical implementations.