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Abstract
In this paper, we consider a finite-buffer bulk-arrival and bulk-service queue with variable server capacity: M X /G Y /1/K + B. The main purpose of this paper is to discuss the analytic and computational aspects of this system. We first derive steady-state departure-epoch probabilities based on the embedded Markov chain method. Next, we demonstrate two numerically stable relationships for the steady-state probabilities of the queue lengths at three different epochs: departure, random, and arrival. Finally, based on these relationships, we present various useful performance measures of interest such as moments of the number of customers in the queue at three different epochs, the loss probability, and the probability that server is busy. Numerical results are presented for a deterministic service-time distribution – a case that has gained importance in recent years.
Acknowledgment
The research of the first author (Dr. Seok Ho Chang) was supported by the Post-doctoral Fellowship Program of Korea Science & Engineering Foundation (KOSEF). The first author acknowledges with thanks the facilities provided by Laboratory for Manufacturing and Productivity, Massachusetts Institute of Technology, where he was invited to the research group as a visiting scholar.
