A Complete and Simple Solution to a Discrete-Time Finite-Capacity BMAP/D/c Queue

Nam K. Kim, Mohan L. Chaudhry, Bong K. Yoon, Kilhwan Kim

Defense Management College, Korea National Defense University, Seoul, South Korea.
Department of Industrial Engineering, Chonnam National University, Gwangju, South Korea.
Department of Management Engineering, Sangmyung University, Cheonan, South Korea.
Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada.

DOI: 10.4236/am.2012.312A297                

Abstract

We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digital telecommunication systems and other related areas. For this queueing system, we present, based on Markov chain analysis, not only the steady-state distributions but also the transient distributions of the system length and of the system waiting time in a simple and unified manner. From these distributions, important performance measures of practical interest can be easily obtained. Numerical examples concerning the superposition of certain video traffics are presented at the end.

Keywords

Discrete-Time Queue; Batch Markovian Arrival Process; Deterministic Service Time; Multiple Server

Conflicts of Interest

The authors declare no conflicts of interest.

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