Analysis of a finite‐buffer bulk‐service queue with discrete‐Markovian arrival process: D‐MAP/Ga,b/1/N

Abstract

Abstract Discrete‐time queues with D‐MAP arrival process are more useful in modeling and performance analysis of telecommunication networks based on the ATM environment. This paper analyzes a finite‐buffer discrete‐time queue with general bulk‐service rule, wherein the arrival process is D‐MAP and service times are arbitrarily and independently distributed. The distributions of buffer contents at various epochs (departure, random, and prearrival) have been obtained using imbedded Markov chain and supplementary variable methods. Finally, some performance measures such as loss probability and average delay are discussed. Numerical results are also presented in some cases. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 345–363, 2003.

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