Analysis of a Multiserver Delay-Loss System with a General Markovian Arrival Process

Abstract

A B STRACT Applying a continuous-time modeling approach, we describe the behavior of a logical output buffer in a switch module of a B-ISDN packet switch with channel grouping by a multi-server delay-loss system �� MAPi/PH/n/m with a superposition of independent MAPs as arrival stream and phase-type distributed service times. We construct the ge­ nerator matrix of the underlying Markov chain and point out its QBD structure with boundary. Then we derive a new representation of its steady-state probability vector in terms of a linear combination of exactly two matrix-geometric components. Moreover, we present a new numerical method to solve the corresponding matrix-quadratic equations. Finally, we develop formulae to calculate the most important performance characteristics of this multi-class delay-loss system.

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