The heavy traffic limit of a class of Markovian queueing models

Authors:
Søren Asmussen
Affiliations:
Department of Mathematics and Computer Science, Institute of Electronic Systems, Aalborg University, Strandvejen 19, DK-9000 Aalborg, Denmark
Venue:
Operations Research Letters
Year:
1987

Citing 3
Cited 0

An asymptotic analysis of a queueing system with Markov-modulated arrivals

Operations Research
Transient behavior of the M/M/1 queue: starting at the origin

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Refining diffusion approximations for queues

Operations Research Letters

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Abstract

Reflected Brownian motion is obtained as the heavy traffic limit of the level component (Q"n) of a class of bivariate Markov chains {(J"n, Q"n)} incorporating those having a matrix-geometric stationary distribution. Approximations for both transient and ergodic behaviour are obtained as a corollary and illustrated for the Markov-modulated M/M/1 queue.