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Homogeneous row-continuous bivariate markov chains with boundaries

Published online by Cambridge University Press:  14 July 2016

J. Keilson  and
M. Zachmann
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Abstract

The matrix-geometric results of M. Neuts are extended to ergodic row-continuous bivariate Markov processes [J(t), N(t)] on state space B = {(j, n)} for which: (a) there is a boundary level N for N(t) associated with finite buffer capacity; (b) transition rates to adjacent rows and columns are independent of row level n in the interior of B. Such processes are of interest in the modelling of queue-length for voice-data transmission in communication systems.

One finds that the ergodic distribution consists of two decaying components of matrix-geometric form, the second induced by the finite buffer capacity. The results are obtained via Green's function methods and compensation. Passage-time distributions for the two boundary problems are also made available algorithmically.

Keywords

MATRIX-GEOMETRICGREEN'S FUNCTIONCOMPENSATION
Type
Part 6 - The Analysis of Stochastic Phenomena
Information
Journal of Applied Probability , Volume 25 , Issue A , 1988 , pp. 237 - 256
Copyright
Copyright © Applied Probability Trust 1988 

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