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Homogeneous Row-Continuous Bivariate Markov Chains with Boundaries

J. Keilson and M. Zachmann
Journal of Applied Probability
Vol. 25, A Celebration of Applied Probability (1988), pp. 237-256
DOI: 10.2307/3214160
Stable URL: http://www.jstor.org/stable/3214160
Page Count: 20
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Homogeneous Row-Continuous Bivariate Markov Chains with Boundaries
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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.

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