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1 results

  • Homogeneous row-continuous bivariate markov chains with boundaries

  • J. Keilson, M. Zachmann
  • Journal:
    Journal of Applied Probability / Volume 25 / Issue A / 1988
    Published online by Cambridge University Press:
    14 July 2016, pp. 237-256
    Print publication:
    1988

  • 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.