Homogeneous row-continuous bivariate markov chains with boundaries

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.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 14 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.