A compensation approach for two-dimensional Markov processes

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Abstract

Several queueing processes may be modeled as random walks on a multidimensional grid. In this paper the equilibrium distribution for the case of a two-dimensional grid is considered. In previous research it has been shown that for some two-dimensional random walks the equilibrium distribution has the form of an infinite series of products of powers which can be constructed with a compensation procedure. The object of the present paper is to investigate under which conditions such an elegant solution exists and may be found with a compensation approach. The conditions can be easily formulated in terms of the random behaviour in the inner area and the drift on the boundaries.
Original languageEnglish
Pages (from-to)783-817
Number of pages35
JournalAdvances in Applied Probability
Volume25
Issue number4
DOIs
Publication statusPublished - 1993

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