A compensation approach for two-dimensional Markov processes

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    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.
    Originele taal-2Engels
    Pagina's (van-tot)783-817
    Aantal pagina's35
    TijdschriftAdvances in Applied Probability
    Nummer van het tijdschrift4
    StatusGepubliceerd - 1993

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