A COMPENSATION APPROACH FOR 2-DIMENSIONAL MARKOV-PROCESSES

Several queueing processes may be modeled as random walks on a multidi mensional grid. In this paper the equilibrium distribution for the cas e 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 el egant solution exists and may be found with a compensation approach. T he conditions can be easily formulated in terms of the random behaviou r in the inner area and the drift on the boundaries.