  We consider homogeneous random walks in the quarter-plane. The necessary
conditions which characterize random walks of which the invariant measure is a
sum of geometric terms are provided in [2,3]. Based on these results, we first
develop an algorithm to check whether the invariant measure of a given random
walk is a sum of geometric terms. We also provide the explicit form of the
invariant measure if it is a sum of geometric terms. Secondly, for random walks
of which the invariant measure is not a sum of geometric terms, we provide an
approximation scheme to obtain error bounds for the performance measures.
Finally, some numerical examples are provided.
