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A continuous-time random walk in the quarter plane with homogeneoustransition rates is considered. Given a non-negative reward function on thestate space, we are interested in the expected stationary performance. Since adirect derivation of the stationary probability distribution is not availablein general, the performance is approximated by a perturbed random walk, whosetransition rates on the boundaries are changed such that its stationaryprobability distribution is known in closed form.  A perturbed random walk for which the stationary distribution is a sum ofgeometric terms is considered and the perturbed transition rates are allowed tobe inhomogeneous. It is demonstrated that such rates can be constructed for anysum of geometric terms that satisfies the balance equations in the interior ofthe state space. The inhomogeneous transitions relax the pairwise-coupledstructure on these geometric terms that would be imposed if only homogeneoustransitions are used.  An explicit expression for the approximation error bound is obtained usingthe Markov reward approach, which does not depend on the values of theinhomogeneous rates but only on the parameters of the geometric terms.Numerical experiments indicate that inhomogeneous perturbation can give smallererror bounds than homogeneous perturbation.

Inhomogeneous perturbation and error bounds for the stationary performance of random walks in the quarter plane