Yanting Chen, Richard J. Boucherie, Jasper Goseling
Published 2015-02-25Version 1
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.
The Invariant Measure of Homogeneous Markov Processes in The Quarter-Plane: Representation in Geometric Terms
Invariant Measure for Quantum Trajectories
On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical case
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