Invariant measures and error bounds for random walks in the quarter-plane based on sums of geometric terms

The Invariant Measure of Random Walks in the Quarter-plane: Representation in Geometric Terms

We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these linear combinations such that the resulting measure may yield an invariant measure of a random walk. We demonstrate that each geometric term must individual...

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

A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation of the stationary probability distribution is not available in general, the performance is approximated by a perturbed random walk, whose transition rates o...

Random Walks in the Quarter-Plane: Invariant Measures and Performance Bounds

On the bounds in Poisson approximation for independent geometric distributed random variables

‎The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method‎. ‎Some results related to random sums of independent geometric distributed random variables are also investigated.

Linear Programming Error Bounds for Random Walks in the Quarter-plane

We consider approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities along the boundaries of the state space. A Markov reward approach is used to bound the approximation error. The main contribution of the work is the formulation ...