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

TL;DR

This paper introduces a linear programming method to bound the error in approximating the performance of quarter-plane random walks using perturbed models with product-form stationary distributions.

Contribution

It formulates a linear program to effectively bound the approximation error for random walks in the quarter-plane using boundary perturbations.

Findings

Linear program accurately bounds approximation errors.

Perturbed models with product-form distributions simplify analysis.

Method applicable to various boundary conditions.

Abstract

We consider the 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 of a linear program that provides the approximation error.