A linear programming approach to Markov reward error bounds for queueing networks

TL;DR

This paper develops a linear programming framework to derive bounds on the stationary performance of complex queueing networks modeled as Markov random walks, accommodating various network features like breakdowns and finite buffers.

Contribution

It generalizes the linear programming approach to a broader class of queueing networks with arbitrary dimensions and transition structures.

Findings

Provides a numerical method for performance bounds

Applicable to networks with breakdowns and finite buffers

Extends previous linear programming techniques

Abstract

In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary performance measures of a perturbed random walk whose stationary distribution is known explicitly. We consider random walks in an arbitrary number of dimensions and with a transition probability structure that is defined on an arbitrary partition of the positive orthant. Within each component of this partition the transition probabilities are homogeneous. This enables us to model queueing networks with, for instance, break-downs and finite buffers. The main contribution of this paper is that we generalize the linear programming approach of [1] to this class of models.