Simple error bounds for the QBD approximation of a special class of two dimensional reflecting random walks

TL;DR

This paper derives simple upper bounds for the approximation error when using QBD methods to model a specific class of two-dimensional reflecting random walks, such as certain queueing networks.

Contribution

It introduces straightforward error bounds for the QBD approximation of 2D-RRWs, including models like two-node Jackson networks with cooperative servers.

Findings

Provided explicit upper bounds for approximation errors.

Applicable to models like two-node Jackson networks.

Simplifies analysis of QBD approximations for 2D-RRWs.

Abstract

This paper considers the QBD approximation of a special class of two-dimensional reflecting random walks (2D-RRWs). A typical example of the 2D-RRWs is a two-node Jackson network with cooperative servers. The main contribution of this paper is to provide simple upper bounds for the relative absolute difference between the time-averaged functionals of the original 2D-RRW and its QBD approximation.