Performance measures for the two-node queue with finite buffers

TL;DR

This paper develops an approximation method using Markov reward approach to evaluate performance measures of two-node queues with finite buffers modeled as two-dimensional random walks, including tandem and coupled queue variants.

Contribution

It introduces a novel approximation scheme for finite-buffer queues based on perturbed random walks with product-form invariant measures.

Findings

The scheme provides bounds on performance measures for finite-buffer queues.

Application to tandem queues demonstrates effectiveness of the approximation.

Extensions to coupled queues with a single finite buffer are also shown.

Abstract

We consider a two-node queue modeled as a two-dimensional random walk. In particular, we consider the case that one or both queues have finite buffers. We develop an approximation scheme based on the Markov reward approach to error bounds in order to bound performance measures of such random walks in terms of a perturbed random walk in which the transitions along the boundaries are different from those in the original model and the invariant measure of the perturbed random walk is of product-form. We then apply this approximation scheme to a tandem queue and some variants of this model, for the case that both buffers are finite. We also apply our approximation scheme to a coupled-queue in which only one of the buffers has finite capacity.