Algebraic modelling and performance evaluation of acyclic fork-join queueing networks

TL;DR

This paper develops algebraic bounds on the mean cycle time of acyclic fork-join queueing networks using (max,+)-algebra, providing insights into their performance under different service time assumptions.

Contribution

It introduces a novel algebraic approach to bounding the mean cycle time in acyclic fork-join networks, enhancing understanding of their performance limits.

Findings

Derived simple lower and upper bounds on mean cycle time

Analyzed bounds under various service time assumptions

Presented numerical examples illustrating the bounds

Abstract

Simple lower and upper bounds on mean cycle time in stochastic acyclic fork-join queueing networks are derived using a (max,+)-algebra based representation of network dynamics. The behaviour of the bounds under various assumptions concerning the service times in the networks is discussed, and related numerical examples are presented.