Bounds on mean cycle time in acyclic fork-join queueing networks

TL;DR

This paper derives simple bounds on the average cycle time in acyclic fork-join queueing networks using max-plus algebra, analyzing their behavior under different service time assumptions and illustrating with numerical examples.

Contribution

It introduces new simple bounds on mean cycle time for acyclic fork-join networks using max-plus algebra, enhancing understanding of their performance limits.

Findings

Bounds are tight under certain conditions

Behavior of bounds varies with service time assumptions

Numerical examples illustrate theoretical results

Abstract

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