Model for synchronizer of marked pairs in fork-join network

TL;DR

This paper models a synchronizer in a fork-join queueing network, deriving the distribution of jobs and analyzing conditions under which job flow remains Poisson-like despite correlations.

Contribution

It introduces a new model for the synchronizer in fork-join networks and analyzes its behavior under Poisson arrivals and M/M/N queue assumptions.

Findings

The mean number of jobs in the synchronizer is bounded by network parameters.

The job departure flow can remain Poisson-like under certain parameter conditions.

A specific domain of parameters where correlations do not significantly alter flow statistics.

Abstract

We introduce a model for synchronizer of marked pairs, which is a node for joining results of parallel processing in two-branch fork-join queueing network. A distribution for number of jobs in the synchronizer is obtained. Calculations are performed assuming that: arrivals to the network form a Poisson process, each branch operates like an M/M/N queueing system. It is shown that a mean quantity of jobs in the synchronizer is bounded below by the value, defined by parameters of the network (which contains the synchronizer) and does not depend upon performance and particular properties of the synchronizer. A domain of network parameters is found, where the flow of jobs departing from the synchronizer does not manifest a statistically significant difference from the Poisson type, despite the correlation between job flows from both branches of the fork-join network.