Ideal synchronizer for marked pairs in fork-join network

TL;DR

This paper introduces a new synchronizer element for fork-join queueing networks, providing approximations for sojourn time distribution and establishing bounds based on network parameters.

Contribution

It presents a novel synchronizer for marked pairs in fork-join networks with derived sojourn time approximations and validity conditions.

Findings

Mean sojourn time is bounded below by network parameters.

Approximations are valid under Poisson arrivals and M/M/N queue assumptions.

The synchronizer's performance bounds are independent of its specific properties.

Abstract

We introduce a new functional element (synchronizer for marked pairs) meant to join results of parallel processing in two-branch fork-join queueing network. Approximations for distribution of sojourn time at the synchronizer are derived along with a validity domain. 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 mean sojourn time at a real synchronizer node 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.