Join-the-Shortest-Queue Model as a Mean Field Approximation to a Local Balancing Network

TL;DR

This paper models a large queueing network with local balancing and shows that as the network size grows, its behavior can be approximated by the well-known join-the-shortest-queue model using mean field techniques.

Contribution

It introduces a new network model with local balancing and demonstrates that its large-scale limit aligns with the classic join-the-shortest-queue model via mean field approximation.

Findings

Mean field approximation converges to join-the-shortest-queue model as N→∞

Constructs a Markov process for the local balancing network

Provides theoretical foundation for large-scale queueing networks

Abstract

In this paper, we consider a queueing network with $N$ nodes, each of which has a fixed number $k$ of neighboring nodes, referred to as the $N$ node network with local balancing. We assume that to each of the $N$ nodes, an incoming job (or task) chooses the shortest queue from this node and its neighboring nodes. We construct an appropriate Markov process for this network and find a mean field approximation to this network as $N\rightarrow\infty$, which turns out to be the standard join-the-shortest-queue model.