A Statistical Mechanical Load Balancer for the Web

TL;DR

This paper introduces a local, distributed load balancing method inspired by statistical mechanics, using a stochastic edge dynamic to generate Erdős-Rényi graphs for improved efficiency in web and computing systems.

Contribution

It proposes a novel local algorithm based on short random walks to achieve maximum-entropy graph states for load balancing without centralized control.

Findings

The edge dynamic effectively produces Erdős-Rényi random graphs.

Node degree distribution confirms maximum-entropy principle.

The method improves load balancing efficiency in large-scale systems.

Abstract

The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge dynamic that can serve as an effective thermalization scheme, and hence, the underlying graphs are expected to attain their maximum-entropy states, which turn out to be Erdos-Renyi (ER) random graphs. We next show that (i) a rate-equation based analysis of node degree distribution does indeed confirm the maximum-entropy principle, and (ii) the edge dynamic can be effectively implemented using short random walks on the underlying graphs, leading to a local algorithm for the generation of ER random graphs. The resulting statistical mechanical system can be adapted to provide a distributed and local (i.e., without any centralized monitoring) mechanism for load balancing, which can have a significant impact in increasing the efficiency and utilization of both the Internet (e.g., efficient web mirroring), and large-scale computing infrastructure (e.g., cluster and grid computing).