Mean-field analysis of load balancing principles in large scale systems

TL;DR

This paper develops a mathematical framework to analyze and compare different load balancing strategies in large-scale heterogeneous server systems using mean-field theory, focusing on their transient and stationary performance.

Contribution

It introduces a high-level mean-field analysis framework for heterogeneous server clusters, enabling the study of various load balancing principles and their performance metrics.

Findings

Derived transient and stationary mean-field limits for load balancing policies

Compared performance measures such as job system time distributions

Provided insights into the effectiveness of different load balancing strategies

Abstract

Load balancing plays a crucial role in many large scale systems. Several different load balancing principles have been proposed in the literature, such as Join-Shortest-Queue (JSQ) and its variations, or Join-Below-Threshold. We provide a high level mathematical framework to examine heterogeneous server clusters in the mean-field limit as the system load and the number of servers scale proportionally. We aim to identify both the transient mean-field limit and the stationary mean-field limit for various choices of load balancing principles, compute relevant performance measures such as the distribution and mean of the system time of jobs, and conduct a comparison from a performance point of view.