Distributed Selfish Load Balancing with Weights and Speeds

TL;DR

This paper analyzes a distributed load balancing protocol for selfish clients in a network with processors of varying speeds and tasks of different weights, providing improved convergence bounds and novel results for complex settings.

Contribution

It introduces new bounds on convergence time for a probabilistic load balancing protocol in heterogeneous environments with weighted tasks and speeds.

Findings

Improved expected convergence time bounds using spectral graph theory.

First results for load balancing with weighted tasks and non-uniform processor speeds.

Protocol effectively reaches Nash equilibria in complex heterogeneous settings.

Abstract

In this paper we consider neighborhood load balancing in the context of selfish clients. We assume that a network of n processors and m tasks is given. The processors may have different speeds and the tasks may have different weights. Every task is controlled by a selfish user. The objective of the user is to allocate his/her task to a processor with minimum load. We revisit the concurrent probabilistic protocol introduced in [6], which works in sequential rounds. In each round every task is allowed to query the load of one randomly chosen neighboring processor. If that load is smaller the task will migrate to that processor with a suitably chosen probability. Using techniques from spectral graph theory we obtain upper bounds on the expected convergence time towards approximate and exact Nash equilibria that are significantly better than the previous results in [6]. We show results for uniform tasks on non-uniform processors and the general case where the tasks have different weights and the machines have speeds. To the best of our knowledge, these are the first results for this general setting.