The Multiplicative Version of Azuma's Inequality, with an Application to Contention Analysis

TL;DR

This paper introduces a multiplicative-error version of Azuma's inequality, extending concentration bounds, and demonstrates its application in simplifying the analysis of contention delays in multithreaded systems.

Contribution

It formulates a novel multiplicative Azuma's inequality and applies it to improve and simplify the analysis of contention delays in randomized multithreaded systems.

Findings

Simplified analysis of contention delays

Corrected previous bounds in multithreaded systems

Extended Azuma's inequality to multiplicative errors

Abstract

Azuma's inequality is a tool for proving concentration bounds on random variables. The inequality can be thought of as a natural generalization of additive Chernoff bounds. On the other hand, the analogous generalization of multiplicative Chernoff bounds does not appear to be widely known. We formulate a multiplicative-error version of Azuma's inequality. We then show how to apply this new inequality in order to greatly simplify (and correct) the analysis of contention delays in multithreaded systems managed by randomized work stealing.