Power-of-two sampling in redundancy systems: the impact of assignment constraints

TL;DR

This paper investigates how assignment constraints affect power-of-two sampling in load balancing, proving that uniform sampling generally outperforms non-uniform sampling in certain redundancy systems.

Contribution

It provides the first rigorous proof that uniform sampling stochastically dominates non-uniform sampling in specific load balancing scenarios with constraints.

Findings

Uniform sampling stochastically dominates non-uniform sampling in four-server systems.

The dominance result extends to arbitrary-size systems under light traffic conditions.

The study offers theoretical validation for the impact of assignment constraints on sampling strategies.

Abstract

A classical sampling strategy for load balancing policies is power-of-two, where any server pair is sampled with equal probability. This does not cover practical settings with assignment constraints which force non-uniform sampling. While intuition suggests that non-uniform sampling adversely impacts performance, this was only supported through simulations, and rigorous statements have remained elusive. Building on product-form distributions for redundancy systems, we prove the stochastic dominance of uniform sampling for a four-server system as well as arbitrary-size systems in light traffic.