Section: New Results

Power-of-d-Choices with Memory: Fluid Limit and Optimality

Abstract: In multi-server distributed queueing systems, the access of stochastically arriving jobs to resources is often regulated by a dispatcher, also known as load balancer. A fundamental problem consists indesigning a load balancing algorithm that minimizes the delays experienced by jobs. During the last twodecades, the power-of-d-choice algorithm, based on the idea of dispatching each job to the least loadedserver out ofdservers randomly sampled at the arrival of the job itself, has emerged as a breakthroughin the foundations of this area due to its versatility and appealing asymptotic properties. In this paper,we consider the power-of-d-choice algorithm with the addition of a local memory that keeps track of thelatest observations collected over time on the sampled servers. Then, each job is sent to a server withthe lowest observation. We show that this algorithm is asymptotically optimal in the sense that the load balancer can always assign each job to an idle server in the large-system limit. Our results quantify and highlight the importance of using memory as a means to enhance performance in randomized load balancing.

Authors: J. Anselmi (CQFD); F. Dufour (CQFD).