Rank-based stochastic differential inclusions and diffusion limits for a load balancing model

TL;DR

This paper extends previous work on load balancing models by establishing a diffusion limit for systems with finite second moment service times, using a novel rank-based stochastic differential inclusion.

Contribution

It introduces a new rank-based stochastic differential inclusion framework applicable to load balancing models with general service time distributions.

Findings

Diffusion limit established for finite second moment service times.

Extension from exponential to general service time distributions.

Introduction of a new stochastic differential inclusion concept.

Abstract

In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of rank-based Brownian particles on the half-line. This paper extends these results from the case of exponential service time to an invariance principle, where service times have finite second moment. The main tool is a new notion of rank-based stochastic differential inclusion, which may be of interest in its own right.