Rank-based stochastic differential inclusions and diffusion limits for a load balancing model
Probability
2024-09-24 v1
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.
Cite
@article{arxiv.2409.15121,
title = {Rank-based stochastic differential inclusions and diffusion limits for a load balancing model},
author = {Rami Atar and Tomoyuki Ichiba},
journal= {arXiv preprint arXiv:2409.15121},
year = {2024}
}