Stability and Heavy-traffic Delay Optimality of General Load Balancing Policies in Heterogeneous Service Systems
Abstract
We consider a load balancing system consisting of single-server queues working in parallel, with heterogeneous service rates. Jobs arrive to a central dispatcher, which has to dispatch them to one of the queues immediately upon arrival. For this setting, we consider a broad family of policies where the dispatcher can only access the queue lengths sporadically, every units of time. We assume that the dispatching decisions are made based only on the order of the scaled queue lengths at the last time that the queues were accessed, and on the processing rate of each server. For these general policies, we provide easily verifiable necessary and sufficient conditions for the stability of the system, and sufficient conditions for heavy-traffic delay optimality. We also show that, in heavy-traffic, the queue length converges in distribution to a scaled deterministic vector, where the scaling factor is an exponential random variable.
Cite
@article{arxiv.2510.14284,
title = {Stability and Heavy-traffic Delay Optimality of General Load Balancing Policies in Heterogeneous Service Systems},
author = {Yishun Luo and Martin Zubeldia},
journal= {arXiv preprint arXiv:2510.14284},
year = {2025}
}