Stability and Heavy-traffic Delay Optimality of General Load Balancing Policies in Heterogeneous Service Systems

2025-10-16

AI Summary

This paper investigates stability and heavy-traffic delay optimality for parallel single-server load balancing systems with heterogeneous service rates, under periodic queue-length observations every $T$ time units; the central dispatcher bases decisions solely on the most recent scaled queue-length ordering and server rates. We propose a general class of scheduling policies that jointly leverage scaled ordering and rate awareness. For the first time, we derive necessary and sufficient conditions for system stability under such policies. Furthermore, we establish sufficient conditions for heavy-traffic delay optimality and prove that, in the heavy-traffic limit, the scaled queue-length vector converges weakly to a deterministic vector multiplied by an exponential random scaling factor. Our analysis integrates stochastic process theory, modeling of periodic information updates, and heavy-traffic scaling limit techniques. This work provides the first rigorous stability criterion and delay optimality guarantee for load balancing in heterogeneous systems operating under limited, periodically updated state information.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

We consider a load balancing system consisting of $n$ 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 $T$ 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.

Problem

• Analyzing stability of load balancing with sporadic queue length access
• Establishing delay optimality conditions for heterogeneous service systems
• Characterizing queue length distribution in heavy-traffic asymptotic regimes

Innovation

• Sporadic queue length access for load balancing
• Stability conditions for heterogeneous service systems
• Heavy-traffic delay optimality with scaled convergence