Load Balancing in Heterogeneous Server Clusters: Insights From a Product-Form Queueing Model

TL;DR

This paper analyzes how server heterogeneity affects load balancing performance in finite-size data center clusters using an exactly solvable product-form queueing model, providing new insights into system behavior.

Contribution

It introduces a novel analytical approach leveraging a product-form queueing model to understand heterogeneity effects in finite-size server clusters.

Findings

Heterogeneity significantly impacts performance metrics.

Exact analysis is possible for finite-size systems.

Numerical evaluations validate analytical insights.

Abstract

Efficiently exploiting servers in data centers requires performance analysis methods that account not only for the stochastic nature of demand but also for server heterogeneity. Although several recent works proved optimality results for heterogeneity-aware variants of classical load-balancing algorithms in the many-server regime, we still lack a fundamental understanding of the impact of heterogeneity on performance in finite-size systems. In this paper, we consider a load-balancing algorithm that leads to a product-form queueing model and can therefore be analyzed exactly even when the number of servers is finite. We develop new analytical methods that exploit its product-form stationary distribution to understand the joint impact of the speeds and buffer lengths of servers on performance. These analytical results are supported and complemented by numerical evaluations that cover a large variety of scenarios.