Performance of Balanced Fairness in Resource Pools: A Recursive Approach

TL;DR

This paper introduces a recursive method to evaluate the performance of resource pools with complex server-job assignment constraints under balanced fairness, enabling polynomial-time analysis for broad pool structures.

Contribution

It presents a novel recursive approach for computing performance metrics in resource pools with assignment constraints, expanding the class of models with explicit analysis.

Findings

Recursive formulas for mean response times under balanced fairness

Polynomial-time analysis for broad classes of pool structures

Enhanced understanding of server-job interaction effects

Abstract

Understanding the performance of a pool of servers is crucial for proper dimensioning. One of the main challenges is to take into account the complex interactions between servers that are pooled to process jobs. In particular, a job can generally not be processed by any server of the cluster due to various constraints like data locality. In this paper, we represent these constraints by some assignment graph between jobs and servers. We present a recursive approach to computing performance metrics like mean response times when the server capacities are shared according to balanced fairness. While the computational cost of these formulas can be exponential in the number of servers in the worst case, we illustrate their practical interest by introducing broad classes of pool structures that can be exactly analyzed in polynomial time. This extends considerably the class of models for which explicit performance metrics are accessible.