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 talk, we will represent these constraints by some assignment graph between jobs and servers. We will 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 will 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.
This is a joint work with Thomas Bonald (Télécom ParisTech) and Fabien Mathieu (Nokia Bell Labs France).