Céline Comte

The multi-source model for dimensioning data networks

Traffic modeling is key to the dimensioning of data networks. Usual models rely on the implicit assumption that each user generates data flows in series, one after the other, the ongoing flows sharing equitably the considered network link. We relax this assumption and consider the more realistic case where users may generate several data flows in parallel, these flows having to share the users access line as well. We qualify this model as multi-source since each user now behaves as an independent traffic source. Usual performance metrics like mean throughput and congestion rate must now be defined at user level rather than at flow level. We derive explicit expressions for these performance metrics under the assumption that flows share bandwidth according to balanced fairness. These results are compared with those obtained by simulation when max-min fairness is imposed, either at flow level or at user level.

Balanced Fair Resource Sharing in Computer Clusters

We represent a computer cluster as a multi-server queue with some arbitrary graph of compatibilities between jobs and servers. Each server processes its jobs sequentially in FCFS order. The service rate of a job at any given time is the sum of the service rates of all servers processing this job. We show that the corresponding queue is quasi-reversible and use this property to design a scheduling algorithm achieving balanced fair sharing of the computing resources.

Poly-symmetry in processor-sharing systems

We consider a system of processor-sharing queues with state-dependent service rates. These are allocated according to balanced fairness within a polymatroid capacity set. Balanced fairness is known to be both insensitive and Pareto-efficient in such systems, which ensures that the performance metrics, when computable, will provide robust insights into the real performance of the system considered. We first show that these performance metrics can be evaluated with a complexity that is polynomial in the system size if the system is partitioned into a finite number of parts, so that queues are exchangeable within each part and asymmetric across different parts. This in turn allows us to derive stochastic bounds for a larger class of systems which satisfy less restrictive symmetry assumptions. These results are applied to practical examples of tree data networks, such as backhaul networks of Internet service providers, and computer clusters.

Performance of Balanced Fairness in Resource Pools: A Recursive Approach

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.