Olivier Brun

Price of Anarchy in Non-Cooperative Load Balancing

We investigate the price of anarchy of a load balancing game with

Price of anarchy in non-cooperative load balancing games

K

Integration of streaming and elastic traffic: a fixed point approach

dispatchers. The service rates and holding costs are assumed to depend on the server, and the service discipline is assumed to be processor-sharing at each server. The performance criterion is taken to be the weighted mean number of jobs in the system, or equivalently, the weighted mean sojourn time in the system. For this game, we first show that, for a fixed amount of total incoming traffic, the worst-case Nash equilibrium occurs when each player routes exactly the same amount of traffic, i.e., when the game is symmetric. For this symmetric game, we provide the expression for the loads on the servers at the Nash equilibrium. Using this result we then show that, for a system with two or more servers, the price of anarchy, which is the worst-case ratio of the global cost of the Nash equilibrium to the global cost of the centralized setting, is lower bounded by

Worst-case analysis of non-cooperative load balancing

K/(2\sqrt{K}-1)

PERFORMANCE OF NON-COOPERATIVE ROUTING OVER PARALLEL NON-OBSERVABLE QUEUES

and upper bounded by

Is the Price of Anarchy the Right Measure for Load-Balancing Games?

\sqrt{K}

Communication kernel for high speed networks in the parallel environment LANDA-HSN

, independently of the number of servers.

Scalable, self-healing, and self-optimizing routing overlays

We investigate the price of anarchy of a load balancing game with K dispatchers. The service rates and holding costs are assumed to depend on the server, and the service discipline is assumed to be processor-sharing at each server. The performance criterion is taken to be the weighted mean number of jobs in the system, or equivalently, the weighted mean sojourn time in the system. Independent of the state of the servers, each dispatcher seeks to determine the routing strategy that optimizes the performance for its own traffic. The interaction of the various dispatchers thus gives rise to a non-cooperative game. For this game, we first show that, for a fixed amount of total incoming traffic, the worst-case Nash equilibrium occurs when each player routes exactly the same amount of traffic, i.e., when the game is symmetric. For this symmetric game, we provide the expression for the loads on the servers at the Nash equilibrium. Using this result, we then show that, for a system with two or more servers, the price of anarchy, which is the worst-case ratio of the global cost of the Nash equilibrium to the global cost of the centralized setting, is lower bounded by K/(2K-1) and upper bounded by K, independent of the number of servers.

Integration of equipment constraints in the network topology design process

We present a fixed point approach to evaluate the quality of service of streaming traffic multiplexed with elastic traffic in multi-service networks. First, we handle elastic traffic and streaming traffic separately, and then we derive a general fixed point formulation integrating both types of traffic in best effort networks. Then, we extend the application of this formulation to multi-service networks where priorities and bandwidth sharing schemes can be applied to different flows. Our approach is mainly oriented towards very large scale networks where traditional simulation techniques are not scalable, and where a large number of flows have to be evaluated in reasonable time. We assess the accuracy of our approach by means of event-driven simulations.

Access network design with capacity-dependent costs

We investigate the impact of heterogeneity in the amount of incoming traffic routed by dispatchers in a non-cooperative load balancing game. For a fixed amount of total incoming traffic, we show that for a broad class of cost functions the worst-case social cost occurs when each dispatcher routes the same amount of traffic, that is, the game is symmetric. Using this result, we give lower bounds on the Price of Anarchy for (i) cost functions that are polynomial on server loads; and (ii) cost functions representing the mean delay of the shortest remaining processing time service discipline.