Josu Doncel

Congestion control of TCP flows in Internet routers by means of index policy

In this paper we address the problem of fast and fair transmission of flows in a router, which is a fundamental issue in networks like the Internet. We model the interaction between a source using the Transmission Control Protocol (TCP) and a bottleneck router with the objective of designing optimal packet admission controls in the router queue. We focus on the relaxed version of the problem obtained by relaxing the fixed buffer capacity constraint that must be satisfied at all time epoch. The relaxation allows us to reduce the multi-flow problem into a family of single-flow problems, for which we can analyze both theoretically and numerically the existence of optimal control policies of special structure. In particular, we show that for a variety of parameters, TCP flows can be optimally controlled in routers by so-called index policies, but not always by threshold policies. We have also implemented the index policy in Network Simulator-3 and tested in a simple topology their applicability in real networks. The simulation results show that the index policy achieves a wide range of desirable properties with respect to fairness between different TCP versions, across users with different round-trip-time and minimum buffer required to achieve full utility of the queue.

Are Mean-field Games the Limits of Finite Stochastic Games?

Mean-field games model the rational behavior of an infinite number of indistinguishable players in interaction. An important assumption of mean-field games is that, as the number of player is infinite, the decisions of an individual player do not affect the dynamics of the mass. Each player plays against the mass. A mean-field equilibrium corresponds to the case when the optimal decisions of a player coincide with the decisions of the mass. Many authors argue that mean-field games are a good approximation of symmetric stochastic games with a large number of players, the rationale behind this being that the impact of one player becomes negligible when the number of players goes to infinity. In this paper, we question this assertion. We show that, in general, this convergence does not hold. In fact, the “tit for tat” principle allows one to define many equilibria in repeated or stochastic games with N players. However, in mean-field games, the deviation of a single player is not visi- ble by the population and therefore the “tit for tat” principle cannot be applied. The conclusion is that, even if N-player games have many equilibria with a good social cost, this may not be the case for the limit game.

Predicting Response Times of Applications in Virtualized Environments

We propose simple queueing models for predicting response times of applications executed in a cloud computing platform under the SaaS model. We assume that each application instance is executed within a virtual machine running on a computing node of a data-center, and that VMs running concurrently on the same node share fairly its capacity. Our main contribution is to explicitly take into account the different behaviors of the different classes of applications (interactive, CPU-intensive or permanent applications). We show that simple expressions of the mean processing times of applications can be obtained using standard results from queueing theory. Experiments on a real virtualized platform show that the mathematical models allow to predict response times accurately.

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

Price of anarchy is an oft-used worst-case measure of the inefficiency of noncooperative decentralized architectures. For a noncooperative load-balancing game with two classes of servers and for a finite or infinite number of dispatchers, we show that the price of anarchy is an overly pessimistic measure that does not reflect the performance obtained in most instances of the problem. We explicitly characterize the worst-case traffic conditions for the efficiency of noncooperative load-balancing schemes and show that, contrary to a common belief, the worst inefficiency is in general not achieved in heavy traffic.

Optimal congestion control of TCP flows for internet routers

In this work we address the problem of fast and fair transmission of ows in a router, which is a fundamental issue in networks like the Internet. We model the interaction between a TCP source and a bottleneck queue with the objective of designing optimal packet admission controls in the bottleneck queue. We focus on the relaxed version of the problem obtained by relaxing the fixed buffer capacity constraint that must be satisfied at all time epoch. The relaxation allows us to reduce the multi-ow problem into a family of single-ow problems, for which we can analyze both theoretically and numerically the existence of optimal control policies of special structure. In particular, we show that for a variety of parameters, TCP ows can be optimally controlled in routers by so-called index policies. We have implemented index policies in Network Simulator-3 (NS-3) and compared its performance with DropTail and RED buffers. The simulation results show that the index policy has several desirable properties with respect to fairness and efficiency.