arXiv subjects

Alexandre Proutiere

Publications and source records attributed to Alexandre Proutiere.

78 records · Page 5Linked to original sources

arXiv2013

Randomized Consensus with Attractive and Repulsive Links

We study convergence properties of a randomized consensus algorithm over a graph with both attractive and repulsive links. At each time instant, a node is randomly selected to interact with a random neighbor. Depending on if the link between the two nodes belongs to a given subgraph of attractive or repulsive links, the node update follows a standard attractive weighted average or a repulsive weighted average, respectively. The repulsive update has the opposite sign of the standard consensus update. In this way, it counteracts the consensus formation and can be seen as a model of link faults or malicious attacks in a communication network, or the impact of trust and antagonism in a social network. Various probabilistic convergence and divergence conditions are established. A threshold condition for the strength of the repulsive action is given for convergence in expectation: when the repulsive weight crosses this threshold value, the algorithm transits from convergence to divergence. An explicit value of the threshold is derived for classes of attractive and repulsive graphs. The results show that a single repulsive link can sometimes drastically change the behavior of the consensus algorithm. They also explicitly show how the robustness of the consensus algorithm depends on the size and other properties of the graphs.

eess.SY↗

arXiv2013

Optimal Distributed Scheduling in Wireless Networks under the SINR interference model

Radio resource sharing mechanisms are key to ensuring good performance in wireless networks. In their seminal paper \cite{tassiulas1}, Tassiulas and Ephremides introduced the Maximum Weighted Scheduling algorithm, and proved its throughput-optimality. Since then, there have been extensive research efforts to devise distributed implementations of this algorithm. Recently, distributed adaptive CSMA scheduling schemes \cite{jiang08} have been proposed and shown to be optimal, without the need of message passing among transmitters. However their analysis relies on the assumption that interference can be accurately modelled by a simple interference graph. In this paper, we consider the more realistic and challenging SINR interference model. We present {\it the first distributed scheduling algorithms that (i) are optimal under the SINR interference model, and (ii) that do not require any message passing}. They are based on a combination of a simple and efficient power allocation strategy referred to as {\it Power Packing} and randomization techniques. We first devise algorithms that are rate-optimal in the sense that they perform as well as the best centralized scheduling schemes in scenarios where each transmitter is aware of the rate at which it should send packets to the corresponding receiver. We then extend these algorithms so that they reach throughput-optimality.

cs.IT↗

arXiv2012

Distributed Optimization: Convergence Conditions from a Dynamical System Perspective

This paper explores the fundamental properties of distributed minimization of a sum of functions with each function only known to one node, and a pre-specified level of node knowledge and computational capacity. We define the optimization information each node receives from its objective function, the neighboring information each node receives from its neighbors, and the computational capacity each node can take advantage of in controlling its state. It is proven that there exist a neighboring information way and a control law that guarantee global optimal consensus if and only if the solution sets of the local objective functions admit a nonempty intersection set for fixed strongly connected graphs. Then we show that for any tolerated error, we can find a control law that guarantees global optimal consensus within this error for fixed, bidirectional, and connected graphs under mild conditions. For time-varying graphs, we show that optimal consensus can always be achieved as long as the graph is uniformly jointly strongly connected and the nonempty intersection condition holds. The results illustrate that nonempty intersection for the local optimal solution sets is a critical condition for successful distributed optimization for a large class of algorithms.

eess.SY↗

arXiv2009

A particle system in interaction with a rapidly varying environment: Mean field limits and applications

We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of fixed capacity). The transition rate of a particle is determined by its state, by the empirical distribution of all the particles and by a rapidly varying environment. The transitions of the environment are determined by the empirical distribution of the particles. We prove the propagation of chaos on the path space of the particles and establish that the limiting trajectory of the empirical measure of the states of the particles satisfies a deterministic differential equation. This deterministic differential equation involves the time averages of the environment process. We apply our results to analyze the performance of communication networks where users access some resources using random distributed multi-access algorithms. For these networks, we show that the environment process corresponds to a process describing the number of clients in a certain loss network, which allows us provide simple and explicit expressions of the network performance.

math.PR↗

arXiv2009

Convergence and Tradeoff of Utility-Optimal CSMA

It has been recently suggested that in wireless networks, CSMA-based distributed MAC algorithms could achieve optimal utility without any message passing. We present the first proof of convergence of such adaptive CSMA algorithms towards an arbitrarily tight approximation of utility-optimizing schedule. We also briefly discuss the tradeoff between optimality at equilibrium and short-term fairness practically achieved by such algorithms.

cs.IT↗

arXiv2008

Asymptotic stability region of slotted-Aloha

We analyze the stability of standard, buffered, slotted-Aloha systems. Specifically, we consider a set of $N$ users, each equipped with an infinite buffer. Packets arrive into user $i$'s buffer according to some stationary ergodic Markovian process of intensity $λ_i$. At the beginning of each slot, if user $i$ has packets in its buffer, it attempts to transmit a packet with fixed probability $p_i$ over a shared resource / channel. The transmission is successful only when no other user attempts to use the channel. The stability of such systems has been open since their very first analysis in 1979 by Tsybakov and Mikhailov. In this paper, we propose an approximate stability condition, that is provably exact when the number of users $N$ grows large. We provide theoretical evidence and numerical experiments to explain why the proposed approximate stability condition is extremely accurate even for systems with a restricted number of users (even two or three). We finally extend the results to the case of more efficient CSMA systems.

cs.IT↗