Section: Scientific Foundations

Scientific Foundations

• Modeling and performance analysis of wireless networks. Our main focus was on cellular networks, mobile ad hoc networks (MANETs) and their vehicular variants called VANETs.

  Our main advances about wireless networks have been based on the development of analytical tools for their performance analysis and on new results from network information theory.

  Concerning cellular networks, the main questions bear on coverage and capacity in large CDMA networks when taking intercell interferences and power control into account. Our main focus has been on the design of: 1) a strategy for the densification and parameterization of UMTS and future OFDM networks that is optimized for both voice and data traffic; 2) new self organization and self optimization protocols for cellular networks e.g. for power control, sub-carrier selection, load balancing, etc.

  Concerning MANETs, we investigated MAC layer scheduling algorithms, routing algorithms and power control. The MAC protocols we considered are based on Aloha and CSMA as well as their cognitive radio extensions. We investigated opportunistic routing schemes for MANETs and VANETs. The focus was on cross layer optimizations allowing one to maximize the transport capacity of multihop networks.

• Theory of network dynamics. TREC is pursuing the analysis of network dynamics by algebraic methods. The mathematical tools are those of discrete event dynamical systems: semi-rings, and in particular network calculus, ergodic theory, perfect simulation, stochastic comparison, inverse problems, large deviations, etc. Network calculus gives results on worst-case performance evaluation; ergodic theory is used to assess the stability of discrete event dynamical systems; inverse problem methods are used to estimate some network parameters from external observations and to design network probing strategies.

• The development of stochastic geometry and random geometric graphs tools. Stochastic geometry is a rich branch of applied probability which allows one to quantify random phenomena on the plane or in higher dimension. It is intrinsically related to the theory of point processes and also to random geometric graphs. Our research is centered on the development of a methodology for the analysis, the synthesis, the optimization and the comparison of architectures and protocols to be used in wireless communication networks. The main strength of this method is its capacity for taking into account the specific properties of wireless links, as well as the fundamental question of scalability.

• Combinatorial optimization and analysis of algorithms. In this research direction started in 2007, we build upon our expertise on random trees and graphs and our collaboration with D. Aldous in Berkeley. Sparse graph structures have proved useful in a number of applications from information processing tasks to the modeling of social networks. We obtained new results in this research direction: computation of the asymptotic for the rank of the adjacency matrix of random graphs, computation of the matching number and the b-matching number of large graphs. We also applied our result to design bipartite graph structures for efficient balancing of heterogeneous loads and to analyze the flooding time in random graphs.

• Economics of networks The premise of this relatively new direction of research, developed jointly with Jean Bolot [SPRINT ATL and then TECHNICOLOR] is that economic incentives drive the development and deployment of technology. Such incentives exist if there is a market where suppliers and buyers can meet. In today's Internet, such a market is missing. We started by looking at the general problem of security on Internet from an economic perspective. A new research direction started on the economic value of user localization in wireless networks. This led to an Infocom'11 paper. We also built on our expertise in random graphs to derive new insights concerning diffusion and cascading behavior in random (possibly clustered) networks.