Geometry of information propagation in massively dense ad hoc networks

Using the fact that effective wireless range decraise in inverse function of local traffic density, we show that a variable traffic density impacts the curvature of paths in a dense wireless ad hoc network the same way a variable optical density bends light paths. We set up the general laws that paths must satisfy in presence of traffic flow density. We quantify the effect and we give some example of configurations treated analytically

Magnetworks: how mobility impacts the design of Mobile Networks

In this paper we study the optimal placement and optimal number of active relay nodes through the traffic density in mobile sensor ad-hoc networks. We consider a setting in which a set of mobile sensor sources is creating data and a set of mobile sensor destinations receiving that data. We make the assumption that the network is massively dense, i.e., there are so many sources, destinations, and relay nodes, that it is best to describe the network in terms of macroscopic parameters, such as their spatial density, rather than in terms of microscopic parameters, such as their individual placements. We focus on a particular physical layer model that is characterized by the following assumptions: i) the nodes must only transport the data from the sources to the destinations, and do not need to sense the data at the sources, or deliver them at the destinations once the data arrive at their physical locations, and ii) the nodes have limited bandwidth available to them, but they use it optimally to locally achieve the network capacity. In this setting, the optimal distribution of nodes induces a traffic density that resembles the electric displacement that will be created if we substitute the sources and destinations with positive and negative charges respectively. The analogy between the two settings is very tight and have a direct interpretation in wireless sensor networks

Continuum Equilibria and Global Optimization for Routing in Dense Static Ad Hoc Networks

We consider massively dense ad hoc networks and study their continuum limits as the node density increases and as the graph providing the available routes becomes a continuous area with location and congestion dependent costs. We study both the global optimal solution as well as the non-cooperative routing problem among a large population of users where each user seeks a path from its origin to its destination so as to minimize its individual cost. Finally, we seek for a (continuum version of the) Wardrop equilibrium. We first show how to derive meaningful cost models as a function of the scaling properties of the capacity of the network and of the density of nodes. We present various solution methodologies for the problem: (1) the viscosity solution of the Hamilton-Jacobi-Bellman equation, for the global optimization problem, (2) a method based on Green's Theorem for the least cost problem of an individual, and (3) a solution of the Wardrop equilibrium problem using a transformation into an equivalent global optimization problem

Continuum Equilibria for Routing in Dense Ad-hoc Networks

International audienceWe consider massively dense ad-hoc networks and study their continuum limits as the node density increases and as the graph providing the available routes becomes a continuous area with location and congestion dependent costs. We study both the global optimal solution as well as the non-cooperative routing problem among a large population of users. Each user seeks a path from its source to its destination so as to minimize its individual cost. We seek for a (continuum version of the) Wardrop equilibrium. We first show how to derive meaningful cost models as a function of the scaling properties of the capacity of the network as a function of the density of nodes. We present various solution methodologies for the problem: (1) the viscosity solution of the Hamilton-Jacobi-Bellman equation, (2) a transformation into an equivalent global optimization problem that is obtained by identifying some potential related to the costs. We finally study the problem in which the routing decisions are taken by a finite number of competing service providers

Reliable multi-hop routing with cooperative transmissions in energy-constrained networks

We present a novel approach in characterizing the optimal reliable multi-hop virtual multiple-input single-output (vMISO) routing in ad hoc networks. Under a high node density regime, we determine the optimal cardinality of the cooperation sets at each hop on a path minimizing the total energy cost per transmitted bit. Optimal cooperating set cardinality curves are derived, and they can be used to determine the optimal routing strategy based on the required reliability, transmission power, and path loss coefficient. We design a new greedy geographical routing algorithm suitable for vMISO transmissions, and demonstrate the applicability of our results for more general networks

Methodologies for Analyzing Equilibria in Wireless Games

Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where rational entities interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure such states at which the network will effectively operate. In this article, we provide non-exhaustive methodologies for characterizing equilibria in wireless games in terms of existence, uniqueness, selection, and efficiency.Comment: To appear in IEEE Signal Processing Magazine, Sep. 200