We consider the problem of energy-efficient broadcasting on dense ad-hoc networks. Ad-hoc networks are generally modeled using random geometric graphs (RGGs). Here, nodes are deployed uniformly in a square area around the origin, and any two nodes which are within Euclidean distance of 1 are assumed to be able to receive each other’s broadcast. A source node at the origin encodes k data packets of information into n (> k) coded packets and transmits them to all its one-hop neighbors. The encoding is such that, any node that receives at least k out of the n coded packets can retrieve the original k data packets. Every other node in the network follows a probabilistic forwarding protocol; upon reception of a previously unreceived packet, the node forwards it with probability p and does nothing with probability 1 − p. We are interested in the minimum forwarding probability which ensures that a large fraction of nodes can decode the information from the source. We deem this a near-broadcast. The performance metric of interest is the expected total number of transmissions at this minimum forwarding probability, where the expectation is over both the forwarding protocol as well as the realization of the RGG. In comparison to probabilistic forwarding with no coding, our treatment of the problem indicates that, with a judicious choice of n, it is possible to reduce the expected total number of transmissions while ensuring a near-broadcast.

In a sensor network, the points in the operational area that are suitably sensed are a two-dimensional spatial coverage process. For randomly deployed sensor networks, typically, the network coverage of two-dimensional areas is analyzed. However, in many sensor network applications, e.g., tracking of moving objects, the sensing process on paths, rather than in areas, is of interest. With such an application in mind, we analyze the coverage process induced on a one-dimensional path by a sensor network that is modeled as a two-dimensional Boolean model. In the analysis, the sensor locations form a spatial Poisson process of density \lambda and the sensing regions are circles of i.i.d. random radii. We first obtain a strong law for the fraction of a path that is k{\hbox{-}}{\rm sensed}, i.e., sensed by (\geq k) sensors. Asymptotic path-sensing results are obtained under the same limiting regimes as those required for asymptotic coverage by a two-dimensional Boolean model. Interestingly, the asymptotic fraction of the area that is 1-sensed is the same as the fraction of a path that is 1-sensed. For k = 1, we also obtain a central limit theorem that shows that the asymptotics converge at the rate of \Theta(\lambda^{1/2}) for k = 1. For finite networks, the expectation and variance of the fraction of the path that is k{\hbox{-}}{\rm sensed} is obtained. The asymptotics and the finite network results are then used to obtain the critical sensor density to k{\hbox{-}}{\rm sense} a fraction \alpha_{k} of an arbitrary path with very high probability is also obtained. Through simulations, we then analyze the robustness of the model when the sensor deployment is nonhomogeneous and when the paths are not rectilinear. Other path coverage measures like breach, support, "length to first sense,? and sensing continuity measures like holes and clumps are also characterized. Finally, we discuss some generalizations of the results like characterization of the coverage process of m{\hbox{-}}{\rm dimensional} "straight line paths? by n{\hbox{-}}{\rm dimensional}, n > m, sensor networks.

We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.