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In this paper, we consider the simultaneous connectivity of primary and secondary networks forming a cognitive model. It is assumed that the cognitive model includes guard zones that prevent the nodes of the secondary network from being active in the vicinity of primary nodes to limit interference. Under these assumptions, we characterize the region of densities, the transmission radii of the nodes in each of the networks, and the guard zones for which the two networks have a unique unbounded connected component. We prove that this model is feasible, that is, there exists simultaneous connectivity with the unique unbounded connected component in each of the networks. We also provide necessary and sufficient conditions for the simultaneous connectivity of this cognitive model. [ABSTRACT FROM AUTHOR]

An achievable bit rate per source-destination pair in a wireless network of n randomly located nodes is determined adopting the scaling limit approach of statistical physics. It is shown that randomly scattered nodes can achieve, with high probability, the same 1/√n transmission rate of arbitrarily located nodes. This contrasts with previous results suggesting that a 1/ √n log n reduced rate is the price to pay for the randomness due to the location of the nodes. The network operation strategy to achieve the result corresponds to the transition region between order and disorder of an underlying percolation model. If nodes are allowed to transmit over large distances, then paths of connected nodes that cross the entire network area can be easily found, but these generate excessive interference. If nodes transmit over short distances, then such crossing paths do not exist. Percolation theory ensures that crossing paths form in the transition region between these two extreme scenarios. Nodes along these paths are used as a backbone, relaying data for other nodes, and can transport the total amount of information generated by all the sources. A lower bound on the achievable bit rate is then obtained by performing pairwise coding and decoding at each hop along the paths, and using a time division multiple access scheme. [ABSTRACT FROM AUTHOR]

A network of nodes in which pairs communicate over a shared wireless medium is analyzed. We consider the maximum total aggregate traffic flow possible as given by the number of users multiplied by their data rate. The model in this paper differs substantially from the many existing approaches in that the channel connections in this network are entirely random: rather than being governed by geometry and a decay-versus-distance law, the strengths of the connections between nodes are drawn independently from a common distribution. Such a model is appropriate for environments where the first-order effect that governs the signal strength at a receiving node is a random event (such as the existence of an obstacle), rather than the distance from the transmitter. It is shown that the aggregate traffic flow as a function of the number of nodes n is a strong function of the channel distribution. In particular, for certain distributions the aggregate traffic flow is at least (Multiple line equation(s) cannot be represented in ASCII text) for some d > O, which is significantly larger than the O(√n) results obtained for many geometric models. The results provide guidelines for the connectivity that is needed for large aggregate traffic. The relation between the proposed model and existing distance-based models is shown in some cases. [ABSTRACT FROM AUTHOR]

This correspondence considers networks where nodes are connected randomly and can fail at random times. It provides scaling laws that allow to find the critical time at which isolated nodes begin to appear in the system as its size tends to infinity. Applications are in the areas of sensor and ad-hoc networks where nodes are subject to battery drainage and ‘blind spots’ formation becomes a primary concern. The techniques adopted are based on the Chen-Stein method of Poisson approximation, which allows to obtain elegant derivations that are shown to improve upon and simplify previous related results that appeared in the literature. Since blind spots are strongly related to full connectivity, we also obtain some scaling results about the latter. [ABSTRACT FROM AUTHOR]

There has been significant recent interest within the networking research community to characterize the impact of mobility on the capacity and delay in mobile ad hoc networks. In this correspondence, the fundamental tradeoff between the capacity and delay for a mobile ad hoc network under the Brownian motion model is studied. It is shown that the two-hop relaying scheme proposed by Grossglauser and Tse (2001), while capable of achieving a per-node throughput of Θ(1), incurs an expected packet delay of Ω(log n/σn²), where σn² is the variance parameter of the Brownian motion model. It is then shown that an attempt to reduce the delay beyond this value results in the throughput dropping to its value under static settings. In particular, it is shown that under a large class of scheduling and relaying schemes, if the mean packet delay is O (nα/σn²), for any α < 0, then the per-node throughput must be O(1/√n). This result is in sharp contrast to other results that have recently been reported in the literature. [ABSTRACT FROM AUTHOR]