Search

Wireless communication in a network of mobile devices is a challenging and resource-demanding task, due to the highly dynamic network topology and the wireless channel randomness. This paper investigates information broadcast schemes in 2-D mobile ad hoc networks where nodes are initially randomly distributed and then move following a random direction mobility model. Based on an in-depth analysis of the popular susceptible-infectious-recovered epidemic broadcast scheme, this paper proposes a novel energy and bandwidth-efficient broadcast scheme, named the energy-efficient broadcast scheme, which is able to adapt to fast-changing network topology and channel randomness. Analytical results are provided to characterize the performance of the proposed scheme, including the fraction of nodes that can receive the information and the delay of the information dissemination process. The accuracy of analytical results is verified using simulations driven by both the random direction mobility model and a real-world trace. [ABSTRACT FROM PUBLISHER]

This paper studies networks where all nodes are distributed on a unit square A\buildrel\triangle\over= [- 1\over 2, 1\over 2]^2 following a Poisson distribution with known density \rho and a pair of nodes separated by an Euclidean distance x are directly connected with probability gr\rho(x){\buildrel{\triangle}\over{=}} g(x/r\rho), independent of the event that any other pair of nodes are directly connected. Here, g:[0,\infty)\rightarrow [0,1] satisfies the conditions of rotational invariance, nonincreasing monotonicity, integral boundedness, and g\left (x\right)=o(1/(x^2\log^2x)); further, r\rho=\sqrt {(\log \rho +b)/(C\rho)} where C=\int\Re^{2}g(\left \Vert {\mmb {x}}\right \Vert)d {\mmb {x}} and b is a constant. Denote the aforementioned network by \cal G\left (\cal X\rho,gr\rho,A\right). We show that as \rho \rightarrow \infty, 1) the distribution of the number of isolated nodes in \cal G\left (\cal X\rho,gr\rho,A\right) converges to a Poisson distribution with mean e^-b; 2) asymptotically almost surely (a.a.s.) there is no component in \cal G\left (\cal X\rho,gr\rho,A\right) of fixed and finite order k> 1; c) a.a.s. the number of components with an unbounded order is one. Therefore, as \rho \rightarrow \infty, the network a.a.s. contains a unique unbounded component and isolated nodes only; a sufficient and necessary condition for \cal G\left (\cal X\rho,gr\rho,A\right) to be a.a.s. connected is that there is no isolated node in the network, which occurs when b\rightarrow \infty as \rho \rightarrow \infty. These results expand recent results obtained for connectivity of random geometric graphs from the unit disk model and the fewer results from the log-normal model to the more general and more practical random connection model. [ABSTRACT FROM AUTHOR]

Connectivity and capacity are two fundamental properties of wireless multihop networks. The scalability of these properties has been a primary concern for which asymptotic analysis is a useful tool. Three related but logically distinct network models are often considered in asymptotic analyses, viz. the dense network model, the extended network model, and the infinite network model, which consider respectively a network deployed in a fixed finite area with a sufficiently large node density, a network deployed in a sufficiently large area with a fixed node density, and a network deployed in \Re^2 with a sufficiently large node density. The infinite network model originated from continuum percolation theory and asymptotic results obtained from the infinite network model have often been applied to the dense and extended networks. In this paper, through two case studies related to network connectivity on the expected number of isolated nodes and on the vanishing of components of finite order k>1 respectively, we demonstrate some subtle but important differences between the infinite network model and the dense and extended network models. Therefore, extra scrutiny has to be used in order for the results obtained from the infinite network model to be applicable to the dense and extended network models. Asymptotic results are also obtained on the expected number of isolated nodes, the vanishingly small impact of the boundary effect on the number of isolated nodes, and the vanishing of components of finite order k>1 in the dense and extended network models using a generic random connection model. [ABSTRACT FROM PUBLISHER]

In this paper, we study transmission power to secure the connectivity of a network. Instead of requiring all nodes to be connected, we require that only a large fraction (e.g., 95%) be connected, which is called the giant component. We show that, with this slightly relaxed requirement on connectivity, significant energy savings can be achieved for a large-scale network. In particular, we assume that a total of n nodes are randomly independently uniformly distributed in a unit square in R2, that each node has uniform transmission power, and that any two nodes are directly connected if and only if the power that was received by one node from the other node, as determined by the log-normal shadowing model, is larger than or equal to a given threshold. First, we derive an upper bound on the minimum transmission power at which the probability of having a giant component of order above qn for any fixed q Ȇ (0, 1) tends to one as n →∞. Second, we derive a lower bound on the minimum transmission power at which the probability of having a connected network tends to one as n →∞. We then show that the ratio of the aforementioned transmission power that was required for a giant component to the transmission power that was required for a connected network tends to zero as n →∞. This result implies significant energy savings if we require that only most nodes (e.g., 95%) be connected rather than requiring all nodes to be connected. This result is also applicable for any other arbitrary channel model that satisfies certain intuitively reasonable conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the phase transition behavior of k-connectivity (k = 1,2,…) in wireless multihop networks where a total of n nodes are randomly and independently distributed following a uniform distribution in the unit cube [0, 1]d (d = 1,2,3), and each node has a uniform transmission range r(n). It has been shown that the phase transition of k-connectivity becomes sharper as the total number of nodes n increases. In this paper, we investigate how fast such phase transition happens and derive a generic analytical formula for the phase transition width of k-connectivity for large enough n and for any fixed positive integer k in d-dimensional space by resorting to a Poisson approximation for the node placement. This result also applies to mobile networks where nodes always move randomly and independently. Our simulations show that to achieve a good accuracy, n should be larger than 200 when k = 1 and d = 1; and n should be larger than 600 when k < 3 and d = 2, 3. The results in this paper are important for understanding the phase transition phenomenon; and it also provides valuable insight into the design of wireless multihop networks and the understanding of its characteristics. [ABSTRACT FROM AUTHOR]

Many wireless multi-hop networks are deployed with some infrastructure support. Existing results on ad-hoc networks are inadequate to fully understand the properties of those networks. In this paper, we study the properties of 1-D infrastructure-based multi-hop networks. Specifically, we consider networks with two types of nodes, i.e. ordinary nodes and powerful nodes. Ordinary nodes are i.i.d. and Poissonly distributed in a unit interval. Powerful nodes are arbitrarily distributed within the same unit interval. These powerful nodes are inter-connected via some backbone infrastructure. The network is said to be connected if each ordinary node is connected (possibly through a multi-hop path) to at least one of the powerful nodes. We obtain analytical results for the connectivity probability and the average number of clusters in the network. We also prove for the first time that the optimum powerful node distribution that minimizes the average number of clusters, and maximizes the asymptotic connectivity probability, is to deploy these powerful nodes in an equi-distant fashion. These results are important for the design and deployment of 1-D infrastructure-based networks. [ABSTRACT FROM PUBLISHER]