The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks

In this paper, we analyze the critical transmitting range for connectivity in wireless ad hoc networks. More specifically, we consider the following problem: assume $n$ nodes, each capable of communicating with nodes within a radius of $r$, are randomly and uniformly distributed in a $d$-dimensional region with a side of length $l$; how large must the transmitting range $r$ be to ensure that the resulting network is connected with high probability? First, we consider this problem for stationary networks, and we provide tight upper and lower bounds on the critical transmitting range for one-dimensional networks, and non-tight bounds for two and three-dimensional networks. Due to the presence of the geometric parameter $l$ in the model, our results can be applied to dense {em as well as sparse} ad hoc networks, contrary to existing theoretical results that apply only to dense networks. We also investigate several related questions through extensive simulations. First, we evaluate the relationship between the critical transmitting range and the minimum transmitting range that ensures formation of a connected component containing a large fraction (e.g. 90%) of the nodes. Then, we consider the mobile version of the problem, in which nodes are allowed to move during a time interval and the value of $r$ ensuring connectedness for a given fraction of the interval must be determined. These results yield insight into how mobility affects connectivit

Investigating Upper Bounds on Network Lifetime Extension for Cell-Based Energy Conservation Techniques in Stationary Ad Hoc Networks

Cooperative cell-based strategies have been recently proposed as a technique for extending the lifetime of wireless adhoc networks, while only slightly impacting network performance. The effectiveness of this approach depends heavilyon the node density: the higher it is, the more consistent energy savings can potentially be achieved. However, nogeneral analyses of network lifetime have been done either for a base network (one without any energy conservationtechnique) or for one using cooperative energy conservation strategies. In this paper, we investigate the lifetime/densitytradeoff under the hypothesis that nodes are distributed uniformly at random in a given region, and that the traffic isevenly distributed across the network. We also analyze the case where the node density is just sufficient to ensure thatthe network is connected with high probability. This analysis, which is supported by the results of extensive simulations,shows that even in this low density scenario, cell-based strategies can significantly extend network lifetime

Hexatic phase and water-like anomalies in a two-dimensional fluid of particles with a weakly softened core

We study a two-dimensional fluid of particles interacting through a spherically-symmetric and marginally soft two-body repulsion. This model can exist in three different crystal phases, one of them with square symmetry and the other two triangular. We show that, while the triangular solids first melt into a hexatic fluid, the square solid is directly transformed on heating into an isotropic fluid through a first-order transition, with no intermediate tetratic phase. In the low-pressure triangular and square crystals melting is reentrant provided the temperature is not too low, but without the necessity of two competing nearest-neighbor distances over a range of pressures. A whole spectrum of water-like fluid anomalies completes the picture for this model potential.Comment: 26 pages, 14 figures; printed article available at http://link.aip.org/link/?jcp/137/10450

The critical transmitting range for Connectivity in Mobile Packet Radio Networks

It is known that the critical transmitting range for connectivity in stationary packet radio networks is $r=c sqrt{frac{log n}{n}}$, for some constant $c!>!0$, under the assumption that $n$ nodes are uniformly distributed in $R=[0,1]^2$. In this note, we investigate how mobility affects this asymptotic result. We consider the well known random waypoint mobility model, whose asymptotic node spatial distribution has been recently derived. We prove that as long as the spatial distribution has a non-null uniform component, the mobile critical transmitting range differs from the stationary one at most by a constant factor. On the contrary, when the uniform component is null there is an asymptotic gap between the mobile and stationary case, i.e. $r!gg!c sqrt{frac{log n}{n}}$ for any constant $c!>!0$. Hence, the asymptotic behavior of the mobile critical transmitting range depends on the choice of the mobility parameters

An Evaluation of Connectivity in Mobile Wireless Ad Hoc Networks

We consider the following problem for wireless ad hoc networks: assume n nodes, each capable of communicating with nodes within a radius of r, are distributed in a d-dimensional region of side l; how large must the transmitting range r be to ensure that the resulting network is connected? We also consider the mobile version of the problem, in which nodes are allowed to move during a time interval and the value of r ensuring connectedness for a given fraction of the interval must be determined. For the stationary case, we give tight bounds on the relative magnitude of r, n and l yielding a connected graph with high probability in l-dimensional networks, thus solving an open problem. The mobile version of the problem when d=2 is investigated through extensive simulations, which give insight on how mobility affects connectivity and reveal a useful trade-off between communication capability and energy consumption

Topology Control in Wireless ad Hoc and Sensor Networks

Topolgy control is one of the most important techniques used in wireless ad hoc and sensor networks to reduce energy consumption, which is essential to extend the network operational time. The goal of this technique is to control the topology of the graph representing the communication links between network nodes, with the purpose of maintaining some global graph theory (e.g., connectivity) while reducing energy consumption, which is strictly related to the nodes\u27 transmitting range

On the Data Gathering Capacity and Latency in Wireless

In this paper, we investigate the fundamental properties of data gathering in wirelesssensor networks, in terms of both transport capacity and latency. We consider a scenarioin which s(n) out of n total network nodes have to deliver data to a set of d(n) sink nodesat a constant rate f(n; s(n); d(n)). The goal is to characterize the maximum achievablerate, and the latency in data delivery. We present a simple data gathering scheme thatachieves asymptotically optimal data gathering capacity and latency with arbitrary net-work deployments when d(n) = 1, and for most scaling regimes of s(n) and d(n) whend(n) > 1 in case of square grid and random node deployments. Differently from mostprevious work, our results and the presented data gathering scheme do not sacrifice en-ergy efficiency to the need of maximizing capacity and minimizing latency. Finally, weconsider the effects of a simple form of data aggregation on data gathering performance,and show that capacity can be increased of a factor f(n) with respect to the case of nodata aggregation, where f(n) is the node density. To the best of our knowledge, theones presented in this paper are the first results showing that asymptotically optimal datagathering capacity and latency can be achieved in arbitrary networks in an energy efficientway