Analysis of connectivity for sensor networks using geometrical probability

Jia, W.; Wang, J.

doi:10.1049/ip-com:20045176

Cited by 13 publications

(9 citation statements)

References 5 publications

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“…Since the nodes located close to the physical boundaries of the network have a limited coverage area, they have a greater probability of isolation. Therefore, the boundary effects play an important role in determining the overall network connectivity.Different approaches have been used in the literature, to try to model the boundary effects including (i) using geometrical probability [28] and dividing the square region into smaller subregions to facilitate asymptotic analysis of the transmission range for k-connectivity [9], [22] and to find mean node degree in different subregions [29], (ii) using a cluster expansion approach and decomposing the boundary effects into corners and edges to yield high density approximations [27] and (iii) using a deterministic grid deployment of nodes in a finite area [30] to approximate the boundary effects with random deployment of nodes [25]. The above approaches provide bounds, rather than exact results, for the probability of node isolation and/or probability of connectivity.…”

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confidence: 99%

A Tractable Framework for Exact Probability of Node Isolation and Minimum Node Degree Distribution in Finite Multihop Networks

Khalid

Durrani

Guo

2014

IEEE Trans. Veh. Technol.

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This paper presents a tractable analytical framework for the exact calculation of the probability of node isolation and the minimum node degree distribution when N sensor nodes are independently and uniformly distributed inside a finite square region. The proposed framework can accurately account for the boundary effects by partitioning the square into subregions, based on the transmission range and the node location. We show that for each subregion, the probability that a random node falls inside a disk centered at an arbitrary node located in that subregion can be expressed analytically in closed-form.Using the results for the different subregions, we obtain the exact probability of node isolation and minimum node degree distribution that serves as an upper bound for the probability of k-connectivity.Our theoretical framework is validated by comparison with the simulation results and shows that the minimum node degree distribution serves as a tight upper bound for probability of k-connectivity. The proposed framework provides a very useful tool to accurately account for the boundary effects in the design of finite wireless networks. Index TermsWireless multi-hop networks, sensor networks, probability of node isolation, node degree distribution, probability of connectivity, k-connectivity.Wireless multi-hop networks, also refereed to as wireless sensor networks and wireless ad hoc networks, consist of a group of sensor nodes deployed over a finite region [1]- [5]. The nodes operate in a decentralized manner without the need of any fixed infrastructure, i.e., the nodes communicate with each other via a single-hop wireless path (if they are in range) or via a multi-hop wireless path. In most of the applications, such wireless networks are formed by distributing a finite (small) number of nodes in a finite area, which is typically assumed to be a square region [6]- [9].Connectivity is a basic requirement for the planning and effective operation of wireless multi-hop networks [10], [11]. The k-connectivity is a most general notion of connectivity and an important characteristic of wireless multi-hop networks [9], [12], [13]. The network being k-connected ensures that there exists at least k independent multi-hop paths between any two nodes. In other words, k-connected network would still be 1-connected if (k − 1) nodes forming the network fail. The probability of node isolation, defined as the probability that a randomly selected node has no connections to any other nodes, plays a key role in determining the overall network connectivity (1-connectivity) [12], [14]. The minimum node degree distribution, which is the probability that each node in the network has at least k neighbours, is crucial in determining the k-connectivity of the network [12].For large-scale wireless sensor networks, assuming Poisson distributed nodes in an infinite area, the connectivity properties such as probability of isolation, average node degree, k-connectivity have been well studied [12], [15]- [21]. When the node locations follow an inf...

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confidence: 99%

A Tractable Framework for Exact Probability of Node Isolation and Minimum Node Degree Distribution in Finite Multihop Networks

Khalid

Durrani

Guo

2014

IEEE Trans. Veh. Technol.

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“…with K 1 independent of the transmit power P T . Correction terms to (6) can be shown to be O( min(C,1) ) but are omitted for the sake of brevity. Note that for m = n = 1 it follows that M i ≈ ω η(℘β) C Γ(C).…”

Section: Connectivity Mass and Scaling Lawsmentioning

confidence: 99%

Connectivity Scaling Laws in Wireless Networks

Coon

Georgiou

Dettmann

2015

IEEE Wireless Commun. Lett.

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Abstract-We present scaling laws that dictate both local and global connectivity properties of bounded wireless networks. These laws are defined with respect to the key system parameters of per-node transmit power and the number of antennas exploited for diversity coding and/or beamforming at each node. We demonstrate that the local probability of connectivity scales like O(z C ) in these parameters, where C is the ratio of the dimension of the network domain to the path loss exponent, thus enabling efficient boundary effect mitigation and network topology control.

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“… The nodes are able to regulate their transition power nodes according to their distance to the desired recipient. This is essential to ensure the network integrity [9].…”

Section: System and Model Energymentioning

confidence: 99%

Optimization of Energy Consumption in Clustered Nodes of WSN Using the Black Hole Algorithm

2014

Int. j. comput. netw. commun. secur.

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Nowadays due to the low cost and easy communication, Wireless Sensor Networks (WSN) have many uses for supervisory activities in a variety of environments. The limitation of the energy available in the nodes of the networks is the main problem that affects the survival of the network. Studies have shown that with the creation of control on the number and location of the cluster heads on, the efficiency of energy can increase which results in increase of the life of the network. However, due to the dynamic nature of the issue and due to continuous changes in cluster heads in any of the network activity, this issue is not applicable to classical methods of modeling. In this study using black hole algorithm (BHA), we determine the number and location of the cluster heads to the best optimization. Fitting the criterion will be based on the minimum consumed energy of each node in the network in every data transmission operation period that will be led to the creation of a balance in energy consumption of cluster heads and consequently longer life of network.

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Analysis of connectivity for sensor networks using geometrical probability

Cited by 13 publications

References 5 publications

A Tractable Framework for Exact Probability of Node Isolation and Minimum Node Degree Distribution in Finite Multihop Networks

A Tractable Framework for Exact Probability of Node Isolation and Minimum Node Degree Distribution in Finite Multihop Networks

Connectivity Scaling Laws in Wireless Networks

Optimization of Energy Consumption in Clustered Nodes of WSN Using the Black Hole Algorithm

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