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...cols have been proposed in order to meet the energy efficiency and scalability requirement of the WSNs. In a WSN, the large part of energy is consumed when the wireless communications are established =-=[10]-=-. With the aim to face this problem, several communication protocols have been proposed. In particular, different techniques were proposed to guarantee transmissions providing efficient energies in Ad...

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... a critical node will potentially bring about a serious protocol failure; whereas distributed algorithms are executed locally with partial nodes, which can prevent any failure caused by a single node =-=[7, 8]-=-. The distributed algorithms have proved to be more robust and scalable than centralized ones. when the sensor nodes are organized efficiently into clusters they consume less energy. The clustering te...

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...ts of a large number of sensor nodes arbitrarily deployed in an unreachable field to give the end-user the ability to instrument, observe, and react to events and phenomena in a specified environment =-=[4, 1]-=-. WSNs have increasingly been used in so many different fields such as military, health, environment and disaster management. Other applications of these sensors ,to name but a few, include habitat ob...

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...epends on the state of the sensors. Consensus problems also called agreement problems, have a long history in the field of computer science, particularly in automata theory and distributed computation=-=[14]-=-. This local interaction gives rise to distributed detection or estimation schemes, more accurate than that of each single sensor and capable of achieving globally optimal decisions, without the need ...

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... a critical node will potentially bring about a serious protocol failure; whereas distributed algorithms are executed locally with partial nodes, which can prevent any failure caused by a single node =-=[7, 8]-=-. The distributed algorithms have proved to be more robust and scalable than centralized ones. when the sensor nodes are organized efficiently into clusters they consume less energy. The clustering te...

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...evertheless, they are sensitive to propagation delays, the noise variance and the energy consumption. Important contributions on consensus algorithms converging on the state can be found in literature=-=[5, 11, 19]-=-. Moreover, when the network size becomes very important, its management becomes more difficult. Using either, the centralized system or the distributed algorithm without fusion center will be complic...

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...finite set of non-overlapping regions having areas in the usual geometric sense are mutually independent, and that the number of points in any region of area A has a Poisson distribution with mean λA =-=[13]-=-. Note that the number of points in a region R depends on its area, but not on its shape or location. The homogeneous Poisson process arises as a limiting two-dimensional point process with respect to...

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...same time, it yields fault tolerance and scalability. There is a substantial amount of theoretical works which explain and clarify the importance of this consensus algorithm than a centralized system =-=[12, 17]-=-. The consensus problem introduced by WSNs can be solved using iterative algorithms. The importance of such algorithms which converge on the state is focussed on their robustness to changes in the net...

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...eneous spatial Poisson processes P P 1 and P P 0 of intensity λ1 = pλ and λ0 = (1 − p)λ respectively. Each non-cluster head joins the cluster of the closest cluster head to form a Voronoi tessellation=-=[16]-=-. The plane is thus divided into zones called the Voronoi cells, each cell corresponding to a P P 1 process point, called its nucleus. If Nv is the random variable denoting the number of PP0 process p...

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...evertheless, they are sensitive to propagation delays, the noise variance and the energy consumption. Important contributions on consensus algorithms converging on the state can be found in literature=-=[5, 11, 19]-=-. Moreover, when the network size becomes very important, its management becomes more difficult. Using either, the centralized system or the distributed algorithm without fusion center will be complic...

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...nce, the value of p given by eq.23 minimizes the energy spent. The other two roots of eq.21 are imaginary. 2.4 Homogeneous Poisson Processes in a Square IF a = b then we have the same results like in =-=[3]-=- 2.5 Homogeneous Poisson Processes in a Circle An other important case is when W0 is the circle of radius r0. Fix the origin and initial line of polar coordinates r and θ so that the origin is the cen...

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...ts of a large number of sensor nodes arbitrarily deployed in an unreachable field to give the end-user the ability to instrument, observe, and react to events and phenomena in a specified environment =-=[4, 1]-=-. WSNs have increasingly been used in so many different fields such as military, health, environment and disaster management. Other applications of these sensors ,to name but a few, include habitat ob...

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...evertheless, they are sensitive to propagation delays, the noise variance and the energy consumption. Important contributions on consensus algorithms converging on the state can be found in literature=-=[5, 11, 19]-=-. Moreover, when the network size becomes very important, its management becomes more difficult. Using either, the centralized system or the distributed algorithm without fusion center will be complic...

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.... Clustering sensors into groups, so that sensors communicate information only to cluster heads and then the cluster heads communicate the aggregated information to the processing center, save energy =-=[8, 18]-=-. Thus, it is advantageous to organize the sensors into clusters; where the data gathered and fused by the sensors is commu1International Journal of Computer Applications (0975 - 8887) Volume 75 - No...

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...∫ a 0 dyy 2 dxx 2 ∫ 1 0 ∫ 1 0 ( 1 3 a3 + 1 3 b3 √ 1 + u 2 du (8) √ 1 + v 2 dv) ) ∫ 1 √ 1 + t2dt 0 3International Journal of Computer Applications (0975 - 8887) Volume 75 - No. 1, Aujust 2013 We have =-=[6]-=-: and E[Nv|N = n] = E[Nv] = λ0 λ1 (14) E[Lv|N = n] = E[Lv] = λ0 2λ 3 2 1 (15) Define C1 to be the total energy used by the sensors in a Voronoi cell to communicate one unit of data to the cluster head...

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...same time, it yields fault tolerance and scalability. There is a substantial amount of theoretical works which explain and clarify the importance of this consensus algorithm than a centralized system =-=[12, 17]-=-. The consensus problem introduced by WSNs can be solved using iterative algorithms. The importance of such algorithms which converge on the state is focussed on their robustness to changes in the net...

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...tribution of bacteria on a slide; d. spatial distribution of defects on a surface or in a volume; e. spatial distribution of oil in a region. 2.2 Definition Spatial Poisson Processes (POINT PROCESSES)=-=[2]-=- Notation: —Let S be a subset of R 2 . (R k ) (Assume S is normalized to have volume 1.) —Let A be the family of all subsets of S. —For AɛA, let |A| denote the size of A. (length, area, volume,...) —L...

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...Other applications of these sensors ,to name but a few, include habitat observing, medical fields, smart offices, spotting chemical or nuclear explosive materials and transportation traffic monitoring=-=[1, 15]-=-. Since they are exposed to atrocious and dynamic environments and limited in their energy level, processing power and sensing ability, WSNs must deliver only processed and concise data. Therefore, an...

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...tial Poisson point processes have been used in many branches of science to model various environmental phenomena. These areas include forestry, technology, geodesy, military applications and many more=-=[20, 9]-=-. a. spatial distribution of stars or galaxies; b. spatial distribution of plants or animals; c. spatial distribution of bacteria on a slide; d. spatial distribution of defects on a surface or in a vo...

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...tial Poisson point processes have been used in many branches of science to model various environmental phenomena. These areas include forestry, technology, geodesy, military applications and many more=-=[20, 9]-=-. a. spatial distribution of stars or galaxies; b. spatial distribution of plants or animals; c. spatial distribution of bacteria on a slide; d. spatial distribution of defects on a surface or in a vo...