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Energy Model with Distance Distribution,” Available at http://grp.pan.uvic.ca/∼yyzhuang/distribution report.pdf, (2009)

by Y Zhuang, J Pan
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Probabilistic Energy Optimization in Wireless Sensor Networks with Variable Size Griding

by Yanyan Zhuang , Jianping Pan
"... Abstract-Due to limited energy supplies, reducing power consumption is an important goal in wireless sensor networks. Clustering techniques are used to reduce power consumption and prolong network lifetime in many existing research efforts, among which grid-based ones are often used due to their si ..."
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Abstract-Due to limited energy supplies, reducing power consumption is an important goal in wireless sensor networks. Clustering techniques are used to reduce power consumption and prolong network lifetime in many existing research efforts, among which grid-based ones are often used due to their simplicity and scalability. However, most existing work uses average distance as a simplification in calculating distance-related power consumption, which leads to a large underestimation of the actual energy depletion rate. In this paper, we propose an energy optimization model based on probabilistic distance distributions, which captures the distance-induced power consumption with high accuracy. We further analyze the uneven traffic distribution in wireless sensor networks and propose a nonuniform griding scheme to balance the energy depletion in all grids. Through our analysis, we are able to obtain the optimal grid size ratio that minimizes the energy consumption. Analytical results are validated through simulation, which shows the promising potentials of our method and the nonuniform griding technique.
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...nce probability density function of the two cases above. The detailed four-step derivation of fD(d) is in [5]. With the same approach, we get the probability density function fDDiag(d) for the diagonal node distance distribution (the case when ( √ 2 − 1) ≤ q ≤ 1/√2 is listed as (4)). Figure 3 shows fDDiag(d) in three cases, where the distances have a range of [0, √ 2(1 + q)]. The curves have a tilted bell shape because the squares diagonal to each other are not of the same size. fDPar(d) for the parallel node distance distribution, when (1 − 1/√2) ≤ q ≤ √2/3, is listed in our technical report [9]. Figure 4 shows three cases of fDPar(d), in which the distance range is [0, √ (1 − q2)2 + q2]. As q gets larger, fDPar(d) gradually changes from a shape similar to a uniform distribution to a tilted bell shape. Apparently, neither fDDiag(d) nor fDPar(d) can be simply approximated by a Gaussian or uniform distribution. IV. PROBABILISTIC ENERGY OPTIMIZATION Energy consumption is an important performance metric for wireless sensor networks, which largely depends on the i=1 i=2 q 1−q i=3 λid λip λip Fig. 5. Many-To-One Traffic Pattern. distance between transceivers. In this section we present our...

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