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= d(R |pi pt |) t
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where d is the density, R is the transmission range, and pt is the location at time t. Each sensor s movement is decided by the combined force applied to that sensor by all neighboring nodes. A sensor keeps on moving until it travels a distance below a certain threshold at a given time. In some cases, the node can move back and forth between two locations leading to an oscillation. If such oscillation is noticed to occur more than a preset limit, the node stays at the center of gravity of the oscillation points. To validate the performance, the approach is implemented and compared to a simulated annealing-based solution, which provides an optimal coverage. The validation results indicated that the proposed self-spreading approach performs very close to optimal in terms of coverage and delivers a superior performance in terms of the total distance traveled and the time to converge. On-Demand Repositioning of Sensors. Instead of relocating the nodes at the deployment phase, sensor relocation can be used on demand to improve certain performance metrics such as coverage, network lifetime, and so on. This can be decided during the network operation based on the changes in either application-level needs or the network state. For instance, the application can be tracking a fast-moving target that may require repositioning of some sensor nodes based on the new location of the target. Furthermore, in some applications, there can be an increasing number of dysfunctional nodes in a particular part of the area necessitating the redistribution of available sensors. In addition to improving coverage, the energy consumption can be reduced through on-demand relocation of sensors in order to reach the best ef cient topology. The approach presented in reference 47 performs sensor relocation to counter holes in coverage caused by sensors failure. The idea is simply to identify some spare sensors from different parts of the network that can be repositioned in the vicinity of the faulty nodes. The selection of the most appropriate choice among multiple candidate spare nodes is based on the recovery time and overhead imposed. Both criteria would favor close-by spares over distant ones. Minimizing the recovery time can be particularly crucial for delay sensitive applications. The overhead can be in the form of energy consumption due to the node s travel and due to the message exchange, especially if spares are picked in a distributed manner. In order to detect the closest redundant sensor with low message complexity, a grid-based approach is proposed. The region is divided into cells with a designated head for each cell. Each cell head advertises/requests redundant nodes for its cell. A quorum-based solution is proposed
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Choice 1: S3 S1 S0
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Choice 2: S3 S1 S0
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Figure 9.15. Cascaded Movement of Sensors; S3 replaces S2, S2 settles in S1 s position and S1 move to where S0 is.
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to detect the intersection of advertisements and requests within the grid. Once the redundant sensor is located, it is relocated to the desired cell without disrupting the data traf c and affecting the network topology. Since directly moving the node can drain signi cant amount of energy, a cascaded movement is proposed. The idea is to determine intermediate sensor nodes on the path and replace those nodes gradually. That is, the redundant sensor will replace the rst sensor node on the path. That node will also move and replace the second sensor node, and so on. For the example shown in Figure 9.15 (which is redrawn from reference 47), rather than directly moving S3 to the location of S0, in choice 2 all sensors S3 , S2 , and S1 move at the same time and replace S2 , S1, and S0, respectively, in order to minimize the relocation time. The path is selected such that it will minimize the total mechanical movement energy and at the same time maximize the remaining energy of sensor nodes. In order to determine such a path, Dijkstra s least-cost path algorithm is used. The overall solution is also revisited to provide a distributed approach for determining the best cascading schedule. When validated, the approach outperformed VOR of reference 48 with respect to the number of sensors involved in the relocation, the total consumed energy, and the total remaining energy. In addition, cascaded movement delivered much better performance than direct movement in terms of relocation time, energy cost, and remaining energy. However, obviously the cost of maintaining a grid, selection of the cell head and redundant nodes will grow dramatically with the increasing number of nodes. For scalability, a hierarchical solution might be needed to restrict the size of the region and the cost of movements. Coverage improvement was the objective of relocating imaging sensors in reference 57. Stationary cameras may not provide the desired coverage when there
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