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friendly and accessible environments Random sensor distribution is generally considered in remote or inhospitable areas, or when a fast deployment of a large amount of sensors is desirable We will consider only random placement in this chapter An example of deterministic placement is considered in ref [45], where the authors proposed path exposure (the likelihood of detecting a target traversing the region using a given path) as the measure of goodness of the sensors that are deployed to perform collaborative target detection A centralized algorithm for placing sensors at selected locations to minimize path exposure is described in ref [45] In most articles in the literature, all sensing radii are equal, while a few articles consider coverage with different sensing radii We will consider only the case of equal sensing radii at each node, since there is limited research done for the case of adjustable ranges [46,47].

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Wu and Yang [47] considered the cases where each sensor is able to select one of two or three adjustable ranges, with the goal of minimizing the overlapped sensing area, extending results from ref [48] There are also several variants regarding the relation between sensing and transmission ranges One common assumption is that sensing radius and communication radius are equal [28] However, some physical measurements indicate that the communication range is normally larger than the reliable sensing range This has implications on the selection of sensors for coverage, and also on the performance of other relevant protocols For example, Xing, Lu, Pless, and Huang [49] show that greedy routing always works when the communication range is twice or more the sensing range, and the area is covered and convex They also consider restricting greedy routing to nodes whose Voronoi regions intersect the source destination line.

Figure 11-26

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Most literature uses the unit-disk graph model for sensing, which is similar to the unit-disk graph model used for communication In this model, the sensor is able to monitor an event if and only if the distance from the sensor to the event is at most S, where S is its sensing radius However, a closer look at the physical layer reveals that sensing ability decreases with distance Instead of the unit-disk graph model, it is more realistic to use a model where the probability of sensing an event depends on the distance from the sensor to that event Liu and Towsley [50] approached the coverage problem from a theoretical perspective and explored the fundamental limits of the coverage of a large-scale sensor network Zhang and Hou [51] studied the fundamental limits of sensor network lifetime that all algorithms can possibly achieve.