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Topology Control in Wireless Ad Hoc and Sensor Networks phần 4

Hình 5.1 Các hiệu ứng biên giới trong RWP các mạng di động: khi một nút được nghỉ ngơi gần biên giới, có khả năng rằng các quỹ đạo đến waypoint tiếp theo đi qua trung tâm của khu vực triển khai (tối khu vực bóng mờ). Trong hình, xác suất mà quỹ đạo của u nút đến waypoint tiếp theo cắt A1 | 56 THE CTR FOR CONNECTIVITY MOBILE NETWORKS u . Ai A 2 Figure 5.1 The border effect in RWP mobile networks when a node is resting close to the border it is likely that the trajectory to the next waypoint crosses the center of the deployment region dark shaded area . In the figure the probability that the trajectory of node u to the next waypoint intersects A1 equals the sum of the areas of A1 and A2 we are assuming R 0 1 2 . resting at a waypoint that is close to the border of R see Figure 5.1 . Since the next waypoint is chosen uniformly at random in R it is very likely that the trajectory connecting node u with its next waypoint will cross the center of R. So the probability of finding a mobile node close to the center of R is higher than the probability of finding the node on the boundary. This means that mobile nodes contribute a nonuniform component to the asymptotic node spatial distribution generated by RWP mobility which we denote by Fm m stands for mobile . On the other hand a node resting at a waypoint contributes a uniform component Fu to the asymptotic RWP distribution since the waypoints are chosen uniformly at random in R. Then the asymptotic node spatial distribution generated by RWP mobility denoted by FRWP is given by FRWP Fm Fu which is nonuniform. The amount of this nonuniformity and hence the intensity of the border effect depends on the relative strength of the two components of FRWP. It is easy to see that a longer pause time strengthens Fu since the nodes remain stationary for a longer time. Conversely Fm is maximal when the pause time is 0 because in this case nodes are constantly moving. The informal argument above is theoretically supported by the following theorem proven in Bettstetter et al. 2003 which derives a very good approximation of FRWP when nodes move in R 0 1 2. Theorem 5.1.1 Bettstetter et al. 2003 The asymptotic spatial density function of a node moving in R 0 1 2 according to the RWP model with pause time tp and velocity v is