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Figure 15.1. A smart dust cloud.
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LTP: A HOP-BY-HOP DATA PROPAGATION PROTOCOL
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The notion of multiple sinks that may be static or moving has also been studied in reference 6, where Trianta lloy et al. introduce NanoPeer Words, which are merging notions from Peer-to-Peer Computing and Smart Dust. Furthermore, there is a setup phase of the smart dust network, during which the smart cloud is dropped in the terrain of interest; when using special control messages (which are very short, inexpensive, and transmitted only once), each smart dust particle is provided with the direction of W. By assuming that each smart dust particle has individually a sense of direction and by using these control messages, each particle is aware of the general location of W. 15.2.2 The Protocol Let d(pi , pj ) be the distance (along the corresponding vertical lines toward W) of particles pi , and pj , and let d(pi , W) the (vertical) distance of pi from W. Let info(E) be the information about the realization of the crucial event E to be propagated. Let p be the particle sensing the event and starting the execution of the protocol. In this protocol, each particle p that has received info(E) does the following: r Search Phase. It uses a periodic low-energy directional broadcast in order to discover a particle nearer to W than itself (i.e., a particle p where d(p , W) < d(p , W)). r Direct Transmission Phase. Then, p sends info(E) to p . r Backtrack Phase. If consecutive repetitions of the search phase fail to discover a particle nearer to W, then p sends info(E) to the particle from which it originally received the information. Note that one can estimate an a priori upper bound on the number of repetitions of the search phase needed, by calculating the probability of success of each search phase as a function of various parameters (such as density, search angle, and transmission range). This bound can be used to decide when to backtrack. For a graphical representation see Figures 15.2 and 15.3.
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Figure 15.2. Example of the search phase.
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ENERGY-EFFICIENT ALGORITHMS IN WIRELESS SENSOR NETWORKS
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Figure 15.3. Example of a transmission.
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15.2.3 Theoretical Analysis Reference 5 rst provides some basic de nitions. De nition 15.2.1. Let hopt (p, W) be the (optimal) number of hops (direct, vertical to W transmissions) needed to reach the wall, in the ideal case in which particles always exist in pairwise distances R on the vertical line from p to W. Let be a smart dust propagation protocol, using a transmission path of length L( , p, W) to send information about event E to wall W. Let h( , p, W) be the actual number of hops (transmissions) taken to reach W. The hops ef ciency of protocol is the ratio Ch = h( , p, W) hopt (p, W)
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Clearly, the number of hops (transmissions) needed characterizes the energy consumption and the time needed to propagate the information E to the wall. Remark that hopt = d(p, W ) , where d(p, W) is the (vertical) distance of p from the wall W. R In the case where the protocol is randomized, or in the case where the distribution of the particles in the cloud is a random distribution, the number of hops h and the ef ciency ratio Ch are random variables and one wishes to study their expected values. The reason behind these de nitions is that when p (or any intermediate particle in the information propagation to W) looks around for a particle as near to W as possible to pass its information about E, it may not get any particle in the perfect direction of the line vertical to W. This dif culty comes mainly from three causes: (a) Due to the initial spreading of particles of the cloud in the area and because particles do not move, there might not be any particle in that direction. (b) Particles of suf cient remaining battery power may not be currently available in the right direction. (c) Particles may temporarily sleep (i.e., not listen to transmissions) in order to save battery power. Note that any given distribution of particles in the smart dust cloud may not allow the ideal optimal number of hops to be achieved at all. In fact, the least possible
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