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r hi .nodeId. the unique ID of the sending node, that is, i. r hi .coreId. the ID of the core with which i is currently associated. hi .coreId = i NITi (parenti ).coreId if i is a core otherwise
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r hi .hops. the number of hops away from the core. hi .hops = 0 NITi (parenti ).hops + 1 if i is a core otherwise
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r hi .degree. the degree of connectivity (the number of neighbors), set to |NITi |. r hi .nodeStability. the estimated stability of the area surrounding i. This value is calculated from nlffi and gives an approximation of the probability that a certain wireless link between i and its neighbor will not break within the next second. The calculation of this value is explained below. r hi .pathStability. the estimated stability of the path from i to its current core in terms of the probability that this path will still exist within the next second. hi .pathStability= 1 NITi (parenti ).pathStability nodeStabilityi if i is a core otherwise
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To ensure that each node and its neighbors will agree on the same information during the core selection process, all the above values are saved into temporary variables whenever a Hello packet is sent out. Upon receiving a Hello packet, the receiving node updates the corresponding entry in its own NIT. Due to the fact that nodes may move, each entry is also associated with a timestamp recording the time at which it was last updated. When an entry is older than (ALLOWED LOSSES HELLO INTERVAL), it is removed from the table, which also results in a link failure event. Every NLFF TIME WINDOW time period, the number of link failures is used to calculate nlff as shown in (6.1) and (6.2) above. By maintaining nlff, each node i is able to estimate the stability of its surrounding area by calculating nodeStabilityi which expresses the probability that a certain wireless link between i and its neighbor will not break within the next second. Although GPS could be used to obtain more accurate estimation, using GPS may not be suitable in many situations, especially for smaller devices. Without knowing nodes geographical locations (via GPS or any other means) or mobility speeds, nodeStabilityi , which is to be incorporated into each outgoing Hello packet, is calculated as follows. For simplicity, we model the time interval node i will wait before detecting the next link failure by the exponential distribution with the average rate of i failures per second. Therefore, the probability that no link failure will be detected within the next t seconds is e i t . Since nodeStabilityi gives an approximation of the probability that a particular link of i will not break within the next second, if i currently has Ni
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ADAPTIVE DYNAMIC BACKBONE MULTICAST (ADBM)
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neighbors, we have (nodeStabilityi )Ni = e i Therefore, nodeStabilityi = e
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Ni
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(6.3)
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Here, i can be estimated by the actual number of link failures detected per second. Since Ni is actually |NITi |, it follows from (6.1) (6.3) that nodeStabilityi = e nlffi (6.4)
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Notice that the exponential distribution used here to model link failures may not perfectly predict the actual link failure probability. However, as stated earlier, the desired behavior of ADB is to form smaller clusters in more dynamic areas and form larger clusters in more static areas. Although there exist more accurate mechanisms (e.g., reference [11]) to predict link stability, this model serves as an easy-to-calculate indicator (due to the memoryless property of the exponential distribution) effective enough2 for ADB to achieve its objective under different mobility conditions. This has been validated by simulation, as shown in Figure 6.2 for instance. The current implementation of the neighbor discovery process assumes that all links are bidirectional, and there is a separate mechanism in the underlying communication layer that discards all packets coming from unidirectional links. For instance, nodes might also exchange their lists of neighbors periodically. Each node then accepts only Hello packets coming from neighbors whose neighbor lists contain its own ID. Core Selection Process. The core selection process is responsible for extracting a subset of nodes to serve as core nodes and associating other ordinary nodes with these cores. In addition, this process ensures that each ordinary node is within the speci ed number of hops away from its core. Unlike most of existing cluster-head election algorithms, a hop limit is not the only parameter used to determine whether a node is allowed to associate with a certain core. The core selection process also ensures that stability of the path between each ordinary node and its own core satis es a certain constraint. The core selection process at each node begins after the node has started for a certain waiting period, usually long enough to allow the node to have heard Hello packets from all of its neighbors. This process decides whether a node should still be serving as a core, or become a child of an existing core by checking for its own
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2 Our goal is not to have absolute accurate prediction, which may require more complicated computation
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and additional information to be collected. Instead, we would like to have a simple indicator that can differentiate node and path stability in a relative sense.
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