java code 128 reader

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java code 128 reader

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r N is the set of the network nodes: N = {1, , n} r e0 : Initial energy (Joules) of each node r bik : Energy consumption (Joules) at node i N for setting up/releasing routes when the sink moves to site k S r cik : Power consumption (Watts) for receiving and transmitting packets at node i N when the sink sojourns at site k S r tmin : Mandatory minimum time (seconds) for which the sink is required to stay at site k S r djk : Euclidean or shortest path distance (meters) between any two sink sites j, k S r dmax : Maximum distance (meters) the sink is allowed to travel each time it moves.

java code 128 reader

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java code 128 reader

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(2.4)

r A: The set of directed edges joining sink sites whose distance is less than or equal to dmax , that is, A = {(j, k) S S : j = k, djk dMAX } / r O: The set of directed edges (0, k), k S, joining a ctitious site 0 (origin) with the sites in S r D: The set of directed edges (k, q + 1), k S, joining the sites in S with a ctitious site q + 1 ( nal destination) r X: The union of A, O, and D The following variables are also considered: r tk : Sojourning time (seconds) of the sink at site k S r zk : Binary variable taking the value 1 if the sink sojourns at site k S (tk > 0); 0 otherwise (tk = 0).

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java code 128 reader

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where N(u) is the set of nodes which are neighbors of u. The relaxation equations imply that nonperimeter nodes having perimeter nodes among their neighbors will tend to move toward perimeter nodes that are closest to them in terms of the number of hops. Perimeter Nodes Are Known. In this second case an algorithm is designed that does not use the fact that perimeter nodes know their exact geographic location. This is done by prefacing the previous relaxation method with a phase where perimeter nodes compute their own approximate virtual coordinates. The algorithm is in three steps. In the rst step, each perimeter node broadcasts a hello message to the entire network so as to discover its relative position (distances in hops) to all other perimeter nodes in the network: Call h(u, v) this distance measured in number of hops between perimeter nodes. In the second step, perimeter nodes broadcast their perimeter vector (i.e., vector of these distances to all other perimeter nodes) to the entire network. Finally, in the third step, every perimeter node uses a triangulation algorithm to compute the coordinates of all other perimeter nodes (including its own coordinates). Coordinates are chosen so as to minimize (h(u, v) d(u, v))2

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r xjk : Binary variable indicating the status of (j, k) X xjk = 1 if and only if arc (j, k) is on the sink movement route; xjk = 0 otherwise r vk : Auxiliary variable used to enforce a unique sink route The MILP formulation is de ned by the following objective function and constraints Max.

(10.1) bik zk e0 (i N) (10.2) (10.3) (10.4)

where d(u, v) represents the Euclidean distance between the virtual coordinates of nodes u and v. Since at the end of the third step perimeter nodes know their own virtual coordinates, nonperimeter nodes can use the previous relaxation algorithm in order to compute their own virtual coordinates. An important point raised by Ratnasamy et al. [13] is that message loss and node failure can cause perimeter nodes to have incomplete knowledge of the interperimeter distances and cause different perimeter nodes compute inconsistent coordinates. To address this problem, they use two designated bootstrapping beacons that ood the network with hello messages in order to canonicalize the computation and make all nodes performing it arrive at the same solution. Without Location Information. In this third case, the assumption that perimeter nodes know they are on the perimeter is relaxed. A preparatory stage is added to the previous algorithm where a subset of nodes identify themselves as perimeter nodes. This is achieved by leveraging one of the bootstrap beacon nodes described before. Since these bootstrap nodes broadcast hello messages to the entire network, every node discovers its distance (in number of hops) to these bootstrap nodes. To decide if they are perimeter nodes, respective nodes use the perimeter node criterion:

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java code 128 reader

java code 128 reader

java code 128 reader

java code 128 reader

java code 128 reader

java code 128 reader

java code 128 reader

java code 128 reader

java code 128 reader

java code 128 reader

java code 128 reader

java code 128 reader