Figure 10.2. Sensor nodes, sink sites, and sink movements. in .NET framework

Encode QR Code in .NET framework Figure 10.2. Sensor nodes, sink sites, and sink movements.
Figure 10.2. Sensor nodes, sink sites, and sink movements.
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are organized according to a 5 5 grid. A link between two nodes indicates that those two nodes are neighbors (i.e., they can hear each other s transmissions). A lightercolored link between two sites indicates that the sink can move from one site to the other and vice versa. Because of the sink neighbors problem, the sink moves throughout the network in an attempt to balance the energy consumption among the nodes. A problem that arises is that of how to let the nodes know what is the new position of the sink. To this aim, when the sink arrives at a new site, it broadcasts a packet f to all the network nodes, making them aware of its current site. When a node has a packet to send, it now sends it toward the new site of the sink. Every routing scheme that works with the topological information provided by f , such as geographic or shortest paths-based routing, is a viable routing for data delivery to the sink. The main advantages of routing independence are the following. It guarantees the longest possible network lifetime given the speci c routing. It allows the network users to design or choose the routing algorithm that best meets the WSN application requirements, which go beyond improving network lifetime and may consider other metrics. Every time the sink leaves a site, it again broadcasts a packet to all nodes to communicate that it has moved. Upon receiving this packet, a node stops forwarding data (remaining packets are buffered) and waits to receive a new packet f from the sink, carrying its new location. While the sink is traveling the senser do not transmit and they buffer the packets. The farther the sink travels, the more it takes to get to the new site and the higher the delay suffered by the data. For containing this delay, a new parameter called dMAX is introduced that represents an upper bound on the distance that the sink can travel from a site to the following one. The pair (S, dMAX ) uniquely de nes a graph of sink sites where there is a link between two sites if and only if their (Euclidean) distance is dMAX . Figure 10.2 shows the four sites (darker squares) the sink (the triangle) can reach from its current position. The lighter lines between the sites of Figure 10.2 indicate that the sink can only move horizontally or vertically in the 5 5 grid. In the case of high rate sink mobility and low data traf c, the energy cost for route construction and release can be signi cant. Therefore, this cost should be explicitly taken into account. Finally, in order to evaluate the impact of different sink mobility rates, the parameter tmin is introduced to represent a mandatory minimum time the sink has to sojourn at a site. (High tmin values slow the sink down, while low tmin values allow it to move faster.) The problem we set out to solve here is the following: Determine the starting site and the route for the mobile sink over the graph (S, dmax ), together with the sojourn times tk tmin of the sink at each visited site k S so that network lifetime is maximized. MILP formulation. Here are the sets, the parameters, and the variables used for formalizing the problem. r Let S be the set of sink sites that is, the locations at which the sink may sojourn: S = {1, . . . , q}.
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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. 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). 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
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