r ij d ij dij 100 ε r 2If some WSN algorithms are to be investigated and theirs

# R ij d ij dij 100 ε r 2if some wsn algorithms are to

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r i,j = d i,j ± d i,j 100 × ε r (2) If some WSN algorithms are to be investigated and theirs performance compared, they should be tested under the identical conditions. Hence, it is recommended to use the identical set of the networks graphs that should have different topologies (grid, random, L-shape, T-shape), scales (ten nodes up to thousands nodes) and node degrees (8 up to 26 neighbors per node). For the storing of all prepared networks, the struct function can be used. %STORE someName=struct(); someName.network(:,:,1)=network_1; save(’file.mat’,’someName’); %LOAD load file.mat; network_1=someName.network(:,:,1); In the previous paragraph we have mention that range of the node degree should be between 8 and 26. This range was taken from the work of Bettstetter [2] and Xue and Kumar [14]. They investigated the required R radio range and average node degree m (average number of neighbors) to ensure the con- nectivity of network. They stated that network is connected if for every pair of nodes there exists one-hop link or one multi- hop link respective. Results of these works showed that node degree in WSNs considered for probability of the connectivity greater than 0 has range of < 8 , 26 > (see Fig. 1). Thus, this node degree range was implemented into the network models so that for each network size N = 50 , 100 , 400 nodes, ten degrees models were implemented, creating the set of 30 networks with different network size and degrees. This network database together with the demonstration Matlab files can be found in [10]. III. R OUTING IN A D H OC N ETWORK The data routing in wireless sensor network is realized on the links comparison base. The considered links between a sender and a receiver can be compared in terms of the length, link quality or residual energy of the node pairs. Nevertheless, the path with the smallest investigated value is selected as the route for the data delivery. For the discovering of the optimal 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 0 20 40 60 80 100 Average node degree [-] Probability of connectivity [%] Fig. 1. Probability of connected network for 802.15.4 radio range (redrawn from [4]). Algorithm: E=createNbrTable 1: row =1; 2: for all node pairs 3: x =abs( x i - x j ); 4: y =abs( y i - y j ); 5: dist =sqrt( x 2 + y 2 ); 6: if dist i,j < R ; 7: plot([ x i , x j ],[ y i , y j ]; % draw edge 8: E( row ,1)= ID i ; 9: E( row ,2)= ID j ; 10: E( row ,3)= dist i , j ; 11: row + + ; E matrix ID i ID j dist i,j 1 2 15.65 1 3 9.21 1 8 21.54 2 1 15.65 2 8 11.12 . . . . . . . . . Fig. 2. Pseudocode of layout visualization and E matrix definition. E matrix is illustrated bellow code. route between two nodes in the graph data structure, a Matlab implementation of Dijkstra’s algorithm can be used. The Dijkstra’s algorithm is implemented within a grShortPath function that is included in grTheory Matlab toolbox [8]. [dSP,sp i,j ]=grShortPath(E,ID i ,ID j ); The grShortPath function takes a E matrix of neighbors, source i and destination j node as an input arguments. It returns a dSP matrix with the shortest path between all node pairs in the network. Furthermore, it returns an sp vectors with the nodes constituting the shortest path between nodes i, j . The E matrix must have an exact form for the
correct grShortPath algorithm processing. It contains three

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• Fall '18
• Mr. Bhullar
• Wireless sensor network

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