Wireless Ad Hoc and Sensor Networks

366 Wireless Ad Hoc and Sensor Networksthe figure. The following steps are followed according to the MPR selectionalgorithm of OEDR:1. Start with an empty MPR set MPR() s of node s : MPR()s = {}2. Nodes p 1 , p 2 , p 4 , and p 5 each have only one neighbor in the one-hopneighbor set Ns (). Add n 1 and n 2 to MPR() s : MPR() s = { n1, n2}3. For each node in N2 () s for which MPR node is not selected ( p 3 ,p 6 , p 7 , and p 8 ), do the following:• For node p 3 , there are two possible paths from s to reach p 3 .MPRFor each of the paths, calculate the MPR costs: C sn , =1,p 34+ 3+ 1 /. 0 5=9; C MPRMPR= 6+ 4+ 1/. 0 2=15. Because C issmaller, select as sn , 2,MPR. p 3sn , 1,p 3n 1 However n 1 is already in the MPRset: MPR() s = { n1, n2}MPR• For node p 6 : CMPRsn , 2,p 6= 6+ 7+ 1/. 02=18; C sn , , p = 5+ 5+ 1/.0 6 =3 6MPR11.67. Because C sn , , p is smaller, select n as MPR and add to3 6 3the MPR set: MPR() s = { n1, n2,n3}MPRMPR• For node p 7 : C sn , 3,p 7 = 5+ 3+ 1/. 0 6=9. 67 ; C sn , , p= 6+ 5+ 1/.0 254 7MPR= 15. Because C sn , , p is smaller, select n as MPR. However,3 7 3 n 3is already in the MPR set: MPR() s = { n1, n2, n3}MPR• For node p 8 : C sn , 4,p 8= 6+ 6+ 1 /. 025 = 16 ; C MPR= 4+ 5+ 1/.0 8 =10.25. Because is smaller, select sn , 5,as p 8MPRC sn , , pn MPR and add to5 85the MPR set: MPR() s = { n , n , n , n }1 2 3 5By following the MPR selection algorithm of the OEDR, the nodesselected as MPRs are n 1 , n 2 , n 3 , and n 5 . In contrast, it can be seen fromFigure 8.1 that the nodes selected as MPRs using the OLSR were n 1 , n 2 ,and n 4 . The following Table 8.1 shows the link costs, calculated accordingto equation (8.1), to reach the two-hop neighbors from s , when the MPRselection is performed, using the OLSR and OEDR protocols:It can be observed from this table that the proposed OEDR protocolsignificantly reduces the cost to reach the two-hop neighbors, when comparedto OLSR. This is achieved by using an efficient MPR selectionalgorithm that considers the energy-delay costs, to select the MPR nodes.TABLE 8.1MPR Selection Algorithm Comparison of OLSR and OEDR ProtocolsCost to Reach the Two-Hop Neighbors (Via the MPR node) According to (1)Protocol p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8OLSR 9 ( n 1 ) 11 ( n 1 ) 15 ( n 2 ) 16 ( n 2 ) 13 ( n 2 ) 18 ( n 2 ) 15 ( n 4 ) 16 ( n 4 )OEDR 9 ( n 1 ) 11 ( n 1 ) 9 ( n 1 ) 16 ( n 2 ) 13 ( n 2 ) 11.67 ( n 3 ) 9.67 ( n 3 ) 10.25 ( )n 5