Wireless Ad Hoc and Sensor Networks

394 Wireless Ad Hoc and Sensor Networks4. Now, all the nodes that are in range with CH n 4 return RESPONSEpackets. Then CH n 4 makes a list of candidate RNs n 5 , n 8 , n 9 , n 12 ,and n 10 .5. CH n 4 sends the list to CH n 7 . CH n 7 checks if it is in range withany of the nodes in the list.6. Nodes n 9 , n 10, and n 12 are in range with both CH n 4 and n 7 . Theyare selected as the common RNs.7. The link_cost_ factors for n 9 , n 10, and n 12 are calculated.8. The node with the maximum link_cost_ factor value is selected asthe relay node and assigned to Relay(n). In this case, Relay(n)={n 12 }.9. Now node n 12 checks if it is in direct range with the BS, and if itis, then it directly routes the information to the BS.10. Otherwise, n 12 is assigned as the relay node, and all the nodesthat are in range with node n 12 and whose distances to the BS areless than their distances to the BS are taken into consideration.Therefore, nodes n 13 , n 16 , n 19, and n 17 are taken into consideration.11. The link_cost_ factor is calculated for n 13 , n 16 , n 19 , n 14, and n 17 . Thenode with the maximum link_cost_ factor is selected as the nextrelay node. In this case Relay(n) = {n 19 }.12. Next, the relay node n 19 checks if it is in range with the BS. If itis, then it directly routes the information to the BS. In this case,n 19 is in direct range, so the information is sent to the BS directly.8.8.3 Optimality Analysis for OEDSRTo prove that the proposed route created by OEDSR protocol is optimalin all cases, it is essential to show the performance analytically.ASSUMPTION 8.8.1All nodes know the position of the BS irrespective of whether they are mobile ornot. When the BS is mobile, it sends out its location information periodically tothe network. This information is sent using a high-power beacon from the BS toall the nodes in the network.THEOREM 8.8.1The link_cost_ factor based routing generates viable RNs to the BS.PROOF Consider the following two cases:CASE I When the CHs are one hop away from the BS, the CH selectsthe BS directly. In this case, there is only one path from the CH to the BS.Hence, the OEDSR algorithm does not need to be used.