Wireless Ad Hoc and Sensor Networks
Wireless Ad Hoc and Sensor Networks Wireless Ad Hoc and Sensor Networks
Optimized Energy and Delay-Based Routing 371p 3p 4p 2 35p 513 n p 1 n 2 2 546p 6s4 5 5n 3n 55 n 46p 7p 85FIGURE 8.6Least-cost spanning tree using the OEDR protocol.protocol for node p 8 . On the other hand, Figure 8.6 shows the least-costspanning tree for node p 8 using the OEDR protocol.To compare the route efficiency of the two protocols, observe the pathfrom the source p 8 to the destination p 3 for both the OLSR and OEDRprotocols. The path using the OLSR protocol is given by p 8 −> n 4 −>s −> n 2 −> p 3 and the cost of the path is: Cost p = ,8, p 6+ 6+ 6+ 4=223according to equation (8.2). On the contrary, the path using the OEDR protocolis p 8 −> n 5 −> s −> n 1 −> p 3 and the cost of the path is: Cost p =8,p 35 + 4 + 4 + 3=16,which is much smaller than the cost using the OLSRprotocol. This clearly shows that the proposed OEDR protocol results ina least cost or optimal cost path from the source to the destination.8.3.5 The OEDR Protocol SummaryThe basic functioning of the OEDR protocol is briefly described in thefollowing steps:1. Neighbor sensing: Each node in the network transmits HELLOpackets to its neighbors. When HELLO packets are received, eachnode updates the information of delay and energy of the linksfrom their neighbors in the neighbor table, along with the energylevel (available energy) of the neighbors.2. Multipoint relay selection: For each node in the network, its neighbortable is used to select the MPR nodes from the one-hop neighborsto reach all the two-hop neighbors with minimum costs,using the MPR selection algorithm given in Section 8.3.3. Topology information declaration: All the nodes in the network thatare selected as MPR nodes transmit TC messages, with energy-delay
372 Wireless Ad Hoc and Sensor Networksinformation of the links from its MPR selectors, and are transmittedto all the nodes in the network through broadcast. Uponreceiving the TC messages, each node in the network records allthe information in the topology table.4. Routing table calculation: Each node in the network proactivelycomputes the routes to all the destination nodes in the networkby using the neighbor table and the topology table of the node.OEDR protocol uses the least-cost spanning tree algorithm tocalculate the optimal routes described in Section 8.3.4, to all thenodes in the network and records the entries in the routing table.Next, the analytical results are given to demonstrate the performanceof the routing scheme.8.4 Optimality Analysis for OEDRTo prove that the proposed OEDR protocol is optimal in all cases, it isessential to analyze the optimality of the MPR selection algorithm andthe optimal route computation algorithm.ASSUMPTION 8.4.1If the one-hop neighbor of a node s has no direct link to at least one of the twohopneighbors of s , then it is not on the optimal path from s to its two-hopneighbors. However, to reach a two-hop neighbor from s through such a node,the path has to go through another one-hop neighbor, which has a direct link tothe two-hop neighbor. This would usually result in more delay and energy beingconsumed than a direct path through the one-hop neighbor, which has a directlink to this two-hop neighbor.THEOREM 8.4.1The MPR selection based on the energy-delay metric and the available energy ofthe RNs will result in an optimal route between any two-hop neighbors.PROOF Consider the following two cases:CASE I When the node in N2 () s has only one neighbor from Ns (), thenthat node in Ns () is selected as an MPR node. In this case, there is onlyone path from the node s to the node in N 2 () s . Hence, the OEDR MPRselection algorithm will select this optimal route between s and the twohopneighbor in N2 (). s
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372 <strong>Wireless</strong> <strong>Ad</strong> <strong>Hoc</strong> <strong>and</strong> <strong>Sensor</strong> <strong>Networks</strong>information of the links from its MPR selectors, <strong>and</strong> are transmittedto all the nodes in the network through broadcast. Uponreceiving the TC messages, each node in the network records allthe information in the topology table.4. Routing table calculation: Each node in the network proactivelycomputes the routes to all the destination nodes in the networkby using the neighbor table <strong>and</strong> the topology table of the node.OEDR protocol uses the least-cost spanning tree algorithm tocalculate the optimal routes described in Section 8.3.4, to all thenodes in the network <strong>and</strong> records the entries in the routing table.Next, the analytical results are given to demonstrate the performanceof the routing scheme.8.4 Optimality Analysis for OEDRTo prove that the proposed OEDR protocol is optimal in all cases, it isessential to analyze the optimality of the MPR selection algorithm <strong>and</strong>the optimal route computation algorithm.ASSUMPTION 8.4.1If the one-hop neighbor of a node s has no direct link to at least one of the twohopneighbors of s , then it is not on the optimal path from s to its two-hopneighbors. However, to reach a two-hop neighbor from s through such a node,the path has to go through another one-hop neighbor, which has a direct link tothe two-hop neighbor. This would usually result in more delay <strong>and</strong> energy beingconsumed than a direct path through the one-hop neighbor, which has a directlink to this two-hop neighbor.THEOREM 8.4.1The MPR selection based on the energy-delay metric <strong>and</strong> the available energy ofthe RNs will result in an optimal route between any two-hop neighbors.PROOF Consider the following two cases:CASE I When the node in N2 () s has only one neighbor from Ns (), thenthat node in Ns () is selected as an MPR node. In this case, there is onlyone path from the node s to the node in N 2 () s . Hence, the OEDR MPRselection algorithm will select this optimal route between s <strong>and</strong> the twohopneighbor in N2 (). s
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