Wireless Ad Hoc and Sensor Networks

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Optimized Energy and Delay-Based Routing 375PROOF This statement means that, using a minimum-cost spanning tree,a node can compute optimal routes to all the destinations in the network.In OEDR, each node knows the links between the MPR nodes and theirselectors, along with the costs of the links between them, from the TCmessages. According to Lemma 1, the intermediate nodes on the optimalpath are selected as MPRs by the previous nodes on the path. As a result,for a given node, the optimal paths to all the destinations are covered bythe network topology known through the MPR nodes. Therefore, the nodecan correctly compute the optimal path for the whole network topology.Theorem 8.4.2 directly follows from Lemma 8.4.1 and Lemma 8.4.2.THEOREM 8.4.2The OEDR protocol results in an optimal-route (the path with the minimumenergy-delay cost) between any source–destination pair.THEOREM 8.4.3For all pairs of nodes s and d, s generating and transmitting a broadcast packet P,d receives a copy of P .PROOF The proof follows on similar lines to (Jacquet et al. 2001). Let kbe the number of hops to d from which a copy of packet P has retransmitted.We shall prove that there exists a minimum k = 1, that is, a onehopneighbor of d eventually forwards the packet.Let n k be the first forwarder at distance k ( k ≥ 2)from d , which hasretransmitted P . There exists a MPR n′ k−1of n k which is at distance k − 1from d . To be convinced, let us imagine a path of length k from n kto d : n k −> n k−1 −> n k−2 −> … −> n 1 −> d and consider for n′ k−1asthe MPR of n k , which covers n k−2(on the optimal route calculated usingOEDR n k−1will be the MPR n′ k−1).Because n′ k−1received a copy of P the first time from n k (the prior transmittersare necessarily two hops away from n′ k−1), n′ k−1will automaticallyforward P : packet P will be retransmitted at distance k − 1 from d andwill reach n k−2 . Similarly, packet P will be retransmitted at distance k − 2,k − 3 , …, 2, 1 until the packet reaches d . Hence, the theorem is proved.8.5 Performance EvaluationThe proposed OEDR algorithm is implemented in the NS-2 simulator asa new routing protocol. Simulations were performed by varying nodemobility and with variable numbers of nodes in the network. The OEDR,OLSR, and AODV routing protocols and IEEE 802.11 MAC protocol areemployed.
376 Wireless Ad Hoc and Sensor NetworksThe average delay of the packets (E2E) is chosen as one of the metricsto evaluate the performance of the protocols. Moreover, the networkthroughput is affected by the decisions of the routing protocol, and thereexists a trade-off between the average delay and the network throughput.Therefore, in an attempt to minimize the average delay, the OEDR protocolmight result in lower network throughput. However, the ratio of throughputto delay (throughput/average delay) is proven to be a more concisemetric that can be used to compare different protocols, according to Jain(1991).The third metric is the energy-delay product, and it is calculated as(total energy used/number of packets received at the destinations) timesthe average delay. Because the OEDR protocol aims at finding the optimalpath with respect to the energy-delay cost of the links, instead of theshortest hops path (like in OLSR), in some cases, it can result in routeswith higher number of hops compared to other routing protocols. Thiscould slightly increase the energy consumption for packet delivery thoughminimizing the overall delay. Therefore, the energy-delay product wouldserve as a more precise metric to compare the performance of differentrouting protocols. The average contention time for a packet at an ad hocnode is calculated as the time interval elapsed between the packet beingready for transmission at the MAC layer to the time when it receives asuccessful CTS message to transmit the packet. The two simulationscenarios are presented next.Example 8.5.1: Varying Node MobilityA network of 100 nodes, randomly distributed in an area of 2000 × 2000 mis simulated by varying the node mobility between 20 and 100 km/h, alongwith the following parameters: simulation time is 100 sec, maximum numberof flows is 50, location of the nodes and the flows are generated randomly,channel bandwidth is 1 Mbps, “two-ray ground” propagation model with a“path-loss exponent” of 4.0 is used, initial energy of each node is 10 J, flowrate is 41 kbps, packet size is 512 B, and the queue limit is 50 packets.According to Figure 8.9, the average E2E delays using the OEDR protocolare much smaller than the delays using the OLSR and AODV protocols,because the proposed OEDR protocol considers the transmission delay ofthe links in the cost function while computing the routes between the sourceand destination. Also, observe that the average packet delays tend toincrease with an increase in node mobility. With the movement of nodes,links get broken (and created) more frequently as the nodes enter and leavethe transmission range of other nodes. Therefore, the routes have to berecomputed dynamically to reflect the changes in network topology.According to Figure 8.10, the throughput/delay values of the OEDRprotocol are always higher than those of OLSR and AODV protocols,
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18. Chaos in Automatic Control, edi
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CRC PressTaylor & Francis Group6000
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Table of Contents1 Background on Ne
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3 Congestion Control in ATM Network
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5.4.2 Distributed Power Controller
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7.3 Adaptive and Distributed Fair S
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9.2.2 Overview.....................
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the number of connections in each l
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y Maheswaran Thiagarajan, and tirel
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2 Wireless Ad Hoc and Sensor Networ
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10 Wireless Ad Hoc and Sensor Netwo
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2BackgroundIn this chapter, we prov
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Background 51u(k)x n (k + 1)x n (k)
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Background 53with x( 0)being the in
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Background 55with tr(.) the matrix
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Background 57nGiven a function ft (
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Background 592.3.2 Lyapunov Stabili
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Background 61as well as Jagannathan
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Background 63The subsequent example
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Background 65Evaluating this along
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Background 67Now, select the feedba
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Background 69is SISL if and only if
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Background 71L 1 (x)L(x, t)L 0 (x)0
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Background 73for some R > 0 such th
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Background 75Evaluating the first d
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Background 77Section 2.4Problem 2.4
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100 Wireless Ad Hoc and Sensor Netw
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4Admission Controller Design for Hi
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Admission Controller Design for Hig
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7Distributed Fair Scheduling in Wir
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Distributed Fair Scheduling in Wire
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9Predictive Congestion Control for
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Predictive Congestion Control for W
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10Adaptive and Probabilistic Power
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Adaptive and Probabilistic Power Co
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