Wireless Ad Hoc and Sensor Networks

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Distributed Fair Scheduling in Wireless Ad Hoc and Sensor Networks 329weights of the flows are chosen as 0.1, 0.075, 0.05, and 0.025, with 4 flowsselecting each of these weights. Observe that the sum of the weights isequal to one. The figure shows that the ADFS algorithm results in fairallocation of bandwidth even when flows have been assigned differentinitial weights.The fairness index ( FI ) (Bennett 1996) is defined asFI =⎛⎜⎝η *∑∑fT ⎞f⎟φ f ⎠f2⎛ T ⎞f⎜ ⎟⎝ φ f ⎠2(7.83)where T f is the throughput of flow f and η is the number of flows.Figure 7.12 displays the FI of networks with different numbers of flows.Note that the fairness indices of ADFS and DFS are close to one, whereasthat of IEEE 802.11 is less than one. This confirms that the proposed ADFSand DFS render fair allocation of bandwidth, whereas IEEE 802.11 doesnot. Delay variations in the network with 64 nodes are presented in10.980.96ADFSDFS802.110.94Fairness index0.920.90.880.860.840.820.80 10 20 30Number of nodes40 50 60FIGURE 7.12Fairness index comparison.
330 Wireless Ad Hoc and Sensor Networks32ADFSDFS802.111Delay variation (sec)0−1−2−3−4 0 20 40 60 80 100 120PacketsFIGURE 7.13Delay variations.Figure 7.13. It can be observed that ADFS results in minimal delay variations,whereas those of DFS and IEEE 802.11 are relatively high. Hugedelay variations can adversely affect the QoS of the network.To evaluate the performance of the proposed algorithm, the networkwith 32 nodes was simulated with different flow rates, such as 200, 250,300, 350, 400, and 500 kbps per flow. Figure 7.14 presents the throughput/weight ratios of 4 randomly selected flows (4, 10, 12, and 26), for the ADFS,DFS, and IEEE 802.11 protocols with different flow rates. The channel getscongested around 300 kbps per flow rate, after which the fairness of theprotocols is evaluated. Observe that using ADFS and DFS protocols, thefour flows get equal throughput/weight ratios after 300 kbps per flow,whereas the throughput/weight ratios of the flows using IEEE 802.11 keepvarying. Although both ADFS and DFS result in fair allocation of bandwidth,notice that the ADFS results in better throughput per flow. The FIof the network is calculated using Equation 7.83. Figure 7.15 presents thefairness indices of the network with different per-flow rates. The fairnessindices of the ADFS and DFS protocols are close to one, showing fairallocation of bandwidth, while those of 802.11 keep decreasing withincrease in per flow rates.The contention time for a packet is calculated as the time from whenthe packet is received by the MAC layer for transmission, to the timewhen it receives a successful CTS message to transmit the packet.
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Wireless Ad Hocand SensorNetworksPr
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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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Optimized Energy and Delay-Based Ro
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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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