Wireless Ad Hoc and Sensor Networks

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Distributed Power Control and Rate Adaptation 269provide the desired level of service by selecting an appropriate targetvalue of queue utilization. The proposed DP solution will utilize a burstmode transmission to control an incoming flow rate by varying an admissibleburst size. Though the IEEE 802.11 burst mode transmits a numberof data packets within a single RTS/CTS/DATA/ACK exchange, it limitsthe time a single RTS/CTS/DATA/ACK exchange can last. Thus, themaximum size of a burst is limited by the selected modulation rate.The proposed scheme will be recursively applied at every link thatconnects transmitting and receiving nodes. The rate selection is performedat the receiving node and then transmitted to the receiver, where rateadaptation is performed and a suitable burst size can be selected andapplied. The proposed DP-based scheme uses the DPC algorithm (Zawodniokand Jagannathan 2004) to calculate the transmission power required forthe lowest supported rate. Similar to DPC, the receiving node performsthe necessary calculation as to what modulation rate and what size of aburst should to be used by the transmitting node.The rate adaptation algorithm uses the state equation for the bufferdynamics at the receiving node. To calculate optimal policy, a cost functionis proposed that includes a cost of queuing packets and a cost oftransmitting a given burst of data. The latter is equal to an energyrequired for a transmission of the burst using a selected modulationrate. The solution dictated by the proposed DP policy is subject tosubsequent adjustments, for instance, the selected modulation rate maybe reduced because of the maximum transmission power supported bythe node.The section is organized as follows. First, the state equation is presented.Next, the cost function is introduced and discussed. Subsequently, adynamic programming solution that uses the Riccati equation is presented.Then, supplementary alterations of rate and burst size are discussed.Finally, the implementation essentials are given.6.9.1 Buffer Occupancy State EquationConsider the queue utilization equation given asq( k+ 1) =q( k ) +u( k ) +w ( k)i i i i(6.40)where k= 012 , , ,…, N−1,N is a time instance, with N being the last stepof the DP algorithm, qi( k)is a queue utilization at node i and at timeinstance k; wi( k) , is the outgoing traffic at time k, and ui( k)is the incomingtraffic at time k. The term wi( k)is dictated by the next-hop node (i + 1)and is considered to be a random variable with a known distribution andexpected value. The proposed scheme controls incoming traffic to minimizea cost function presented next.
270 Wireless Ad Hoc and Sensor Networks6.9.2 Cost FunctionThe proposed cost function includes both the cost of queue occupancyand the cost of transmitting a given burst of data. The latter is thenapproximated with a quadratic form to obtain an optimal control law,which can be derived using the standard Riccati equation. Moreover, thissolution is proven to be stable and will converge.6.9.2.1 Queue Occupancy CostConsider a known, ideal queue utilization, q ideal , which renders desiredsystem performance in terms of throughput and delay. The buffer cost insuch a case can be selected as a quadratic function of error between idealand actual queue utilization:2Bq ( ( k )) = γ ⋅( q( k) −qideal )ii(6.41)where g is a scaling factor and qi( k)is the current queue utilization. Insuch a case, the cost of queue utilization is the lowest for qi( k)=qideal, andincreases when the utilization is lower or higher than desired.To get a quadratic cost function as in the Riccatti equation, the statevariable is substituted by transiting queue utilization by a constantq idealx(k)=q(k)qi i − ideal(6.42)Now, the state equation can be rewritten asx ( k+ 1) = x ( k ) +u( k ) +w ( k)i i i i(6.43)and the cost function is expressed asBx ( ( k )) = γ ⋅( x( k))ii2(6.44)The selection of the parameter gamma will influence the convergenceof the queue utilization dynamics to a target value. The bigger the gammaparameter, the more effort (cost) will be spent on converging to the targetqueue utilization and corresponding performance level. However, thiswill render higher cost for transmissions, thus consuming more energythan in the case of a lower gamma.6.9.2.2 Transmission CostThe wireless nodes consume energy to transmit packets. This energy dependson transmission power needed for successful transmission and durationof transmission. The selection of the modulation rate adds complexity tothis term, because duration of transmission will vary with modulation
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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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Distributed Fair Scheduling in Wire
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8Optimized Energy and Delay-Based R
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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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