Wireless Ad Hoc and Sensor Networks
Wireless Ad Hoc and Sensor Networks Wireless Ad Hoc and Sensor Networks
Congestion Control in ATM Networks and the Internet 113where the packet losses are defined because of overflows asck ( ) = max( 0, ek ( )). The dynamics of the buffer can be written in terms ofthe buffer occupancy errors as:ek ( + 1) = Sat [ f( x( k)) − x + Tu( k) + d( k)].pd(3.39)The objective is to select a suitable traffic rate uk ( ), such that the availablebandwidth can be exploited up to its peak packet rate (PPR).3.4.2 End-to-End Congestion Control SchemeDefine the traffic rate input, uk ( ), as1uk ( ) = (T x d − f ( x ( k )) + k v e ( k ))(3.40)where k v is a diagonal gain matrix, f( x( k))is the traffic accumulation atthe bottleneck link/egress buffer, and T is the measurement interval. Then,the error in buffer length system becomesek ( + 1) = Sat[ kek ( ) + dk ( )]pv(3.41)If an adaptive estimator is employed to estimate the bottleneck queueand hence the traffic accumulation, f ˆ(), ⋅ at the destination buffer, then thebuffer-length error is written as:ek ( + 1 ) = Sat[ kek ( ) + fˆ() ⋅ + dk ( )]pv(3.42)Then uk ( ) will be defined as1uk ( ) = (T x d − f ˆ( x ( k )) + k v e ( k ))(3.43)The proposed rate-based methodology uses packet-arrival rate at theingress node and packet-arrival rate at the egress node to estimate thenetwork traffic accumulation or flow. The estimated value and the packetaccumulation at egress node are together used to compute the rate uk ( ) bywhich the source has to reduce or increase its rate. If uk ( ) is a positivevalue, it indicates that the buffer space is available and the sources canincrease their rates, whereas if uk ( ) is negative, it indicates that there are
114 Wireless Ad Hoc and Sensor Networkspacket losses at the egress node and the sources have to decrease theirrates. The updated traffic rate based on uk ( ) minimizes the differencebetween the actual and desired buffer length, while providing fairnessamong all sources. The details of the stability analysis shown in thefollowing section suggests that the error in queue length e(k) is boundedand the packet losses are also bounded and finite for any initial state ofthe network.3.4.2.1 Stability AnalysisLEMMA 3.4.1xThe nonlinear system yk ( + 1) = SatAyk ( ( )), for A ∈R 2 2 , where sat(y) is of theformsat( y ) = 1,> 1i= y , || y ≤ii1(3.44)= − 1, y i
- Page 86 and 87: Background 63The subsequent example
- Page 88 and 89: Background 65Evaluating this along
- Page 90 and 91: Background 67Now, select the feedba
- Page 92 and 93: Background 69is SISL if and only if
- Page 94 and 95: Background 71L 1 (x)L(x, t)L 0 (x)0
- Page 96 and 97: Background 73for some R > 0 such th
- Page 98 and 99: Background 75Evaluating the first d
- Page 100: Background 77Section 2.4Problem 2.4
- Page 103 and 104: 80 Wireless Ad Hoc and Sensor Netwo
- Page 105 and 106: 82 Wireless Ad Hoc and Sensor Netwo
- Page 107 and 108: 84 Wireless Ad Hoc and Sensor Netwo
- Page 109 and 110: 86 Wireless Ad Hoc and Sensor Netwo
- Page 111 and 112: 88 Wireless Ad Hoc and Sensor Netwo
- Page 113 and 114: 90 Wireless Ad Hoc and Sensor Netwo
- Page 115 and 116: 92 Wireless Ad Hoc and Sensor Netwo
- Page 117 and 118: 94 Wireless Ad Hoc and Sensor Netwo
- Page 119 and 120: 96 Wireless Ad Hoc and Sensor Netwo
- Page 121 and 122: 98 Wireless Ad Hoc and Sensor Netwo
- Page 123 and 124: 100 Wireless Ad Hoc and Sensor Netw
- Page 125 and 126: 102 Wireless Ad Hoc and Sensor Netw
- Page 127 and 128: 104 Wireless Ad Hoc and Sensor Netw
- Page 129 and 130: 106 Wireless Ad Hoc and Sensor Netw
- Page 131 and 132: 108 Wireless Ad Hoc and Sensor Netw
- Page 133 and 134: 110 Wireless Ad Hoc and Sensor Netw
- Page 135: 112 Wireless Ad Hoc and Sensor Netw
- Page 139 and 140: 116 Wireless Ad Hoc and Sensor Netw
- Page 141 and 142: 118 Wireless Ad Hoc and Sensor Netw
- Page 143 and 144: 120 Wireless Ad Hoc and Sensor Netw
- Page 145 and 146: 122 Wireless Ad Hoc and Sensor Netw
- Page 147 and 148: 124 Wireless Ad Hoc and Sensor Netw
- Page 149 and 150: 126 Wireless Ad Hoc and Sensor Netw
- Page 151 and 152: 128 Wireless Ad Hoc and Sensor Netw
- Page 153 and 154: 130 Wireless Ad Hoc and Sensor Netw
- Page 155 and 156: 132 Wireless Ad Hoc and Sensor Netw
- Page 157 and 158: 134 Wireless Ad Hoc and Sensor Netw
- Page 159 and 160: 136 Wireless Ad Hoc and Sensor Netw
- Page 161 and 162: 138 Wireless Ad Hoc and Sensor Netw
- Page 163 and 164: 140 Wireless Ad Hoc and Sensor Netw
- Page 165 and 166: 142 Wireless Ad Hoc and Sensor Netw
- Page 167 and 168: 144 Wireless Ad Hoc and Sensor Netw
- Page 170 and 171: 4Admission Controller Design for Hi
- Page 172 and 173: Admission Controller Design for Hig
- Page 174 and 175: Admission Controller Design for Hig
- Page 176 and 177: Admission Controller Design for Hig
- Page 178 and 179: Admission Controller Design for Hig
- Page 180 and 181: Admission Controller Design for Hig
- Page 182 and 183: Admission Controller Design for Hig
- Page 184 and 185: Admission Controller Design for Hig
114 <strong>Wireless</strong> <strong>Ad</strong> <strong>Hoc</strong> <strong>and</strong> <strong>Sensor</strong> <strong>Networks</strong>packet losses at the egress node <strong>and</strong> the sources have to decrease theirrates. The updated traffic rate based on uk ( ) minimizes the differencebetween the actual <strong>and</strong> desired buffer length, while providing fairnessamong all sources. The details of the stability analysis shown in thefollowing section suggests that the error in queue length e(k) is bounded<strong>and</strong> the packet losses are also bounded <strong>and</strong> finite for any initial state ofthe network.3.4.2.1 Stability AnalysisLEMMA 3.4.1xThe nonlinear system yk ( + 1) = SatAyk ( ( )), for A ∈R 2 2 , where sat(y) is of theformsat( y ) = 1,> 1i= y , || y ≤ii1(3.44)= − 1, y i
Change language