Wireless Ad Hoc and Sensor Networks

Congestion Control in ATM Networks and the Internet 87T( k)ek () − ek ( − 1)tkv= [ kv1 k v2 ] , the error vector e1= [() e k ] with ek ( − 1)being theTpast value of buffer occupancy. Then, the closed-loop error in bufferoccupancy system becomes:ek ( + 1) = kek ( ) + f̃( xk ( )) + dk ( ),v(3.12)where the traffic-flow modeling error is given bỹf( x( k)) f( x( k)) fˆ( x ( k ))(3.13)= −ˆ(),The controller presented in Equation 3.10 without the traffic-estimationterm is defined to be a proportional controller, whereas the controllerpresented in Equation 3.11, without the traffic-estimation term, isdefined as a proportional plus derivative traffic controller. In either case,the error in buffer occupancy system expressed in terms of cell losses isdriven by the network traffic flow modeling error and the unknowndisturbances. In this chapter, it is envisioned that by appropriately usingan adaptive NN in discrete-time to provide the traffic estimate, f ⋅ theerror in buffer length, and hence the cell losses and delay can be minimizedand fairness can be ensured. Note, that for an end-to-end congestioncontrol scheme, the nonlinear function f (), ⋅ includes theunknown bottleneck queue and therefore, estimating the nonlinear functionwould help design an efficient controller because the bottleneckqueue level is always unknown. The proposed approach is readily applicableto both hop-by-hop, as well as end-to-end scenarios. A comparisonin terms of QoS, obtained for the multilayered NN with and withoutoffline training is also included.The location of the closed-loop poles in the gain matrix k v,dictates thetrade off between the cell transfer or transmission delay and cell losseswith the buffer utilization (Jagannathan and Talluri 2002). In otherwords, smaller cell losses imply long latency or transmission delay andvice versa. The buffer-length error system expressed in Equation 3.12 isused to focus on selecting discrete-time NN-tuning algorithms that guaranteethe cell losses, ck ( ), by appropriately controlling the buffer-lengtherror ek ( ).For the case of a single source sending traffic onto the network switch,the feedback rate calculated using Equation 3.10 or Equation 3.11 is ascalar variable, whereas if multiple sources are sending traffic, the feedbackrate, uk ( ), has to be shared fairly among the sources. The most widely