Wireless Ad Hoc and Sensor Networks

Congestion Control in ATM Networks and the Internet 93Z −1Z −1Z −1Z −1X(k − 5)X(k − 4)X(k − 3)X(k − 2)X(k − 1)V TW TZ −1 ˆ ( )InputX(k)Purelin Tansig PurelinFIGURE 3.4Two-layer neural network architecture for traffic approximation.is a scalar value, which gives the approximated value of the traffic at eachswitch. The size of the weight matrix for Vk is 6 by 6 and for Wk ˆ ( ) it isa 6 by 1 vector at each switch. The activation function, φ(), ⋅ used in theinput and the output layers at each node is linear, whereas a tangentsigmoid function is used at each node in the hidden layer. Each switchwill have its own NN congestion controller.The feedback gain, k v , is selected as [0.1 0] T. The initial adaptationgain α, is taken as 0.9 and is updated using the projection algorithm asα ( ) 01 .k =.TThe parameter Γ is chosen to be 0.001 as per the( 01 . + φ( xk ( )) φ( xk ( )))requirement, and the buffer occupancy is considered empty initially. Theinitial weights are all chosen as zero for the case of NN with no offlinetraining. Here, one can select any initial values for the weights. In this paper,a comparison is shown between NN, with and without a training phase.Using 4000 frames of data, which is randomly chosen from a Star Warsmovie, the NN is trained by the well-known backpropagation algorithm(Jagannathan 2006). We saved the weights after training and deployedthem as initial weights for the online training. The weight-tuning updatesderived therein were deployed for online training. The network modeland the traffic sources used in this work are discussed next.3.3.3.2 Network Model and Performance MetricsThe network model used in simulations is similar to that shown inFigure 3.2 with several ATM switches in tandem. The maximum buffer