Wireless Ad Hoc and Sensor Networks

82 Wireless Ad Hoc and Sensor Networksconnection is sent back to the source. Tuning laws are provided for theNN weights and closed-loop convergence and stability is proven using aLyapunov-based analysis. It is shown that the controller guarantees thedesired performance, even in the presence of self-similar traffic withbounded uncertainties, without any initial learning phase for the NN.However, by providing offline training to the NN, the QoS is shown toimprove. Here, the objective is to obtain a finite bound on the cell losseswhile reducing the transmission delay, utilizing the available buffer spaceand simultaneously ensuring fairness. Simulation results are provided tojustify the theoretical conclusions during simulated congestion. Thoughthe simulation results and analysis are geared towards ATM, the methodologycan be easily applicable to the Internet in the end-to-end scenario.3.2 BackgroundBackground on the approximation property is presented in the followingsubsection.3.2.1 Neural Networks and Approximation PropertyFor the past several decades, NN-based algorithms have sprung up incomputer science and engineering. This popularity is because the NN-basedschemes possess function approximation and learning capabilities that canbe used readily in several applications. One such application, as describedin this chapter, is to predict the network traffic for congestion control. TheNN-based methods can be broadly categorized based on the learningscheme they employ both offline and online. The offline learning schemesare used to train the NN. Once trained, the NN weights are not updatedand the NN is inserted in the application. Unfortunately, the offline learningscheme pursued using backpropagation algorithm (Jagannathan 2006) isknown to have convergence and weight-initialization problems.The online learning NN scheme proposed in this chapter — though itrequires more real-time computations, relaxes the offline training phase,avoids the weight initialization problems, and performs learning andadaptation simultaneously. This scheme also bypasses the problem ofgathering data for offline training because such data is usually hard tocome by for several applications. However, if similar a priori data is available,one can use the data to train the network offline and use the weightsobtained from the training as initial weights for online training. Overallconvergence and stability is proven for the proposed approach. Once theweights are trained, both offline and online, the weights can be fixed.