Wireless Ad Hoc and Sensor Networks

164 Wireless Ad Hoc and Sensor Networks4.6.1 Adaptive Estimator ModelPrevious six values of buffer occupancy were used as inputs to the NNas a trade-off between approximation and computation. The greater thenumber of past values of buffer occupancy used, the better is the approximation,but large numbers of past values increase the computation, whichin turn not only causes delays at the network switches but also wastesresources. As the number of inputs to the ARMAX model at each switchis 6 and the output is a single value, the parameter vector, Wk ˆ ( ) , is a6 by 1 vector for each switch. The regression vector, φ(.) , will then consistof current and past values of buffer occupancy. The initial adaptationgain, α, is taken as 0.1 and is updated using the projection algorithm as01 .α( k)=T . The buffer occupancy for both the switches is consideredempty, initially. The initial parameter estimates are chosen( 01 . + φ( xk ( )) φ( xk ( )))as ˆ( ) = [0 0 0 0 0 0] T for each switch. However, one can select any initialvalues for the parameters. The parameter-tuning updates derived hereinwere deployed for the simulation. The network model and the trafficsources used in the simulations are discussed next.θ 1x dck4.6.2 Network ModelThe network model used in simulations is similar to that shown inFigure 4.1 and Figure 4.2. For each simulation, the buffer length at theingress node/switch, , is selected to be as small as 10 cells and it isaltered to go as high as 350 cells. Cell losses, ( ), are defined as xk ( )− x dwhen xk ( ) > x d . The CLR is defined as the total number of cells discardedat the destination owing to buffer flows divided by the total number ofcells transmitted. Target cell transfer or transmission delay is the totaltime taken by a source to complete its transmission from its starting point.The transmission delay is defined as Ta− Ti, where T i is the intended timeto transmit the data, and T a is the total actual time needed to transmitthe data. If the source sends its data before its intended time, then anegative value is obtained, indicating that the source has completed itstransmission well before its target time. On the other hand, if a delay isencountered, then it is typically represented by a positive value, implyingthat the sources took longer than their intended time.In the simulations, a two-switch scenario is considered. Four MPEGsources are assumed to be transmitting at Switch 1. The output ofSwitch 1 is connected to Switch 2. In addition, Switch 2 also allows4 MPEG sources. Initially, it is assumed that the physically availablebandwidth at both switches is equal to the PCR of all the sources.Four sources are to be admitted at Switch 1 and four at Switch 2. Inaddition, at 3000 units of time, the output of Switch 1 is admitted atSwitch 2.