Wireless Ad Hoc and Sensor Networks

94 Wireless Ad Hoc and Sensor Networkssize at the switch x d , is varied along 150, 200, 250, 300, and 350 cells. Celllosses ck ( ) are defined as xk ( ) − x d , when xk ( ) > x d . The CLR is defined asthe total number of cells discarded at the receiver, due to buffer overflows,divided by the total number of cells sent onto the network. The transmissiondelay is defined asTransmission delay = Tc− To,(3.31)where Tcand Todenote the time to complete the transmission by a source,with and without feedback, respectively. Initially, no additional delays areinjected into the feedback, besides the delayed feedback from the simulatordue to congestion, whereas additional delays were injected later toevaluate the performance of the controller, in the event that the feedbackdelays increase due to other uncertainties or hardware.Each source is assumed to possess infinite buffer and the service rateat the buffer is altered as a result of the feedback from the ingress switch.If the virtual source is an ATM switch, then the buffer size is finite and itreceives feedback from other switches. Also, if there is no feedback, thearrival and service rates at the buffer of a source/virtual are equal andthis is referred to as an open-loop scenario. With feedback, the service rateat the buffer of a source or a virtual source is adjusted using the feedback,uk ( ), in Equation 3.19. The service rate at the source will become thearrival rate at the destination. In the case of multiple sources, the feedbackuk ( ) is computed using Equation 3.19 and is divided among thesources fairly using Equation 3.15 to maintain a minimum rate. In oursimulations, several traffic sources were considered. Because the proposedmethodology is compared with thresholding, adaptive ARMAX and onelayerNN-based methods, they are discussed subsequently. The simulationscenario and the results presented along with the parameters are onpar with that of other works (Chang and Chang 1993, Benhamohamedand Meerkov 1993, Jain 1996, Liu and Douligeris 1997, Bonomi et al. 1995).3.3.3.3 Threshold MethodologyIn the threshold-based controller (Liu and Douligeris 1997), a CNC is generatedwhen the ratio of occupied buffer length is greater than a thresholdvalue Q t . Consequently, all sources reduce their transmission rates to 50%from their current rates when a CNC is received. For simplicity, a bufferthreshold value of 40% is selected, similar to the work published by otherresearchers, which implies that we have chosen = 0.4.3.3.3.4 Adaptive ARMAX and One-Layer Neural NetworkIn the adaptive ARMAX method (Jagannathan and Talluri 2000), thetraffic accumulation is given by a linear in the parameter ARMAXQ t