On the convergence of a direct adaptive controller for ATM ABR congestion control

One of the more challenging and yet unresolved issues which is paramount to the success of ATM networks is that of congestion control for available bit rate (ABR) traffic. Unlike other ATM service categories, ABR provides a feedback mechanism, allowing interior nodes to dictate source rates. Previous work has demonstrated how linear adaptive control theory can be utilized to create a stable and efficient control system for the purposes of ATM ABR congestion control. This paper investigates our previously proposed adaptive controller that uses a finite impulse response (FIR) filter to approximately invert the FIR plant. Specifically, convergence issues are addressed in depth. In doing so, a proof is provided for the convergence of the normalized least mean square (NLMS) adaptive algorithm employing a DC tap (drift tap), allowing the proof to extend beyond the (often-assumed) zero-mean case. Using a set of reasonable assumptions, parameter convergence in the mean and mean square is proven. Other issues pertaining to the stability of this controller are presented