3 Stability and Optimality of Continuous Time M-ary Rate Control Mechanisms D.N. Ranasinghe, Department of Statistics and Computer Science, University of Colombo, Sri Lanka* W.A. Gray, Department of Computing Mathematics, University of Wales College of Cardiff, United Kingdom. A.M. Davidson, Department of Applied Mathematics, University of Wales College of Cardiff, United Kingdom. Abstract In feedback rate control mechanisms of both rate and window domains, M-ary control class can be considered as an extension of the widely implemented binary control class. In this paper, the stability properties of the class of continuos time M-ary rate controls are analytically established using dynamic theoretic tools. The dynamic behaviour is shown to exhibit a Hopf bifurcation where the stability of the system changes at a critical param- eter value. The uniqueness of the optimal controller is established where the optimality criterion is defined as the convergence rate invariance property. This contrasts with the non unique and mutually exclusive controls of the discrete time M-ary rate control class. As a consequence of the rate-window duality, performance implications of this analysis for a recently proposed window control algorithm of the M-ary form are discussed. One such implication is that, the systemic stability of a partially distributed implementation of the window controller is guaranteed stable. •This research was carried out while the author was at the Department of Computing Mathematics, University of Wales College of Cardiff, and was funded by a British Council TCT award. S. V. Raghavan et al. (eds.), Computer Networks, Architecture and Applications © Springer Science+Business Media Dordrecht 1995