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 parameter 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.
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Ranasinghe, D.N., Gray, W.A., Davidson, A.M. (1995). Stability and Optimality of Continuous Time M-ary Rate Control Mechanisms. In: Raghavan, S.V., Jain, B.N. (eds) Computer Networks, Architecture and Applications. IFIP — The International Federation for Information Processing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-34887-2_3
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DOI: https://doi.org/10.1007/978-0-387-34887-2_3
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