Feedback-based congestion control schemes become an integral part of the connectionless ABR (Available Bit Rate) service class in ATM networks. The major objective of the proposed research is to build a theoretical foundation to feedback congestion control schemes. The basis of the foundation is the fixed-point model, which captures the feed-back feature of ABR congestion control schemes in a system of delay differential equations and produce fixed-point constant solutions in terms of the source cell rates and the buffer lengths. lamely, we consider a broad class of schemes which can produce a stable buffer length even when sources always try to transmit at their maximum rates. Analyses of the fixed point model in the context of ABR feedback control schemes have generated a number of results regarding stabilities of fixed-point solutions. The proposed research will first compare the stability region of parameter space derived from the delay differential equations with that obtained by discrete simulation techniques. We are interested in effects of incorporating details of control protocols in simulation on resulting changes in the stability region. Besides, the fixed point model will be investigated in the environments where ABR bandwidth changes in time as the number of CBR and VBR connections changes. Since the fixed-point model is constructed in a general context, application of the model to several control theoretic strategies (such as a proportional plus derivative control) will be investigated. When a congestion develops (either due to a new active ABR source or due to a reduced ABR bandwidth), buffer lengths increase before they stabilize to a new steady-state buffer length. Since buffer transients are inevitable, we will investigate strategies that can control the buffer transients in a predictable manner. We will first characterize transients in terms of bounds: the maximum overshoot in buffer lengths, the rise time until the buffer length reaches its maximum, and the settling time for the buffer length to reach its new steady-state value. According to the fixed-point model, relationships between the set of parameters and the transient bounds will be investigated. The relationships are to be studied in increasingly complex network configurations.
