Feedback-based flow control of B-ISDN/ATM networks with significant propagation delays

This thesis studies the role of feedback in flow control for ATM networks with significant propagation delays. We consider networks with either a single or two bottleneck nodes.; The single node system consists of multiple, feedback dependent, Markov modulated fluid sources feeding a single bottleneck. The release rates of such sources is determined by the state of the Markov chain as well as feedback from the bottleneck node. This source model allows us to consider both Variable Bit Rate (VBR) and Available Bit Rate (ABR) sources. We assume that the node provides feedback on its congestion levels at regular intervals to all sources. Sources modulate their release rates in response to the delayed feedback. In this context we study systems with different feedback policies: (a) static feedback policies, like binary feedback policy, (b) dynamic feedback policies like additive increase/multiplicative decrease, and (c) binary hysteresis policies. While all sources have the same round-trip delay in these systems, we also study an extension where the different sources may have different delays. We consider a generalized system that allows us to study the above four cases in a unified manner and show the overall system is a piecewise deterministic Markov process (PDP). We show that the stationary distribution of this PDP satisfies a system of ordinary differential equations subject to a set of split boundary conditions and obtain an explicit solution to these differential equations using spectral decomposition. To this end we investigate the related eigenvalue problem. We provide an algorithm to reduce the original eigenvalue problem to multiple smaller eigenvalue problems which can be solved either in closed from or for which efficient numerical algorithms are available. Based on these analytical results we conduct a numerical investigation of the system with static binary feedback, with dynamic feedback, and with heterogeneous propagation delays.; The two node system is an extension of the single node system consisting of two bottleneck nodes and two classes of sources. We show that the two node system can also be characterized as a PDP and its stationary distribution satisfies a system of partial differential equations with a set of boundary conditions.