Robust stability for sampled-data control systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57857/1/RobStabSampDataSCL1989.pd

Towards Stability Analysis of Data Transport Mechanisms: a Fluid Model and an Application

The Transmission Control Protocol (TCP) utilizes congestion avoidance and control mechanisms as a preventive measure against congestive collapse and as an adaptive measure in the presence of changing network conditions. The set of available congestion control algorithms is diverse, and while many have been studied from empirical and simulation perspectives, there is a notable lack of analytical work for some variants. To gain more insight into the dynamics of these algorithms, we: (1) propose a general modeling scheme consisting of a set of functional differential equations of retarded type (RFDEs) and of the congestion window as a function of time; (2) apply this scheme to TCP Reno and demonstrate its equivalence to a previous, well known model for TCP Reno; (3) show an application of the new framework to the widely-deployed congestion control algorithm TCP CUBIC, for which analytical models are few and limited; and (4) validate the model using simulations. Our modeling framework yields a fluid model for TCP CUBIC. From a theoretical analysis of this model, we discover that TCP CUBIC is locally uniformly asymptotically stable -- a property of the algorithm previously unknown.Comment: IEEE INFOCOM 201

Benchmark problems for robust control design

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76996/1/AIAA-20949-475.pd

Overlay TCP for Multi-Path Routing and Congestion Control

We consider the problem of multi-path routing in the Internet. Currently, Internet routing protocols select only a single path between a source and a destination. However, due to many policy routing decisions, singlepath routing may limit the achievable throughput. In this paper, we envision a scenario where applicationlevel routers are overlaid on the Internet to allow multi-path routing. Using minimal congestion feedback signals from the overlay routers, we present an algorithm that can be implemented at the sources to stably and optimally split the flow between each source-destination pair. We then show that the connection-level throughput region of such a multi-path routing/congestion control scheme can be larger than that of a singlepath congestion control scheme.