Abate, Alessandro (Univ. of California, at Berkeley), Chen, Minghua (Univ. of California, at Berkeley), Sastry, Shankar (Univ. of California, at Berkeley)

Analysis of an Implementable Application Layer Scheme for Flow Control Over Wireless Networks

Scheduled for presentation during the Mini-Symposium "Control and Estimation in Networks" (TuA08), Tuesday, July 25, 2006, 11:40−12:05, Room I

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 20, 2024

Abstract

This paper deals with the problem of congestion control and packets exchange on a wireless network. The mathematical model of the protocol is inspired by and extends a known fluid flow scheme for the control of congestion on a wired network. The necessity to introduce a specific wireless model is motivated by the presence of channel error; often this error (due to intrinsic noise or channel corruption) is not known exactly. This motivates the approximation of parts of the structure of the model with binary functions, whose switching point can be precisely known. These new discontinuous elements, while in practice greatly simplifying the structure of the algorithm (they carry a single bit of information), complicate the theoretical analysis of its dynamical properties. We therefore approximate them with continuous functions with proper limiting behavior: they thus preserve the simple shape and yield themselves to analysis as well. Given this setup, we then investigate the important issues of existence and uniqueness of the equilibrium for the dynamical system, and of local asymptotic stability. Furthermore, we show that this equilibrium solves a concave net utility optimization problem, of which the classical one for wired networks is a special case. The take away point of this work is that the scheme we propose to handle the traffic on a wireless network is not only innovative and meaningful, but has also the potential to be modified and translated into practical implementation.