Congestion Control in Networks with Dynamic Flows

Congestion control in wireline networks has been studied extensively since the seminal work by Mazumdar et al in 1998. It is well known that this global optimization problem can be implemented in a distributed manner. Stability and fairness are two main design objectives of congestion control mechanisms. Most literatures make the assumption that the number of flows is fixed in the network and each flow has infinite backlog for transfer in developing congestion control schemes. However, this assumption may not hold in reality. Thus, there is a need to study congestion control algorithm in the presence of dynamic flows. It is only until recently that short-lived flows have been taken into account. In this thesis, we study utility maximization problems for networks with dynamic flows. In particular, we consider the case where each class of flows arrives according to a Poisson process and has a length given by a certain distribution. The goal is to maximize the long-term expected system utility, which is a function of the number of flows and the rate (identical within a given class) allocated to each flow. Our investigation shows that, as long as the average work brought by the arrival processes is strictly within the network stability region, the fairness and stability issues are independent. While stability can be guaranteed by, for example, a FIFO policy, utility maximization becomes an unconstrained optimization. We also provide a queueing interpretation of this seemingly surprising result and show that not all utility functions make sense under dynamic flows. Finally, we use simulation results to show that our algorithm indeed maximizes the expected system utility

On resilient control of dynamical flow networks

Resilience has become a key aspect in the design of contemporary infrastructure networks. This comes as a result of ever-increasing loads, limited physical capacity, and fast-growing levels of interconnectedness and complexity due to the recent technological advancements. The problem has motivated a considerable amount of research within the last few years, particularly focused on the dynamical aspects of network flows, complementing more classical static network flow optimization approaches. In this tutorial paper, a class of single-commodity first-order models of dynamical flow networks is considered. A few results recently appeared in the literature and dealing with stability and robustness of dynamical flow networks are gathered and originally presented in a unified framework. In particular, (differential) stability properties of monotone dynamical flow networks are treated in some detail, and the notion of margin of resilience is introduced as a quantitative measure of their robustness. While emphasizing methodological aspects -- including structural properties, such as monotonicity, that enable tractability and scalability -- over the specific applications, connections to well-established road traffic flow models are made.Comment: accepted for publication in Annual Reviews in Control, 201

Method And System For Dynamic Stochastic Optimal Electric Power Flow Control

A dynamic stochastic optimal power flow (DSOPF) control system is described for performing multi-objective optimal control capability in complex electrical power systems. The DSOPF system and method replaces the traditional adaptive critic designs (ACDs) and secondary voltage control, and provides a coordinated AC power flow control solution to the smart grid operation in an environment with high short-term uncertainty and variability. The DSOPF system and method is used to provide nonlinear optimal control, where the control objective is explicitly formulated to incorporate power system economy, stability and security considerations. The system and method dynamically drives a power system to its optimal operating point by continuously adjusting the steady-state set points sent by a traditional optimal power flow algorithm.Clemson UniversityGeorgia Tech Research CorporationThe Curators Of The University Of Missour

Convergence Analysis of Mixed Timescale Cross-Layer Stochastic Optimization

This paper considers a cross-layer optimization problem driven by multi-timescale stochastic exogenous processes in wireless communication networks. Due to the hierarchical information structure in a wireless network, a mixed timescale stochastic iterative algorithm is proposed to track the time-varying optimal solution of the cross-layer optimization problem, where the variables are partitioned into short-term controls updated in a faster timescale, and long-term controls updated in a slower timescale. We focus on establishing a convergence analysis framework for such multi-timescale algorithms, which is difficult due to the timescale separation of the algorithm and the time-varying nature of the exogenous processes. To cope with this challenge, we model the algorithm dynamics using stochastic differential equations (SDEs) and show that the study of the algorithm convergence is equivalent to the study of the stochastic stability of a virtual stochastic dynamic system (VSDS). Leveraging the techniques of Lyapunov stability, we derive a sufficient condition for the algorithm stability and a tracking error bound in terms of the parameters of the multi-timescale exogenous processes. Based on these results, an adaptive compensation algorithm is proposed to enhance the tracking performance. Finally, we illustrate the framework by an application example in wireless heterogeneous network

FAST TCP: Motivation, Architecture, Algorithms, Performance

We describe FAST TCP, a new TCP congestion control algorithm for high-speed long-latency networks, from design to implementation. We highlight the approach taken by FAST TCP to address the four difficulties which the current TCP implementation has at large windows. We describe the architecture and summarize some of the algorithms implemented in our prototype. We characterize its equilibrium and stability properties. We evaluate it experimentally in terms of throughput, fairness, stability, and responsiveness