Weibo Gong

Bio: Weibo Gong is an academic researcher from University of Massachusetts Amherst. The author has contributed to research in topics: Queueing theory & Queue. The author has an hindex of 38, co-authored 165 publications receiving 10602 citations.

Fluid-based analysis of a network of AQM routers supporting TCP flows with an application to RED

Abstract: In this paper we use jump process driven Stochastic Differential Equations to model the interactions of a set of TCP flows and Active Queue Management routers in a network setting. We show how the SDEs can be transformed into a set of Ordinary Differential Equations which can be easily solved numerically. Our solution methodology scales well to a large number of flows. As an application, we model and solve a system where RED is the AQM policy. Our results show excellent agreement with those of similar networks simulated using the well known ns simulator. Our model enables us to get an in-depth understanding of the RED algorithm. Using the tools developed in this paper, we present a critical analysis of the RED algorithm. We explain the role played by the RED configuration parameters on the behavior of the algorithm in a network. We point out a flaw in the RED averaging mechanism which we believe is a cause of tuning problems for RED. We believe this modeling/solution methodology has a great potential in analyzing and understanding various network congestion control algorithms.

On designing improved controllers for AQM routers supporting TCP flows

Abstract: In this paper we study a previously developed linearized model of TCP and active queue management (AQM). We use classical control system techniques to develop controllers well suited for the application. The controllers are shown to have better theoretical properties than the well known RED controller. We present guidelines for designing stable controllers subject to network parameters like load level propagation delay etc. We also present simple implementation techniques which require a minimal change to RED implementations. The performance of the controllers are verified and compared with RED using ns simulations. The second of our designs, the proportional integral (PI) controller is shown to outperform RED significantly.

A control theoretic analysis of RED

Abstract: We use a previously developed nonlinear dynamic model of TCP to analyze and design active queue management (AQM) control systems using random early detection (RED). First, we linearize the interconnection of TCP and a bottlenecked queue and discuss its feedback properties in terms of network parameters such as link capacity, load and round-trip time. Using this model, we next design an AQM control system using the RED scheme by relating its free parameters such as the low-pass filter break point and loss probability profile to the network parameters. We present guidelines for designing linearly stable systems subject to network parameters like propagation delay and load level. Robustness to variations in system loads is a prime objective. We present no simulations to support our analysis.

Analysis and design of controllers for AQM routers supporting TCP flows

Abstract: In active queue management (AQM), core routers signal transmission control protocol (TCP) sources with the objective of managing queue utilization and delay. It is essentially a feedback control problem. Based on a recently developed dynamic model of TCP congestion-avoidance mode, this paper does three things: 1) it relates key network parameters such as the number of TCP sessions, link capacity and round-trip time to the underlying feedback control problem; 2) it analyzes the present de facto AQM standard: random early detection (RED) and determines that REDs queue-averaging is not beneficial; and 3) it recommends alternative AQM schemes which amount to classical proportional and proportional-integral control. We illustrate our results using ns simulations and demonstrate the practical impact of proportional-integral control on managing queue utilization and delay.

Code red worm propagation modeling and analysis

Abstract: The Code Red worm incident of July 2001 has stimulated activities to model and analyze Internet worm propagation. In this paper we provide a careful analysis of Code Red propagation by accounting for two factors: one is the dynamic countermeasures taken by ISPs and users; the other is the slowed down worm infection rate because Code Red rampant propagation caused congestion and troubles to some routers. Based on the classical epidemic Kermack-Mckendrick model, we derive a general Internet worm model called the two-factor worm model. Simulations and numerical solutions of the two-factor worm model match the observed data of Code Red worm better than previous models do. This model leads to a better understanding and prediction of the scale and speed of Internet worm spreading.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Lévy processes and infinitely divisible distributions

Abstract: Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Feedback Systems: An Introduction for Scientists and Engineers

Abstract: This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl strm and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. strm and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences.Covers the mathematics needed to model, analyze, and design feedback systems Serves as an introductory textbook for students and a self-contained resource for researchers Includes exercises at the end of every chapter Features an electronic solutions manual Offers techniques applicable across a range of disciplines

Adaptive Control

Abstract: This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

A Brief History of Generative Models for Power Law and Lognormal Distributions

Abstract: Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a lognormal distribution. In trying to learn enough about these distributions to settle the question, I found a rich and long history, spanning many fields. Indeed, several recently proposed models from the computer science community have antecedents in work from decades ago. Here, I briefly survey some of this history, focusing on underlying generative models that lead to these distributions. One finding is that lognormal and power law distributions connect quite naturally, and hence, it is not surprising that lognormal distributions have arisen as a possible alternative to power law distributions across many fields.