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289
A Duality Model of TCP and Queue Management Algorithms
- IEEE/ACM Trans. on Networking
, 2002
"... We propose a duality model of congestion control and apply it to understand the equilibrium properties of TCP and active queue management schemes. Congestion control is the interaction of source rates with certain congestion measures at network links. The basic idea is to regard source rates as p ..."
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Cited by 307 (37 self)
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We propose a duality model of congestion control and apply it to understand the equilibrium properties of TCP and active queue management schemes. Congestion control is the interaction of source rates with certain congestion measures at network links. The basic idea is to regard source rates as primal variables and congestion measures as dual variables, and congestion control as a distributed primal-dual algorithm carried out over the Internet to maximize aggregate utility subject to capacity constraints. The primal iteration is carried out by TCP algorithms such as Reno or Vegas, and the dual iteration is carried out by queue management such as DropTail, RED or REM. We present these algorithms and their generalizations, derive their utility functions, and study their interaction.
Feedback Control Real-Time Scheduling: Framework, Modeling, and Algorithms
- Journal of Real-Time Systems, Special Issue on Control-Theoretical Approaches to Real-Time Computing
, 2002
"... This paper presents a feedback control real-time scheduling (FCS) framework for adaptive real-time systems. An advantage of the FCS framework is its use of feedback control theory (rather than ad hoc solutions) as a scientific underpinning. We apply a control theory based methodology to systematical ..."
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Cited by 274 (47 self)
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This paper presents a feedback control real-time scheduling (FCS) framework for adaptive real-time systems. An advantage of the FCS framework is its use of feedback control theory (rather than ad hoc solutions) as a scientific underpinning. We apply a control theory based methodology to systematically design FCS algorithms to satisfy the transient and steady state performance specifications of real-time systems. In particular, we establish dynamic models of real-time systems and develop performance analyses of FCS algorithms, which are major challenges and key steps for the design of control theory based adaptive real-time systems. We also present a FCS architecture that allows plug-ins of different real-time scheduling policies and QoS optimization algorithms. Based on our framework, we identify different categories of real-time applications where different FCS algorithms should be applied. Performance evaluation results demonstrate that our analytically tuned FCS algorithms provide robust transient and steady state performance guarantees for periodic and aperiodic tasks even when the task execution times vary by as much as 100% from the initial estimate.
On Designing Improved Controllers for AQM Routers Supporting TCP Flows
- IN PROCEEDINGS OF IEEE INFOCOM
, 2000
"... In this paper we study a previously developed linearized model of TCP and 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 ..."
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Cited by 270 (16 self)
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In this paper we study a previously developed linearized model of TCP and 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, propogation 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.
Internet Congestion Control.
- IEEE Control Systems Magazine,
, 2002
"... Abstract This article reviews the current TCP congestion control protocols and overviews recent advances that have brought analytical tools to this problem. We describe an optimization-based framework that provides an interpretation of various flow control mechanisms, in particular, the utility bei ..."
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Cited by 194 (25 self)
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Abstract This article reviews the current TCP congestion control protocols and overviews recent advances that have brought analytical tools to this problem. We describe an optimization-based framework that provides an interpretation of various flow control mechanisms, in particular, the utility being optimized by the protocol's equilibrium structure. We also look at the dynamics of TCP and employ linear models to exhibit stability limitations in the predominant TCP versions, despite certain built-in compensations for delay. Finally, we present a new protocol that overcomes these limitations and provides stability in a way that is scalable to arbitrary networks, link capacities, and delays.
Control-Theoretic Techniques and Thermal-RC Modeling for Accurate and Localized Dynamic Thermal Management
, 2001
"... This paper proposes the use of formal feedback control theory as a way to implement adaptive techniques in the processor architecture. Dynamic thermal management (DTM) is used as a test vehicle, and variations of a PID controller (Proportional-Integral-Differential) are developed and tested for adap ..."
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Cited by 169 (16 self)
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This paper proposes the use of formal feedback control theory as a way to implement adaptive techniques in the processor architecture. Dynamic thermal management (DTM) is used as a test vehicle, and variations of a PID controller (Proportional-Integral-Differential) are developed and tested for adaptive control of fetch "toggling." To accurately test the DTM mechanism being proposed, this paper also develops a thermal model based on lumped thermal resistances and thermal capacitances. This model is computationally efficient and tracks temperature at the granularity of individual functional blocks within the processor. Because localized heating occurs much faster than chip-wide heating, some parts of the processor are more likely to be "hot spots" than others.
Analysis and Design of Controllers for AQM Routers Supporting TCP Flows
- IEEE Transactions on Automatic Control
, 2002
"... 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 TCPs congestion-avoidance mode, this paper does t ..."
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Cited by 135 (5 self)
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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 TCPs congestion-avoidance mode, this paper does three things. First, it relates key network parameters such as the number of TCP sessions, link capacity and round-trip time to the underlying feedback control problem. Second, it analyzes the present de facto AQM standard: random early detection (RED) and determines that REDs queue-averaging is not beneficial. Finally, 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.
Scalable Laws for Stable Network Congestion Control
- In Proceedings of Conference on Decision and Control
, 2001
"... This paper discusses flow control in networks, in which sources control their rates based on feedback signals received from the network links, a feature present in current TCP protocols. We develop a congestion control system which is arbitrarily scalable, in the sense that its stability is maintain ..."
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Cited by 115 (26 self)
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This paper discusses flow control in networks, in which sources control their rates based on feedback signals received from the network links, a feature present in current TCP protocols. We develop a congestion control system which is arbitrarily scalable, in the sense that its stability is maintained for arbitrary network topologies and arbitrary amounts of delay. Such a system can be implemented in a decentralized way with information currently available in networks plus a small amount of additional signaling.
Stability criteria for switched and hybrid systems
- SIAM Review
, 2007
"... The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities, an ..."
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Cited by 114 (8 self)
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The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities, and to review some problems that remain open. An important contribution of our work is to bring together material from several areas of research and to present results in a unified manner. We begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions. Closely related to the concept of stability are the notions of exponential growth rates and converse Lyapunov theorems, both of which are discussed in detail. In particular, results on common quadratic Lyapunov functions and piecewise linear Lyapunov functions are presented, as they represent constructive methods for proving stability, and also represent problems in which significant progress has been made. We also comment on the inherent difficulty of determining stability of switched systems in general which is exemplified by NP-hardness and undecidability results. We then proceed by considering the stability of switched systems in which there are constraints on the switching rules, through both dwell time requirements and state dependent switching laws. Also in this case the theory of Lyapunov functions and the existence of converse theorems is reviewed. We briefly comment on the classical Lur’e problem and on the theory of stability radii, both of which contain many of the features of switched systems and are rich sources of practical results on the topic. Finally we present a list of questions and open problems which provide motivation for continued research in this area.
Using MIMO feedback control to enforce policies for interrelated metrics with application to the Apache Web server
- In Proceedings of the Network Operations and Management Symposium 2002
, 2002
"... Policy-based management provides a means for IT systems to operate according to business needs. Unfortunately, there is often an “impedance mismatch ” between the policies administrators want and the controls they are given. Consider the Apache web server. Administrators want to control CPU and memo ..."
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Cited by 109 (9 self)
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Policy-based management provides a means for IT systems to operate according to business needs. Unfortunately, there is often an “impedance mismatch ” between the policies administrators want and the controls they are given. Consider the Apache web server. Administrators want to control CPU and memory utilizations, but this must be done indirectly by manipulating tuning parameters such as MaxClients and KeepAlive. There has been much interest in using feedback control to bridge the impedance mismatch. However, these efforts have focused on a single metric that is manipulated by a single control and hence have not considered interactions between controls such as those that are common in computing systems. This paper shows how multiple-input, multiple-output (MIMO) control theory can be used to enforce policies for interrelated metrics. MIMO is used both to model the target system, Apache in our case, and to design feedback controllers. The MIMO model captures the interactions between KA and MC, and can be used to identify infeasible metric policies. In addition, MIMO control techniques can provide considerable benefit in handling trade-offs between speed of metric convergence and sensitivity to random fluctuations while enforcing the desired policies.
Dynamics of TCP/RED and a Scalable Control
- IN PROCEEDINGS OF IEEE INFOCOM 2002
, 2002
"... We demonstrate that the dynamic behavior of queue and average window is determined predominantly by the stability of TCP/RED, not by AIMD probing nor noise traffic. We develop a general multi-link multi-source model for TCP/RED and derive a local stability condition in the case of a single link with ..."
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Cited by 108 (13 self)
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We demonstrate that the dynamic behavior of queue and average window is determined predominantly by the stability of TCP/RED, not by AIMD probing nor noise traffic. We develop a general multi-link multi-source model for TCP/RED and derive a local stability condition in the case of a single link with heterogeneous sources. We validate our model with simulations and illustrate the stability region of TCP/RED. These results suggest that TCP/RED becomes unstable when delay increases, or more strikingly, when link capacity increases. The analysis illustrates the difficulty of setting RED parameters to stabilize TCP: they can be tuned to improve stability, but only at the cost of large queues even when they are dynamically adjusted. Finally, we present a simple distributed congestion control algorithm that maintains stability for arbitrary network delay, capacity, load and topology.
