We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using a gradient projection algorithm. In this system, sources select transmission rates that maximize their own benefits, utility minus bandwidth cost, and network links adjust bandwidth prices to coordinate the sources' decisions. We allow feedback delays to be different, substantial, and time varying, and links and sources to update at different times and with different frequencies. We provide asynchronous distributed algorithms and prove their convergence in a static environment. We present measurements obtained from a preliminary prototype to illustrate the convergence of the algorithm in a slowly time-varying environment. We discuss its fairness property.

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Optimization flow control—I: basic algorithm and convergence

Theory and experiments show that as the per-flow product of bandwidth and latency increases, TCP becomes inefficient and prone to instability, regardless of the queuing scheme. This failing becomes increasingly important as the Internet evolves to incorporate very high-bandwidth optical links and more large-delay satellite links.To address this problem, we develop a novel approach to Internet congestion control that outperforms TCP in conventional environments, and remains efficient, fair, scalable, and stable as the bandwidth-delay product increases. This new eXplicit Control Protocol, XCP, generalizes the Explicit Congestion Notification proposal (ECN). In addition, XCP introduces the new concept of decoupling utilization control from fairness control. This allows a more flexible and analytically tractable protocol design and opens new avenues for service differentiation.Using a control theory framework, we model XCP and demonstrate it is stable and efficient regardless of the link capacity, the round trip delay, and the number of sources. Extensive packet-level simulations show that XCP outperforms TCP in both conventional and high bandwidth-delay environments. Further, XCP achieves fair bandwidth allocation, high utilization, small standing queue size, and near-zero packet drops, with both steady and highly varying traffic. Additionally, the new protocol does not maintain any per-flow state in routers and requires few CPU cycles per packet, which makes it implementable in high-speed routers.

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Congestion control for high bandwidth-delay product networks

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.

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Analysis and design of controllers for AQM routers supporting TCP flows

This article reviews the current transmission control protocol (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.

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Internet congestion control

We propose a duality model of end-to-end congestion control and apply it to understanding the equilibrium properties of TCP and active queue management schemes. 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 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 algorithms such as DropTail, RED or REM. We present these algorithms and their generalizations, derive their utility functions, and study their interaction.

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A duality model of TCP and queue management algorithms

We describe a new active queue management scheme, random exponential marking (REM), that aims to achieve both high utilization and negligible loss and delay in a simple and scalable manner. The key idea is to decouple the congestion measure from the performance measure such as loss, queue length, or delay. While the congestion measure indicates excess demand for bandwidth and must track the number of users, the performance measure should be stabilized around their targets independent of the number of users. We explain the design rationale behind REM and present simulation results of its performance in wireline and wireless networks.

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REM: active queue management

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REM: Active queue management*

We proposed earlier an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. The control mechanism is derived as a gradient projection algorithm to solve the dual problem. In this paper we extend the algorithm to a scaled gradient projection. The diagonal scaling matrix approximates the diagonal terms of the Hessian and can be computed at individual links using the same information required by the unscaled algorithm. We prove the convergence of the scaled algorithm and present simulation results that illustrate its superiority to the unscaled algorithm.

Optimization flow control with Newton-like algorithm

Random Early Marking (REM) consists of a link algorithm, that probabilistically marks packets inside the network, and a source algorithm, that adapts source rate to observed marking. The marking probability is exponential in a link congestion measure, so that the end-to-end marking probability is exponential in a path congestion measure. Marking allows a source to estimate its path congestion measure and adjusts its rate in a way that aligns individual optimality with social optimality. We describe the REM algorithm, summarize its key properties, and present some simulation results that demonstrate its stability, fairness and robustness.

Random Early Marking

We proposed earlier an optimization approach to reactive flow control where the objective of the control is to maximize the aggregate utility of all sources over their transmission rates. The control mechanism is derived as a gradient projection algorithm to solve the dual problem. We extend the algorithm to a scaled gradient projection. The diagonal scaling matrix approximates the diagonal terms of the Hessian and can be computed at individual links using the same information required by the unsealed algorithm. We prove the convergence of the scaled algorithm and present simulation results that illustrate its superiority to the unsealed algorithm.

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S. Athuraliya

Papers

REM: active queue management

REM: Active queue management*

Optimization flow control with Newton-like algorithm

Random Early Marking

Optimization flow control with Newton-like algorithm