A duality model of TCP and queue management algorithms

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

Heterogeneous Congestion Control: Efficiency, Fairness and Design

When heterogeneous congestion control protocols that react to different pricing signals (e.g. packet loss, queueing delay, ECN marking etc.) share the same network, the current theory based on utility maximization fails to predict the network behavior. Unlike in a homogeneous network, the bandwidth allocation now depends on router parameters and flow arrival patterns. It can be non-unique, inefficient and unfair. This paper has two objectives. First, we demonstrate the intricate behaviors of a heterogeneous network through simulations and present a rigorous framework to help understand its equilibrium efficiency and fairness properties. By identifying an optimization problem associated with every equilibrium, we show that every equilibrium is Pareto efficient and provide an upper bound on efficiency loss due to pricing heterogeneity. On fairness, we show that intra-protocol fairness is still decided by a utility maximization problem while inter-protocol fairness is the part over which we don¿t have control. However it is shown that we can achieve any desirable inter-protocol fairness by properly choosing protocol parameters. Second, we propose a simple slow timescale source-based algorithm to decouple bandwidth allocation from router parameters and flow arrival patterns and prove its feasibility. The scheme needs only local information

Network equilibrium of heterogeneous congestion control protocols

When heterogeneous congestion control protocols that react to different pricing signals share the same network, the resulting equilibrium may no longer be interpreted as a solution to the standard utility maximization problem. We prove the existence of equilibrium under mild assumptions. Then we show that multi-protocol networks whose equilibria are locally non-unique or infinite in number can only form a set of measure zero. Multiple locally unique equilibria can arise in two ways. First, unlike in the single-protocol case, the set of bottleneck links can be non-unique with heterogeneous protocols even when the routing matrix has full row rank. The equilibria associated with different sets of bottleneck links are necessarily distinct. Second, even when there is a unique set of bottleneck links, network equilibrium can still be non-unique, but is always finite and odd in number. They cannot all be locally stable unless it is globally unique. Finally, we provide various sufficient conditions for global uniqueness. Numerical examples are used throughout the paper to illustrate these results

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

Equilibrium of Heterogeneous Congestion Control: Optimality and Stability

When heterogeneous congestion control protocols that react to different pricing signals share the same network, the current theory based on utility maximization fails to predict the network behavior. The pricing signals can be different types of signals such as packet loss, queueing delay, etc, or different values of the same type of signal such as different ECN marking values based on the same actual link congestion level. Unlike in a homogeneous network, the bandwidth allocation now depends on router parameters and flow arrival patterns. It can be non-unique, suboptimal and unstable. In Tang et al. (“Equilibrium of heterogeneous congestion control: Existence and uniqueness,” IEEE/ACM Trans. Netw., vol. 15, no. 4, pp. 824–837, Aug. 2007), existence and uniqueness of equilibrium of heterogeneous protocols are investigated. This paper extends the study with two objectives: analyzing the optimality and stability of such networks and designing control schemes to improve those properties. First, we demonstrate the intricate behavior of a heterogeneous network through simulations and present a framework to help understand its equilibrium properties. Second, we propose a simple source-based algorithm to decouple bandwidth allocation from router parameters and flow arrival patterns by only updating a linear parameter in the sources’ algorithms on a slow timescale. It steers a network to the unique optimal equilibrium. The scheme can be deployed incrementally as the existing protocol needs no change and only new protocols need to adopt the slow timescale adaptation

Thermodynamic metrics and optimal paths

A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.Comment: 5 page

Implementation of Provably Stable MaxNet

MaxNet TCP is a congestion control protocol that uses explicit multi-bit signalling from routers to achieve desirable properties such as high throughput and low latency. In this paper we present an implementation of an extended version of MaxNet. Our contributions are threefold. First, we extend the original algorithm to give both provable stability and rate fairness. Second, we introduce the MaxStart algorithm which allows new MaxNet connections to reach their fair rates quickly. Third, we provide a Linux kernel implementation of the protocol. With no overhead but 24-bit price signals, our implementation scales from 32 bit/s to 1 peta-bit/s with a 0.001% rate accuracy. We confirm the theoretically predicted properties by performing a range of experiments at speeds up to 1 Gbit/sec and delays up to 180 ms on the WAN-in-Lab facility