Analysis of Dynamic Congestion Control Protocols: A Fokker-Planck Approximation

We present an approximate analysis of a queue with dynamically changing input rates that are based on implicit or explicit feedback. This is motivated by recent proposals for adaptive congestion control algorithms [RaJa 88, Jac 88], where the sender\u27s window size at the transport level is adjusted based on perceived congestion level of a bottleneck node. We develop an analysis methodology for a simplified system; yet it is powerful enough to answer the important questions regarding stability, convergence (or oscillations), fairness and the significant effect that delayed feedback plays on performance. Specifically, we find that, in the absence of feedback delay, the linear increase/exponential decrease algorithm of Jacobson and Ramakrishnan-Jain [Jac 88, RaJa 88] is provably stable and fair. Delayed feedback on the other hand, introduces oscillations for every individual user as well as unfairness across those competing for the same resource. While the simulation study of Zhang [Zha 89] and the fluid-approximation study of Bolot and Shanker [BoSh 90] have observed the oscillations in cumulative queue length and measurements by Jacobson [Jac 88] have revealed some of the unfairness properties, the reasons for these have not been identified. We identify quantitatively the cause of these effects, via-a-vis the systems parameters and properties of the algorithm used. The model presented is fairly general and can be applied to evaluate the performance of a wide range of feedback control schemes. It is an extension of the classical Fokker-Planck equation. Therefore, it addresses traffic viability (to some extent) that fluid approximation techniques do not address

Analysis of Error Control and Congestion Control Protocols

This thesis presents an analysis of a class of error control and congestion control protocols used in computer networks. We address two kinds of packet errors: (a) independent errors and (b) congestion-dependent errors. Our performance measure is the expected time and the standard deviation of the time to transmit a large message, consisting of N packets. The analysis of error control protocols. Assuming independent packet errors gives an insight on how the error control protocols should really work if buffer overflows are minimal. Some pertinent results on the performance of go-back-n, selective repeat, blast with full retransmission on error (BFRE) and a variant of BFRE, the Optimal BFRE that we propose, are obtained. We then analyze error control protocols in the presence of congestion-dependent errors. We study the selective repeat and go-back-n protocols and find that irrespective of retransmission strategy, the expected time as well as the standard deviation of the time to transmit N packets increases sharply the face of heavy congestion. However, if the congestion level is low, the two retransmission strategies perform similarly. We conclude that congestion control is a far more important issue when errors are caused by congestion. We next study the performance of a queue with dynamically changing input rates that are based on implicit or explicit feedback. This is motivated by recent proposals for adaptive congestion control algorithms where the sender\u27s window size is adjusted based on perceived congestion level of a bottleneck node. We develop a Fokker-Planck approximation for a simplified system; yet it is powerful enough to answer the important questions regarding stability, convergence (or oscillations), fairness and the significant effect that delayed feedback plays on performance. Specifically, we find that, in the absence of feedback delay, a linear increase/exponential decrease rate control algorithm is provably stable and fair. Delayed feedback, however, introduces cyclic behavior. This last result not only concurs with some recent simulation studies, it also expounds quantitatively on the real causes behind them

Large-scale games in large-scale systems

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean field limit and dynamical system viewpoints. Under regularity assumptions and specific time-scaling techniques, the evolution of the mean field limit can be expressed in terms of deterministic or stochastic equation or inclusion (difference or differential). In this paper, we overview recent advances of large-scale games in large-scale systems. We focus in particular on population games, stochastic population games and mean field stochastic games. Considering long-term payoffs, we characterize the mean field systems using Bellman and Kolmogorov forward equations.Comment: 30 pages. Notes for the tutorial course on mean field stochastic games, March 201

Dynamic Time Windows and Generalized Virtual Clocks-Combined Closed-Loop/Open-Loop Mechanisms for Congestion Control of Data Traffic in High Speed Wide Area Networks

This paper presents a set of mechanisms for congestion control of data traffic in high speed wide area networks (HSWANs) along with preliminary performance results. The model of the network assumes reservation of resources based on average requirements. The mechanisms address (a) the different network time constants (short term and medium-term), (b) admission control that allows controlled variance of traffic as a function of medium-term congestion, and (c) prioritized scheduling which is based on a new fairness criterion. This latter criterion is perceived as the appropriate fairness measure for HSWANs. Preliminary performance studies show that the queue length statistics at switching nodes (mean, variance and max) are approximately proportional to the end-point \u27time window\u27 size. Further, * when network utilization approaches unity, the time window mechanism can protect the network from buffer overruns and excessive queueing delays, and * when network utilization level is smaller, the time window may be increased to allow a controlled amount of variance that attempts to simultaneously meet the performance goals of the end-user and that of the network. The prioritized scheduling algorithms proposed and studied in this paper are a generalization of the Virtual Clock algorithm [Zhang 1989]. The study here investigates * necessary and sufficient conditions for accomplishing desired fairness, * simulation and (limited analytical results for expected waiting times, * ability to protect against misbehaving users, and * relationship between end-point admission control (Time-Window) and internal scheduling (\u27Pulse\u27 and Virtual Clock) at the switch

Differential Models, Numerical Simulations and Applications

This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems

On the Dynamics and Significance of Low Frequency Components of Internet Load

Dynamics of Internet load are investigated using statistics of round-trip delays, packet losses and out-of-order sequence of acknowledgments. Several segments of the Internet are studied. They include a regional network (the Jon von Neumann Center Network), a segment of the NSFNet backbone and a cross-country network consisting of regional and backbone segments. Issues addressed include: (a) dominant time scales in network workload; (b) the relationship between packet loss and different statistics of round-trip delay (average, minimum, maximum and standard-deviation); (c) the relationship between out of sequence acknowledgments and different statistics of delay; (d) the distribution of delay; (e) a comparison of results across different network segments (regional, backbone and cross-country); and (f) a comparison of results across time for a specific network segment. This study attempts to characterize the dynamics of Internet workload from an end-point perspective. A key conclusion from the data is that efficient congestion control is still a very difficult problem in large internetworks. Nevertheless, there are interesting signals of congestion that may be inferred from the data. Examples include (a) presence of slow oscillation components in smoothed network delay, (b) increase in conditional expected loss and conditional out-of-sequence acknowledgments as a function of various statistics of delay, (c) change in delay distribution parameters as a function of load, while the distribution itself remains the same, etc. The results have potential application in heuristic algorithms and analytical approximations for congestion control

Congestion Avoidance Testbed Experiments

DARTnet provides an excellent environment for executing networking experiments. Since the network is private and spans the continental United States, it gives researchers a great opportunity to test network behavior under controlled conditions. However, this opportunity is not available very often, and therefore a support environment for such testing is lacking. To help remedy this situation, part of SRI's effort in this project was devoted to advancing the state of the art in the techniques used for benchmarking network performance. The second objective of SRI's effort in this project was to advance networking technology in the area of traffic control, and to test our ideas on DARTnet, using the tools we developed to improve benchmarking networks. Networks are becoming more common and are being used by more and more people. The applications, such as multimedia conferencing and distributed simulations, are also placing greater demand on the resources the networks provide. Hence, new mechanisms for traffic control must be created to enable their networks to serve the needs of their users. SRI's objective, therefore, was to investigate a new queueing and scheduling approach that will help to meet the needs of a large, diverse user population in a "fair" way