【作者】 丁大为；

【导师】 朱杰；

【作者基本信息】 上海交通大学 ， 电子科学与技术， 2008， 博士

【摘要】 由于计算机和通信技术的不断进步,以TCP(Transmission Control Protocol)/IP(Internet Protocol)为基础的互联网逐步普及并得到了巨大的发展。然而随着网络规模的迅速扩大、用户数量的急剧增加和网络应用类型的不断丰富,网络拥塞现象也日益严重。网络拥塞的直接后果是整个网络性能的下降,包括数据包丢弃率增大、时间延迟增加,以及吞吐量下降等,严重时甚至导致网络崩溃。网络拥塞控制是改善网络性能、增加网络鲁棒性和提高服务质量(QoS)的主要手段。当前互联网拥塞控制包括两方面:基于源端的TCP拥塞控制机制和基于链路端的队列管理机制。这两方面相互影响、相互作用,成为解决目前互联网拥塞问题的主要途径之一,形成了计算机网络、通信、自动控制等学科交叉的一个新的研究热点。本文采用非线性动力学分析方法来研究互联网拥塞控制系统中存在的复杂非线性动力学现象,如分岔(bifurcation)、混沌(chaos)等,并用成熟的分岔、混沌控制方法来抑制互联网中的这些非线性现象。相对于传统的基于随机理论和排队论的方法,非线性动力学分析可以得到更加精确的结论,这对于互联网拥塞控制系统的建模、改进当前互联网拥塞控制算法和探索新的适合未来高带宽时延乘积网络的拥塞控制机制都非常关键,具有非常重要的理论意义和应用价值。本文主要研究内容和创新之处包括以下几个方面:(1).提出一种简化互联网拥塞控制系统离散模型动力学行为控制方法。当源端既有TCP流又有UDP(User Datagram Protocol)流、链路端采用RED(Random Early Detection)算法时,分析了该模型的分岔、混沌现象,并采用标准和扩展时延反馈控制(Time-delayed Feedback Control, TDFC)方法来控制系统状态或者参数,从而达到稳定系统平均队列长度的混沌行为的目的。进一步,将该模型扩展到源端是TCP Westwood流、链路端采用RED算法,分析得到了TCP Westwood/RED拥塞控制的动力学模型,并利用该模型分析了系统在不同参数变化时存在倍周期分岔和混沌行为。(2).提出互联网拥塞控制系统频闪(Stroboscopic)模型混沌行为控制的混合控制(hybrid control)方法。采用一种既包含状态反馈又包含参数摄动的混合控制策略来控制频闪模型的混沌轨道,将其稳定到不动点。而且,获得了包含两条拥塞链路的串联网络的拥塞控制系统频闪模型,并研究了两个瓶链路之间的相互影响,对其系统状态进行控制。结果表明,只要对关键节点进行控制,就可以稳定整个系统。(3).证明互联网拥塞控制系统对偶(Dual)模型存在霍普夫分岔行为,并提出一种控制其分岔行为的控制方法。理论分析表明,当分岔参数(通信延迟)超过某一临界值,系统失去稳定性,并且发生霍普夫分岔。同时,利用摄动法(Perturbation Method, PM),确定了该分岔的方向和分岔周期解的稳定性。其次,采用时间延迟反馈的方法有效地推迟了系统霍普夫分岔的发生,扩大了系统的稳定区间。(4).分析TCP/RED拥塞控制系统流体流模型(Fluid-Flow Model, FFM)当通信延迟变化时存在的霍普夫分岔现象,提出一种简单的控制器来扩大系统的稳定性。理论分析和仿真实验表明,当系统的通信延迟超过某一临界值,系统将出现霍普夫分岔行为,即系统状态由稳定的平衡点变为极限环。并且,霍普夫分岔的方向和周期解的稳定性可以通过中心流形定理(Center Manifold Theorem, CMT)和正规形理论(Normal Form Theory, NFT)来确定。进一步,通过在系统的一个状态变量上加入一种时间延迟反馈控制器,控制霍普夫分岔的发生,进而扩大系统对通信延迟的稳定性区间。更多还原

【Abstract】 Since the rapid progress made in computer and communication technology, the TCP (Transmission Control Protocol) / IP (Internet Protocol)-based Internet has developed enormously. However, with the growing size, popularity and application of the Internet, congestion has become an increasing serious issue. Congestion can cause significant deterioration of network performance, including package drop probability, time delay and network throughput, and even cause the happening of congestion collapse. Network congestion control is the main method for improving the performance, increasing the robustness and strenghthening the quality of service of the whole network.At present, the congestion control strategy of Internet consists of two parts: a source algorithm carried out by TCP at hosts and a link algorithm by AQM (Active Queue Management) schemes at routers. The combination of both parts has been the main approach to solve the Internet congestion control problem and is now considered a research hotspot which intercrosses several disciplines, such as computer networks, communication and automatic control.In this dissertation, nonlinear dynamic analysis is applied to interpret the occurrence of nonlinear phenomenon (such as bifurcation and chaos) in Internet congestion control systems. Moreover, bifurcation and chaos control methods are used to eliminate nonlinear behavior in the Internet. Comparing traditional stochastic theory and queuing theory, the nonlinear dynamic analysis is expected to lead to more precise results. Thus it is important to model the Internet congestion control systems, improve the present congestion control scheme and explore new congestion control strategies for future high bandwidth-delay-product networks. Therefore, research of the Internet congestion control systems has very important theoretical significance and application values.The main contents and contributions of this dissertation can be summarized as follows:(1). Nonlinear dynamic behavior and its control problem in a discrete-time model of a simple Internet congestion control system are studied. It is shown that the system has complex dynamic behaviors, such as bifurcation and chaos, with TCP and UDP (User Data Protocol) flows at sources and RED (Random Early Detect) algorithm at router. Then, we apply standard and extended time-delayed feedback control (TDFC) approaches to control the system state or parameters in order to stabilize the chaotic behavior of average queue size of the system. Furthermore, this model is extended to systems with TCP Westwood flows and RED gateway. The existence of period-doubling bifurcation and chaotic behaviors is also indicated in the system with variation of parameters.(2). The control of dynamic behavior in stroboscopic model of Internet congestion control system is studied. A hybrid control strategy using both state feedback and parameter perturbation is applied to control the chaotic orbits embedded in the stroboscopic model in order to stabilize it to an equilibrium point. Moreover, this model is extended to a network with two bottleneck links. The interaction of two bottleneck links is investigated. The result indicates that the whole network can be stabilized when a key node is controlled.(3). The analysis and control of Hopf bifurcation in a Dual model of Internet congestion control system are studied. It is indicated that the model loses stability and a Hopf bifurcation occurs when bifurcation parameter (communication delay) passes through a critical value. Moreover, by using the perturbation method, we have analyzed the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Then a time-delayed feedback control strategy is applied to the system for postponing onset of undesirable Hopf bifurcation and increasing stability region of the system.(4). The analysis and control of Hopf bifurcation in a Fluid-Flow model of Internet congestion control system are studied. Theoretical analysis and numerical simulations show that a Hopf bifurcation occurs in the system when communication delay passes through a critical value. This means that the state of system changes from an equilibrium point to a limit cycle. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions have also been investigated by applying the center manifold theorem and the normal form theory. Then a time-delay feedback controller is added to the system for controlling the Hopf bifurcation, which can increase stability region of the system.更多还原