基于网络演算的自相似网络性能上界模型研究
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摘要
网络所承载的通信量是一切网络研究的基础，它不仅能够直接反映网络性能的好坏，而且在某种意义上可以用来表示网络动力学行为特征，一直以来从网络通信量的角度来研究网络性能倍受人们关注。随着信息社会的到来和网络技术的发展，Internet等高速网络已经逐步形成了一个开放的复杂巨系统。随之而来，网络通信量呈现“爆炸式”增长，其固有统计特征发生了改变，这使得基于通信量的网络性能研究也变得越来越重要。自相似性(Self-Similarity)作为高速网络通信量的一种重要统计特征，对网络性能具有影响作用。因此，基于自相似通信量的网络性能建模对高速网络的发展有着深远意义。
到目前为止，人们已经对基于通信量的网络性能或网络自相似通信量等方面分别进行了深入研究，但这些研究均是针对网络性能或自相似通信量单独进行的，缺乏基于自相似通信量的网络性能方面的研究。此外，目前对自相似通信量的研究也主要集中于分析、建模等方面，缺乏自相似通信量控制方面的深入研究。为了提高自相似网络性能，研究如何有效实施自相似网络的服务质量(Quality of Service, QoS)控制，以避免自相似网络拥塞，将具有重要的研究价值。本论文针对自相似性对网络性能所造成的影响，利用网络演算(Network Calculus)理论的方法综合系统地研究了基于自相似通信量的网络性能模型。本论文的主要工作和创新性成果如下：
(1)基于网络演算理论提出了适应于自相似通信量控制的分形整形器模型及其性能模型
在对自相似通信量的控制研究方面，综述了目前国内外在网络自相似通信量研究方面所做的主要研究工作，基于现有研究成果，引入网络演算理论，给出了适应于自相似通信量控制的分形整形器(Fractal Regulator)的一般数学模型，推导了无损和有损两种分形整形器的输出特性与输入流的自相似参数以及整形器的整形曲线(Shaping Curve)之间的关系，分析了分形整形器的队列长度与延迟等性能，讨论了分形整形器的引入对网络端到端延迟、数据丢失总数以及平均丢失率等性能的影响。上述分析工作和得出的结果对自相似通信量控制方案的评价和分形整形器参数的设计具有实际意义，为基于自相似通信量的网络性能研究提供基础。
(2)利用网络演算理论，提出了基于分形整形器的通用处理器共享(Generalized Processor Sharing, GPS)系统的性能统计上界与确定上界模型
在对基于自相似通信量的单节点网络性能研究方面，综述了国内外在GPS系统性能方面所做的主要研究工作，基于已有研究成果，引入分形整形器来对传输到GPS系统入口处的自相似通信量进行整形，建立了以自相似通信量作为输入的GPS系统的性能统计上界模型和性能确定上界模型，包括队列长度统计上界和确定上界、延迟统计上界和确定上界、有效带宽确定上界以及延迟抖动确定上界等性能模型。数学分析表明，基于分形整形器的GPS系统的性能统计上界模型和确定上界模型能够反映通信量的自相似性，并把其输出可用带宽公平地分配给各通信流，并隔离不同的通信流。
(3)基于网络演算理论提出了自相似通信量的端到端延迟上界模型
在对以自相似通信量作为输入的网络端到端延迟研究方面，利用网络演算理论计算了自相似通信量端到端延迟确定上界问题，推导了利用GPS调度器和分形整形器作为节点模型的自相似通信量端到端延迟理想确定上界及其近似确定上界。数学分析表明，自相似通信量的端到端延迟确定上界随通信量自相似参数的增大而有所减小，这有利于改善通信量自相似程度越高延迟越大所导致的网络性能下降。
(4)基于网络演算理论提出了一种保证服务性能模型
在对保证服务(Guaranteed Service)性能模型研究方面，提出了一种通用的保证服务性能模型，在边沿-核心(Edge-Core)网络模型的基础上，基于到达曲线(Arrival Curve)和服务曲线(Service Curve)概念给出了网络节点的二级调度模型，利用网络演算理论推导了该模型的队列长度上界和延迟上界、端到端延迟上界和端到端延迟抖动上界以及有效带宽上界等性能保证。数学分析表明，基于网络演算理论的保证服务性能模型为保证服务网络环境提供QoS的有效控制、调度和管理提供一定的参考作用。
Network teletraffic is the foundation of all network researches, not only it canreflect the quality of network performance directly, but also it can be used forexpressing the behavior characteristic of network dynamics in some degree. For a longtime, people pay more attentions to continuously studying network performance basedon teletraffic. As the development of network technology and the arrival of informationsociety, Internet, as well as all kinds of high speed networks gradually has alreadyformed one open, complex giant system. Following with that, network teletraffic hasexploded, and its inherent characteristic has changed, which causes that the researcheson network performance based on teletrafflc become more and more important. As onekind of main statistical characteristic of high speed network teletraffic, Self-Similarityhas the influence on network performance. Therefore, to make a model of networkperformance based on self-similar teletraffie has the profound significance for thedevelopment of high-speed networks.
So far, network performance based on teletraffic or self-similar teletraffic has beenresearched separately, aiming at the network performance or the self-similar networklonely, lacking in studying network performance based on self-similar teletraffic. Inaddition, more researchers pay attentions to analyzing and modeling the self-similarteletraffic of high-speed networks, lacking for thorough research in the aspect ofself-similar network control. In order to improve the performance of self-similarnetwork, it is important to study how to implement the control of Quality of Service(QoS) of self-similar network, so that it can avoid self-similar network congestion.Considering the influence of self-similarity on network performance, the model ofnetwork performance is studied synthetically and systemically based on self-similarteletraffic using network calculus in this paper. The main work and contributions arepresented in the following aspects:
(1)To adapt to control self-similar teletraffic, the mathematical model of thefractal regulator (or fractal shaper) and the performance model of it with networkcalculus are proposed.
On the researches of controlling self-similar teletrattic control, an overview of thecurrent major works on this field are presented, and then, on the basis of these currentresearch results, using network calculus theory, a general mathematical model of the fractal regulator for controlling self-similar teletraffic is proposed. The relationshipsbetween the output properties of the lossless fractal regulator and the loss fractalregulator and the self-similar parameter of the input traffic and the shaper curve and theshapers are derived. The performance of two kinds of the fractal regulator is analyzed,such as, queue length and delay. At last, the influences of the introduction of the fractalregulator on the end-to-end delay, the packets lost totals and the average lost rate arediscussed. These works and results of the analyses have practical significance for theevaluation of the control strategy of self-similar teletraffic and the configuration of theparameter of the fractal regulator parameter, as well as, provide the foundation for theresearch of the network performance based on self-similar teletraffic.
(2) Using network calculus, the statistical and deterministic models of the upperbounds on the performance of General Processor Sharing (GPS), based on the fractalregulator with self-similar teletraffic input, are proposed.
On the researches of the performance of the network single-node with self-similarteletraffic input, an overview of the current main works on the GPS system is presented.Based on the research results, the self-similar teletraffic on the ingress of the GPSsystem is reshaped and regulated by the fractal regulator, and the models of thestatistical and deterministic upper bounds on the performance of the GPS system withthe self-similar teletraffic input are proposed. These models include the statistical anddeterministic upper bounds on queue length, on delay, and the deterministic upperbounds on effective bandwidth and on delay jitter of the GPS system. Numericalexamples and results are presented to demonstrate that, the models of the statistical anddeterministic upper bounds on the performance of the GPS system based on the fractalregulators can reflect the self-similar characteristic of the self-similar teletraffic; theGPS system based on the fractal regulators fairly assigned its available outputbandwidth for each flow, and isolates from different flows.
(3) Using network calculus, the deterministic upper bounds on end-to-end delay ofthe network system with self-similar teletraffic input are derived.
On the researches of bounds on end-to-end delay of the network with theself-similar teletraffic input, the upper bounds on end-to-end delay in guaranteed servicewith network calculus are studied. The deterministic upper bounds on the ideaend-to-end delay as well as the approximate end-to-end delay, which used the GPSdispatcher and the fractal regulators as the node model, are derived. Numerical examples and results indicate that, the deterministic upper bounds on end-to-end delaythe system with self-similar teletraffic input increase along with the self-similarparameter reducing. This is advantageous to the improvement of the performance drop,which is owed to that the higher degree of the self-similarity of network teletraffic, thelonger delay.
(4)Using network calculus, a performance model in guaranteed service isproposed.
On the researches of performance models in guaranteed service, a generalperformance model in guaranteed service is proposed. On the basis of edge-corenetwork model, and using the arrival curve and the service curve, a two level schedulingmodel of the network node is proposed, and the upper bounds on queue length, delay,end-to-end delay, end-to-end delay jitter, and effective bandwidth of the performancemodel are derived. Numerical examples and results demonstrate that, the performancemodel in guaranteed service with network calculus provides a reference for the activecontrol, the scheduling strategy and the management of the guaranteed service networksproviding for QoS.
到目前为止，人们已经对基于通信量的网络性能或网络自相似通信量等方面分别进行了深入研究，但这些研究均是针对网络性能或自相似通信量单独进行的，缺乏基于自相似通信量的网络性能方面的研究。此外，目前对自相似通信量的研究也主要集中于分析、建模等方面，缺乏自相似通信量控制方面的深入研究。为了提高自相似网络性能，研究如何有效实施自相似网络的服务质量(Quality of Service, QoS)控制，以避免自相似网络拥塞，将具有重要的研究价值。本论文针对自相似性对网络性能所造成的影响，利用网络演算(Network Calculus)理论的方法综合系统地研究了基于自相似通信量的网络性能模型。本论文的主要工作和创新性成果如下：
(1)基于网络演算理论提出了适应于自相似通信量控制的分形整形器模型及其性能模型
在对自相似通信量的控制研究方面，综述了目前国内外在网络自相似通信量研究方面所做的主要研究工作，基于现有研究成果，引入网络演算理论，给出了适应于自相似通信量控制的分形整形器(Fractal Regulator)的一般数学模型，推导了无损和有损两种分形整形器的输出特性与输入流的自相似参数以及整形器的整形曲线(Shaping Curve)之间的关系，分析了分形整形器的队列长度与延迟等性能，讨论了分形整形器的引入对网络端到端延迟、数据丢失总数以及平均丢失率等性能的影响。上述分析工作和得出的结果对自相似通信量控制方案的评价和分形整形器参数的设计具有实际意义，为基于自相似通信量的网络性能研究提供基础。
(2)利用网络演算理论，提出了基于分形整形器的通用处理器共享(Generalized Processor Sharing, GPS)系统的性能统计上界与确定上界模型
在对基于自相似通信量的单节点网络性能研究方面，综述了国内外在GPS系统性能方面所做的主要研究工作，基于已有研究成果，引入分形整形器来对传输到GPS系统入口处的自相似通信量进行整形，建立了以自相似通信量作为输入的GPS系统的性能统计上界模型和性能确定上界模型，包括队列长度统计上界和确定上界、延迟统计上界和确定上界、有效带宽确定上界以及延迟抖动确定上界等性能模型。数学分析表明，基于分形整形器的GPS系统的性能统计上界模型和确定上界模型能够反映通信量的自相似性，并把其输出可用带宽公平地分配给各通信流，并隔离不同的通信流。
(3)基于网络演算理论提出了自相似通信量的端到端延迟上界模型
在对以自相似通信量作为输入的网络端到端延迟研究方面，利用网络演算理论计算了自相似通信量端到端延迟确定上界问题，推导了利用GPS调度器和分形整形器作为节点模型的自相似通信量端到端延迟理想确定上界及其近似确定上界。数学分析表明，自相似通信量的端到端延迟确定上界随通信量自相似参数的增大而有所减小，这有利于改善通信量自相似程度越高延迟越大所导致的网络性能下降。
(4)基于网络演算理论提出了一种保证服务性能模型
在对保证服务(Guaranteed Service)性能模型研究方面，提出了一种通用的保证服务性能模型，在边沿-核心(Edge-Core)网络模型的基础上，基于到达曲线(Arrival Curve)和服务曲线(Service Curve)概念给出了网络节点的二级调度模型，利用网络演算理论推导了该模型的队列长度上界和延迟上界、端到端延迟上界和端到端延迟抖动上界以及有效带宽上界等性能保证。数学分析表明，基于网络演算理论的保证服务性能模型为保证服务网络环境提供QoS的有效控制、调度和管理提供一定的参考作用。
Network teletraffic is the foundation of all network researches, not only it canreflect the quality of network performance directly, but also it can be used forexpressing the behavior characteristic of network dynamics in some degree. For a longtime, people pay more attentions to continuously studying network performance basedon teletraffic. As the development of network technology and the arrival of informationsociety, Internet, as well as all kinds of high speed networks gradually has alreadyformed one open, complex giant system. Following with that, network teletraffic hasexploded, and its inherent characteristic has changed, which causes that the researcheson network performance based on teletrafflc become more and more important. As onekind of main statistical characteristic of high speed network teletraffic, Self-Similarityhas the influence on network performance. Therefore, to make a model of networkperformance based on self-similar teletraffie has the profound significance for thedevelopment of high-speed networks.
So far, network performance based on teletraffic or self-similar teletraffic has beenresearched separately, aiming at the network performance or the self-similar networklonely, lacking in studying network performance based on self-similar teletraffic. Inaddition, more researchers pay attentions to analyzing and modeling the self-similarteletraffic of high-speed networks, lacking for thorough research in the aspect ofself-similar network control. In order to improve the performance of self-similarnetwork, it is important to study how to implement the control of Quality of Service(QoS) of self-similar network, so that it can avoid self-similar network congestion.Considering the influence of self-similarity on network performance, the model ofnetwork performance is studied synthetically and systemically based on self-similarteletraffic using network calculus in this paper. The main work and contributions arepresented in the following aspects:
(1)To adapt to control self-similar teletraffic, the mathematical model of thefractal regulator (or fractal shaper) and the performance model of it with networkcalculus are proposed.
On the researches of controlling self-similar teletrattic control, an overview of thecurrent major works on this field are presented, and then, on the basis of these currentresearch results, using network calculus theory, a general mathematical model of the fractal regulator for controlling self-similar teletraffic is proposed. The relationshipsbetween the output properties of the lossless fractal regulator and the loss fractalregulator and the self-similar parameter of the input traffic and the shaper curve and theshapers are derived. The performance of two kinds of the fractal regulator is analyzed,such as, queue length and delay. At last, the influences of the introduction of the fractalregulator on the end-to-end delay, the packets lost totals and the average lost rate arediscussed. These works and results of the analyses have practical significance for theevaluation of the control strategy of self-similar teletraffic and the configuration of theparameter of the fractal regulator parameter, as well as, provide the foundation for theresearch of the network performance based on self-similar teletraffic.
(2) Using network calculus, the statistical and deterministic models of the upperbounds on the performance of General Processor Sharing (GPS), based on the fractalregulator with self-similar teletraffic input, are proposed.
On the researches of the performance of the network single-node with self-similarteletraffic input, an overview of the current main works on the GPS system is presented.Based on the research results, the self-similar teletraffic on the ingress of the GPSsystem is reshaped and regulated by the fractal regulator, and the models of thestatistical and deterministic upper bounds on the performance of the GPS system withthe self-similar teletraffic input are proposed. These models include the statistical anddeterministic upper bounds on queue length, on delay, and the deterministic upperbounds on effective bandwidth and on delay jitter of the GPS system. Numericalexamples and results are presented to demonstrate that, the models of the statistical anddeterministic upper bounds on the performance of the GPS system based on the fractalregulators can reflect the self-similar characteristic of the self-similar teletraffic; theGPS system based on the fractal regulators fairly assigned its available outputbandwidth for each flow, and isolates from different flows.
(3) Using network calculus, the deterministic upper bounds on end-to-end delay ofthe network system with self-similar teletraffic input are derived.
On the researches of bounds on end-to-end delay of the network with theself-similar teletraffic input, the upper bounds on end-to-end delay in guaranteed servicewith network calculus are studied. The deterministic upper bounds on the ideaend-to-end delay as well as the approximate end-to-end delay, which used the GPSdispatcher and the fractal regulators as the node model, are derived. Numerical examples and results indicate that, the deterministic upper bounds on end-to-end delaythe system with self-similar teletraffic input increase along with the self-similarparameter reducing. This is advantageous to the improvement of the performance drop,which is owed to that the higher degree of the self-similarity of network teletraffic, thelonger delay.
(4)Using network calculus, a performance model in guaranteed service isproposed.
On the researches of performance models in guaranteed service, a generalperformance model in guaranteed service is proposed. On the basis of edge-corenetwork model, and using the arrival curve and the service curve, a two level schedulingmodel of the network node is proposed, and the upper bounds on queue length, delay,end-to-end delay, end-to-end delay jitter, and effective bandwidth of the performancemodel are derived. Numerical examples and results demonstrate that, the performancemodel in guaranteed service with network calculus provides a reference for the activecontrol, the scheduling strategy and the management of the guaranteed service networksproviding for QoS.
引文
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