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Dynamical Analysis of an Internet-Based Video System

机译：基于Internet的视频系统的动力学分析

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摘要

The dissemination of video applications across the Internet still remains the driving force for Internet traffic growth. Generally, video streaming systems are characterized with irregular transmitting pattern and fluctuation which usually leads to transmission delay and frame loss. Furthermore, the democratic platform created by peer-to-peer (P2P) network for video streaming suggests complex dynamical behaviour with difficult predictable performance. The existence of flash crowd and peer churn situations in P2P streaming systems obtained from random arrival and departure of peers exhibits chaotic attributes. In this paper, a P2P streaming system(UStream) was modelled using a system of first order differential equations. The dynamics of UStream were analysed using equilibrium points and eigenvalues structure. Instability region was tracked through numerical investigation. The numerical simulation conducted using the Mathematica package software showed that UStream exhibits spiral fixed point and strange attractors with certain initial conditions which confirms experimental measurement and observations. Also, the system responds exponentially with time and reflects instability pattern for the first 20 seconds and 500 seconds when investigated with client-to-server(CS)and P2P network models respectively.
机译：在整个Internet上传播视频应用程序仍然是Internet流量增长的驱动力。通常，视频流系统的特征在于不规则的传输模式和波动，这通常会导致传输延迟和帧丢失。此外，由点对点（P2P）网络创建的用于视频流的民主平台表明，复杂的动态行为具有难以预测的性能。从对等点的随机到达和离开获得的P2P流系统中，存在闪光人群和对等搅动情况表现出混乱的属性。本文利用一阶微分方程组对P2P流系统（UStream）进行建模。使用平衡点和特征值结构分析了UStream的动力学。通过数值研究跟踪了不稳定区域。使用Mathematica软件包进行的数值模拟表明，UStream在某些初始条件下表现出螺旋定点和奇怪的吸引子，这证实了实验测量和观察结果。而且，当分别使用客户端到服务器（CS）和P2P网络模型进行调查时，系统在前20秒和500秒内会以指数方式响应并反映不稳定模式。

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