Fluid Model for a Data Network with α-Fair Bandwidth Sharing and General Document Size Distributions : Two Examples of Stability
Fluid Model for a Data Network with α-Fair Bandwidth Sharing and General Document Size Distributions : Two Examples of Stability
复制标题
具有 α-公平带宽共享和一般文档大小分布的数据网络的流体模型：两个稳定性示例
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
R. J. Williams
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文献类型：
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作者：
H. C. Gromoll;R. J. Williams
拥塞控制机制的设计和分析是现代数据网络（如Internet）的一个具有挑战性的问题。在不同层次的数学模型已被引入，努力提供洞察力的一些方面，这个问题。Roberts和Massoulié [13]引入并研究的一个模型旨在捕获网络中文档到达和离开的动态，其中带宽在对应于单个弹性文档的连续传输的流之间公平共享。在这里，我们考虑在Mo和Walrand [14]引入的带宽共享策略家族下的该模型。对于一般分布的到达间隔时间和文档大小，除了少数特殊情况，这是一个开放的问题，建立稳定的随机流水平模型的标称条件下，每个资源上的平均负载小于其容量。作为研究该模型的一步，在另一项工作中[8]，我们引入了一个度量值过程来描述剩余文档大小的动态演变，并证明了一个流动限制结果：在温和的假设下，对应于一系列流水平模型的重标度测度值过程（具有固定网络结构）是紧的，序列的任何弱极限点几乎必然是某个流体模型的解。在[8]中还描述了流体模型的不变状态。在本文中，我们回顾的随机流水平模型的结构，描述我们的流体模型近似，然后给出两个有趣的例子，网络拓扑结构的流体模型的稳定性可以建立在标称条件下。这两种类型的网络是线性网络和树型网络。
The design and analysis of congestion control mechanisms for modern data networks such as the Internet is a challenging problem. Mathematical models at various levels have been introduced in an effort to provide insight to some aspects of this problem. A model introduced and studied by Roberts and Massoulié [13] aims to capture the dynamics of document arrivals and departures in a network where bandwidth is shared fairly amongst flows that correspond to continuous transfers of individual elastic documents. Here we consider this model under a family of bandwidth sharing policies introduced by Mo and Walrand [14]. With generally distributed interarrival times and document sizes, except for a few special cases, it is an open problem to establish stability of this stochastic flow level model under the nominal condition that the average load on each resource is less than its capacity. As a step towards the study of this model, in a separate work [8], we introduced a measure valued process to describe the dynamic evolution of the residual document sizes and proved a fluid limit result: under mild assumptions, rescaled measure valued processes corresponding to a sequence of flow level models (with fixed network structure) are tight, and any weak limit point of the sequence is almost surely a solution of a certain fluid model. The invariant states for the fluid model were also characterized in [8]. In this paper, we review the structure of the stochastic flow level model, describe our fluid model approximation and then give two interesting examples of network topologies for which stability of the fluid model can be established under a nominal condition. The two types of networks are linear networks and tree networks.