具有带宽共享和一般文档大小分布的网络的流体限制
Fluid limits for networks with bandwidth sharing and general document size distributions
摘要：
我们考虑一个随机模型的互联网拥塞控制，介绍了Massoulié和Roberts [电信系统15（2000）185- 201]，它代表了随机变化的流量在网络中的带宽之间共享的文件传输。相反，早期的工作凯利和威廉姆斯[安。14（2004）1055- 1083]，本论文允许到达间隔和文档大小一般分布，而不是指数分布。此外，我们允许相当一般的带宽共享策略类别，其包括Mo和Walrand的加权$α$公平策略[IEEE/ACM Transactions on Networking 8（2000）556- 567]，以及某些其它基于效用的调度策略。为了描述系统的演化，度量值过程用于跟踪通过网络的所有流的剩余文档大小。我们提出了一个流体模型（或形式泛函大数定律近似）与随机流水平模型。在较弱的条件下，证明了对应于一系列这样的模型（具有固定的网络结构）的适当重标度的测度值过程是紧的，并且该序列的任何弱极限点几乎必然是流体模型解.对于加权$α$ -公平策略的特殊情况，我们还刻画了流体模型的不变状态。
英文摘要：
We consider a stochastic model of Internet congestion control, introduced by Massoulié and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows in a network where bandwidth is shared among document transfers. In contrast to an earlier work by Kelly and Williams [Ann. Appl. Probab. 14 (2004) 1055--1083], the present paper allows interarrival times and document sizes to be generally distributed, rather than exponentially distributed. Furthermore, we allow a fairly general class of bandwidth sharing policies that includes the weighted $α$-fair policies of Mo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567], as well as certain other utility based scheduling policies. To describe the evolution of the system, measure valued processes are used to keep track of the residual document sizes of all flows through the network. We propose a fluid model (or formal functional law of large numbers approximation) associated with the stochastic flow level model. Under mild conditions, we show that the appropriately rescaled measure valued processes corresponding to a sequence of such models (with fixed network structure) are tight, and that any weak limit point of the sequence is almost surely a fluid model solution. For the special case of weighted $α$-fair policies, we also characterize the invariant states of the fluid model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
