Performance of queueing networks

排队网络的性能

• 批准号: 4551-2006
• 负责人: McDonald, David
• 金额: $ 1.68万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=361722
• 关键词: Performance; queueing; networks

Complex manufacturing plants or telecommunication networks may be modelled as queueing networks.  Orders or packets progress from node to node and wait in queues to obtain service. The performance of the network is usually measured by the throughput or the rate at which orders or packets successfully travers the network. Other considerations include the rarity of network overloads and the mean time to transit the network. My first project involves a constructive large deviation theory for estimating the probability of rare events like network overload.  Rare events need a mathematical investigation since simulation can only generate such events with a lot of computational effort.  I am interested in the state of the network at the moment of overload since one can use this as the starting point for investigating a proposed overload recovery algorithm.  I am also interested in rare events in multitype networks and polling networks which defy current large deviations analysis. My second project involves a mean field analysis of the Internet protocols. We have described the evolution of the histogram of all the transmission window sizes of the sources transmitting through a bottleneck router.  The theoretical distribution has been confirmed by network measurement.  We want to use our tools to investigate some proposed control protocols.  The analysis also raises interesting questions about network turbulence.  There may simultaneous exist a fluid regime where HTTP sources transmit files without loss as well as a lossy regime with periodic burst of packet losses.  These regimes may be viewed as metastable states of a Markov chain.  Since the theory of large deviations for measure (or histogram) valued processes is incomplete we have lots of scope for new mathematical discoveries as well as interesting applications.

复杂的制造工厂或电信网络可以被建模为排队网络，订单或数据包从一个节点到另一个节点，排队等待服务。网络的性能通常通过吞吐量或订单或数据包成功通过网络的速率来衡量。其他考虑因素包括网络过载的罕见性和通过网络的平均时间。我的第一个项目涉及一个建设性的大偏差理论，用于估计罕见事件（如网络过载）的概率。罕见事件需要数学研究，因为模拟只能通过大量的计算工作来生成此类事件。我对过载时的网络状态感兴趣，因为可以将其作为研究建议的过载恢复算法的起点。我也对多类型网络和轮询网络中的罕见事件感兴趣，这些事件违背了当前的大偏差分析。我的第二个项目涉及互联网协议的平均场分析。我们描述了通过瓶颈路由器传输的源的所有传输窗口大小的直方图的演变。理论分布已经被网络测量所证实。我们想使用我们的工具来研究一些建议的控制协议。分析还提出了关于网络湍流的有趣问题。可能同时存在一个流体状态，HTTP源传输文件而不丢失由于测度（或直方图）值过程的大偏差理论是不完整的，因此我们有许多新的数学发现和有趣的应用。