Developing new mathematical methods for stochastic networks: Renovating events, networks with spatial interaction and random fluids

为随机网络开发新的数学方法：更新事件、具有空间相互作用的网络和随机流体

• 批准号: EP/E033717/1
• 负责人: Sergey Foss
• 金额: $ 37.41万
• 依托单位: Heriot-Watt University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2007
• 资助国家: 英国
• 起止时间: 2007 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE033717%2F1
• 关键词: Developing; new; mathematical; methods; stochastic

This proposal aims at the development of new models and techniques in the area of Stochastic Networks. We propose three themes: (i) the investigation of stability via renovation events,(ii) the investigation of stability for networks with spatial interaction, and (iii) the development of performance techniques for random fluids.Stochastic networks play an important role as mathematical models of various modern complex systems, such as the Internet, mobile networks and traffic networks. Although these systems are quite different from the engineering point of view, they share common characteristics as regards the mathematical models used in describing them and, in effect, predicting their behaviour.We are seeking support for a postdoctoral research fellow for 36 months, some computing equipment, funds for research exchanges and funds for participation in scientific conferences.The research fellow is expected to contribute to the topics described below.

该提案旨在随机网络领域的新模型和技术的发展。我们提出三个主题：随机网络作为各种现代复杂系统（如Internet、移动的网络和交通网络）的数学模型发挥着重要作用。虽然这些系统从工程的角度来看有很大的不同，但它们在描述它们时所使用的数学模型方面具有共同的特征，实际上，预测它们的行为。研究交流基金和参加科学会议的基金。研究员将对下述专题作出贡献。

项目成果

On Large Delays in Multi-Server Queues with Heavy Tails

关于重尾多服务器队列中的大延迟

• DOI: 10.1287/moor.1120.0539
• 发表时间: 2012
• 期刊: Mathematics of Operations Research
• 影响因子: 1.7
• 作者: Foss S

Lower limits for distribution tails of randomly stopped sums

• DOI: 10.1137/s0040585x97983328
• 发表时间: 2008-11
• 期刊: Theory of Probability and Its Applications
• 影响因子: 0.6
• 作者: D. Denisov;D. Korshunov;S. Foss

Limit theorems for a random directed slab graph

随机有向平板图的极限定理

• DOI: 10.48550/arxiv.1005.4806
• 发表时间: 2010
• 作者: Denisov D

Stochastic Sequences with a Regenerative Structure that May Depend Both on the Future and on the Past

具有可能既取决于未来又取决于过去的再生结构的随机序列

• DOI: 10.1239/aap/1386857859
• 发表时间: 2016
• 期刊: Advances in Applied Probability
• 影响因子: 1.2
• 作者: Foss S

Ergodicity of a stress release point process seismic model with aftershocks

余震应力释放点过程地震模型的遍历性

• DOI: 10.48550/arxiv.0912.0551
• 发表时间: 2009
• 作者: Brémaud P