Rigorous Approximations of Stochastic Network Dynamics, with Applications to Real-World Networks
随机网络动力学的严格近似及其在现实世界网络中的应用
基本信息
- 批准号:1538706
- 负责人:
- 金额:$ 25万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2015
- 资助国家:美国
- 起止时间:2015-09-01 至 2018-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Stochastic networks are comprised of "jobs" in the form of packets or customers that arrive to a network and wait in buffers at different nodes of the networks until their processing requirements are fulfilled. Stochastic variability arises from randomness in arrival and processing times, as well as from routing and scheduling decisions. Such networks are ubiquitous and arise as models in diverse fields ranging from telecommunications and service systems to biological systems. A better understanding of these networks has the potential to lead to new algorithms that dramatically improve performance and enable the support of novel network applications. This award supports the development of a general mathematical framework for the analysis of two broad classes of stochastic networks: large-scale load-balancing networks that arise, for example, in web-server farms, and queueing networks that use scheduling policies involving prioritization, which are relevant for real-time scheduling in computer networks and health care systems. The goal is to identify tractable approximations of both transient dynamics and equilibrium behavior, rigorously establish their accuracy for suitable values of network parameters, and to use them to gain insight into network design. There will be mentorship of graduate students, a multidisciplinary project for an undergraduate student and opportunity for outreach. The project also involves interactions with industry, which increases the potential of impacting the design of real networks.Stochastic networks are typically too complex to admit an exact analysis. The goal then is to obtain tractable approximations, whose accuracy can be rigorously justified in a suitable (asymptotic) regime of network parameters via limit theorems for suitably scaled state processes. While there is a well developed mathematical theory of "scaling limits" for certain classes of networks, it does not cover the networks considered in this project, which involve many servers at a single node, general service distributions and non-head of the line scheduling policies. One of the challenges is that Markovian scaling limits of these networks are typically not finite-dimensional. The research will develop tractable infinite-dimensional Markovian representations of these systems, involving interacting measure-valued processes and infinite-dimensional Skorokhod maps, and rigorously establish scaling limit theorems. The analysis will combine methods from different fields, including probability, stochastic analysis, dynamical systems, partial differential equations and optimization. The tools developed will potentially be applicable more broadly for the study of analogous stochastic models arising in other applications. Simulations will also be carried out to ascertain the validity of these approximations for finite systems.
随机网络由数据包或客户形式的“作业”组成,它们到达网络并在网络的不同节点的缓冲区中等待,直到它们的处理要求得到满足。随机可变性来自于到达和处理时间的随机性,以及路由和调度决策。这种网络无处不在,并在从电信和服务系统到生物系统等不同领域中作为模式出现。更好地理解这些网络有可能导致新算法的出现,从而显著提高性能并支持新的网络应用程序。该奖项支持开发一种通用数学框架,用于分析两大类随机网络:例如,在web服务器农场中出现的大规模负载平衡网络,以及使用涉及优先级的调度策略的排队网络,这与计算机网络和卫生保健系统中的实时调度相关。目标是确定瞬态动力学和平衡行为的可处理近似,严格建立其对网络参数合适值的准确性,并使用它们来深入了解网络设计。将有研究生的指导,一个本科生的多学科项目和拓展的机会。该项目还涉及与工业界的互动,这增加了影响实际网络设计的潜力。随机网络通常过于复杂,无法进行精确的分析。然后,目标是获得易于处理的近似,其精度可以通过适当缩放状态过程的极限定理在适当(渐近)的网络参数范围内严格证明。虽然对于某些类型的网络有一个完善的“扩展限制”数学理论,但它并没有涵盖本项目中考虑的网络,它涉及单个节点上的许多服务器,一般服务分布和非线路调度策略。其中一个挑战是这些网络的马尔可夫缩放限制通常不是有限维的。该研究将开发这些系统的可处理的无限维马尔可夫表示,涉及相互作用的测量值过程和无限维Skorokhod映射,并严格建立缩放极限定理。分析将结合不同领域的方法,包括概率、随机分析、动力系统、偏微分方程和优化。所开发的工具将有可能更广泛地适用于在其他应用中产生的类似随机模型的研究。还将进行模拟以确定这些近似对有限系统的有效性。
项目成果
期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Rare Nash Equilibria and the Price of Anarchy in Large Static Games
- DOI:10.1287/moor.2018.0929
- 发表时间:2017-02
- 期刊:
- 影响因子:0
- 作者:D. Lacker;K. Ramanan
- 通讯作者:D. Lacker;K. Ramanan
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Kavita Ramanan其他文献
Quenched large deviation principles for random projections of math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg" class="math"msubsupmrowmiℓ/mi/mrowmrowmip/mi/mrowmrowmin/mi/mrow/msubsup/math balls
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- DOI:
10.1016/j.jfa.2025.110937 - 发表时间:
2025-09-15 - 期刊:
- 影响因子:1.600
- 作者:
Patrick Lopatto;Kavita Ramanan;Xiaoyu Xie - 通讯作者:
Xiaoyu Xie
The $\ell_r$-Levy-Grothendieck problem and $r\rightarrow p$ norms of Levy matrices
$ell_r$-Levy-Grothendieck 问题和 Levy 矩阵的 $r
ightarrow p$ 范数
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Kavita Ramanan;Xiaoyu Xie - 通讯作者:
Xiaoyu Xie
The fundamental martingale with applications to Markov Random Fields
基本鞅及其在马尔可夫随机场中的应用
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Kevin Hu;Kavita Ramanan;William Salkeld - 通讯作者:
William Salkeld
On the large deviation rate function for marked sparse random graphs
关于有标记稀疏随机图的大偏差率函数
- DOI:
- 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
Kavita Ramanan;S. Yasodharan - 通讯作者:
S. Yasodharan
A Mimicking Theorem for processes driven by fractional Brownian motion
分数布朗运动驱动过程的拟态定理
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Kevin Hu;Kavita Ramanan;William Salkeld - 通讯作者:
William Salkeld
Kavita Ramanan的其他文献
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{{ truncateString('Kavita Ramanan', 18)}}的其他基金
Rare Events and High-Dimensional Stochastic Systems
稀有事件和高维随机系统
- 批准号:
2246838 - 财政年份:2023
- 资助金额:
$ 25万 - 项目类别:
Standard Grant
Interacting Particle Systems and Mean-field games Workshops
交互粒子系统和平均场游戏研讨会
- 批准号:
2207572 - 财政年份:2022
- 资助金额:
$ 25万 - 项目类别:
Standard Grant
Analysis of High-Dimensional Stochastic Systems
高维随机系统分析
- 批准号:
1954351 - 财政年份:2020
- 资助金额:
$ 25万 - 项目类别:
Continuing Grant
2018 Stochastic Networks Conference and Summer School in Applied Probability
2018年随机网络会议暨应用概率暑期学校
- 批准号:
1822084 - 财政年份:2018
- 资助金额:
$ 25万 - 项目类别:
Standard Grant
"High-dimensional random phenomena and rare events"
《高维随机现象和罕见事件》
- 批准号:
1713032 - 财政年份:2017
- 资助金额:
$ 25万 - 项目类别:
Continuing Grant
Women's Intellectual Networking Research Symposium
女性知识网络研究研讨会
- 批准号:
1727318 - 财政年份:2017
- 资助金额:
$ 25万 - 项目类别:
Standard Grant
Problems at the Interface of Stochastics and Analysis
随机学与分析的交叉问题
- 批准号:
1407504 - 财政年份:2014
- 资助金额:
$ 25万 - 项目类别:
Continuing Grant
Stability, Sensitivity and Optimization of Stochastic Systems
随机系统的稳定性、敏感性和优化
- 批准号:
1234100 - 财政年份:2012
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$ 25万 - 项目类别:
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Travel Grant for the Applied Probability Society Conference
应用概率学会会议旅费补助金
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1114608 - 财政年份:2011
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$ 25万 - 项目类别:
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Analysis of Large-Scale Stochastic Systems
大规模随机系统分析
- 批准号:
1052750 - 财政年份:2010
- 资助金额:
$ 25万 - 项目类别:
Standard Grant
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