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悬殊报告四十七:From RG-Factorizations to Black Hole Effect in Stochastic Models

来源:数学与统计学院     作者:     时间:2016/11/2 9:45:31  0次

数学与统计院学术报告[2016] 047号

(高水平大学建设系列报告059)

讲座题目: From RG-Factorizations to Black Hole Effect in Stochastic Models

讲座人:   李泉林  教授  (燕山大学)

讲座时间:2016112 1500--1600

讲座地点:   科技楼   514                               

报告内容:This talk contains two parts: The first one is to introduce our research on numerical computation in general stochastic models from 1997 to 2009. Our purpose is to extend and generalize the matrix-geometric solution by Marcel F. Neuts to be able to deal with more general stochastic models due to those practical needs from more and more stochastic systems. To that end, we found two types of (abbreviated as UDL-type and LDU-type) RG-factorizations from any irreducible Markov process (and other processes) through a constructive censoring technique with higher skill. Our results are simple and beautiful, and also they are easily applicable to computation of the steady-state probability vectors of general Markov processes by means of the UDL-type RG-factorization as well as calculation of various transient performance measures of stochastic models in terms of the LDU-type RG-factorization. Notice that our research improves and develops Neuts’ theory into a new and unified framework because of applying the UDL-type and LDU-type RG-factorizations.Some detailed information is given in my book: Constructive Computation in Stochastic Models with Applications: The RG-Factorizations, Springer, 2010; and its Springer homepage:

http://link.springer.com/book/10.1007/978-3-642-11492-2

The second one of this talk is to introduce our works on Nonlinear Markov Processes in Big Networks through mean-field theory and RG-factorizations. We have applied the mean-field theory as well as RG-factorizations to discuss such nonlinear Markov processes from practically large-scale stochastic systems including supermarket models, work stealingmodels, bike-sharing systems and healthcare systems. Based on this, we found that Black Hole Effect is a basic phenomenon in Big (Economy) Networks. For understanding the black hole effect, we are developing three key topics: (a) Multiple stable domains, and cross-domain movement; (b) existence of black hole effect, and metrology of black hole effect; and (c) loss of resources from black hole effect, and useful relationship between network efficiency and network benefit under artificial control mechanisms. Our results provide some irregular characteristics and insight in the study of large-scale stochastic systems, which may be useful in design, optimization, control and management of many real applied systems.


报告人简历:李泉林教授、博士生导师,1998年毕业于中国科学院应用数学所,先后访问过University of Winnipeg, Carleton University, Complutense University of Madrid, University of Hong Kong, Hong Kong University of Science and Technology, Chinese University of Hong Kong, University of Macau 等学校,主持和参与国家自然科学基金6项,入选2004 年教育部“新世纪优秀人才支持计划” ,在国内外重要学术期刊和会议发表论文50多篇。

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数学与统计学院

2016-11-02

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