From RG-Factorizations of Stochastic Models to Black Hole Effect in Big Networks

Release:2017-03-03 Viewed:26

Lecture

LecturerQuan-Lin Li  School of Economics and Management, Yanshan University

ThemeFrom RG-Factorizations of Stochastic Models to Black Hole Effect in Big Networks

TimeMarch 8 2017Wednesday16:00pm-1700pm

Place3rd Lecture room .

AbstractThis talk contains two parts: The first one is to introduce our research on numerical computation in general stochastic models. Our purpose is to extend and generalize the matrix-geometric solution by Marcel F. Neuts to be able to deal with more general Markov processes due to various needs. From more and more practical stochastic systems. To that end, we use the censoring technique to set up two types of (abbreviated as UDL-type and LDU-type) RG-factorizations for any irreducible Markov process and further for Markov reward processes and Markov decision processes. 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 transient performance measures of stochastic models in terms of the LDU-type (and UDL-type) RG-factorizations.The second part 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 the RG-factorizations to discussing nonlinear Markov processes from some practically large-scale stochastic systems including supermarket models, work stealing models, bike-sharing systems, healthcare systems and so forth. For some practical Big (Economy) Networks with active control mechanisms, we found that Black Hole Effect is a basic phenomenon. To understand the black hole effect, we develop three key topics: (a) Metastability, 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 from multiple stable domains. We establish useful relationship between network efficiency and network benefit under artificial control mechanisms. Therefore, our results provide some irregular characteristics and insights in the study of large-scale stochastic systems, and they may be useful in design, optimization, control and management of many real applied systems.