排队论前沿问题研讨会

发布时间:2018年10月23日 作者:刘源远   消息来源:    阅读次数:[]


报告安排I

报告地点:数理楼小报告厅

报告时间:2018年10月31号(星期三)上午8:00-12:00

 

  1. 报告题目:A Kernel Method for Random Walks in the Quarter Plane

报告人:Yiqiang Q. Zhao 教授,Carleton University  

摘  要:Behaviour of multi-dimensional random walks is one of the

central focuses in probability, particularly in applied probability. Two-dimensional random walks are such examples. In this talk, we discuss stationary tail asymptotic properties for random walks in the quarter plane, which are random walks with reflective boundaries and find many important applications such as queueing systems. For a stable system, say a discrete-time ergodic two-dimensional (the state space in the quarter plane) Markov chain, the unique stationary distribution is one of the key performance metrics. However, except very few special cases, no closed form or explicit solutions for such systems. For this reason and also with its own importance, behaviour of tail asymptotics in the joint stationary distribution is a key topic in applied probability. We introduce a kernel method to study the behaviour and show that there is a total of four different types of tail asymptotics.

 

Based on joint work with Hui Li, Javad Tavakoli, and many others.

 

报告人简介: Yiqiang Q. Zhao, 加拿大卡尔顿(Carleton)大学教授,科学学院副院长。现为《Queueing Systems》、《Operation Research Letters》、《Stochastic Models》、《Advances in Operations Research》等国际期刊的编委。曾担任卡尔顿大学数学与统计系主任和加拿大统计学会概率分会主席。他在应用概率和排队论领域做出了很多开创性的工作,在国际同行里享有很高的声誉。他在《Advances in Applied Probability》、《Operations Research》、《Queueing System》、等国际一流学术刊物上发表论文100余篇,先后应邀多次在国际性的学术会议上作特邀报告。

 

 

  1. 报告题目 D-Dimensional Sticky Brownian Motions: Some Conjectures

报告人: 戴洪帅 副教授, 山东财经大学

Sticky Brownian motions as time-changed semimartingale reflecting Brownian motions have important applications in many fields such as queuing theory and mathematical finance. In this talk, we are concerned with stationary distributions of a general multidimensional sticky Brownian motion provided it is stable. We conjecture tail behaviors of their stationary distributions. Due to recent studies, these conjectures are true for some special cases.

 

报告人简介 戴洪帅博士2010年毕业于中南大学。2012-2013年在卡尔顿大学做博士后研究。 2015年至今,在山东财经大学统计学院工作。主要从事排队论、随机分析、应用统计的研究。近期的研究兴趣为多维反射过程的平稳分布的尾渐进性估计。

 

  1. 报告题目: A Complete Solution to Mean Field Linear Quadratic Control

报告人:王炳昌  副研究员, 山东大学

报告摘要: This work studies social optima and Nash games for mean field linear quadratic control systems, where subsystems are coupled via dynamics and individual costs.For the social control problem, we first obtain a set of forward-backward stochastic differential equations (FBSDE) from variational analysis, and construct a feedback-type control by decoupling the FBSDE. By using solutions of two Riccati equations, we design a set of decentralized control laws, which is further proved to be asymptotically social optimal. Two equivalent conditions are given for uniform stabilization of the systems in different cases.For the game problem, we first design a set of decentralized control from variational analysis, and then show that such set of decentralized control constitute an asymptotic Nash equilibrium by exploiting the stabilizing solution of a nonsymmetric Riccati equation.It is verified that the proposed decentralized control laws are equivalent to the feedback strategies of mean field control in previous works. This may illustrate the relationship between open-loop and feedback solutions of mean field control (games).

报告人简介王炳昌, 20083月在中南大学获得硕士学位; 2011 7 , 在中国科学院系统科学所获得博士学位; 201110—20129月,在加拿大阿尔伯塔大学做博士后; 2012 9 —20139月,在澳大利亚的纽卡斯尔大学做Research Academic; 201310至今,在山东大学控制科学与工程学院任副研究员。201411—20155月,访问加拿大卡尔顿大学,做Research Associate201611—20171月,访问香港理工大学,做Research Associate。曾获亚洲控制会议青年作者奖提名,IEEE, Beijing分会青年作者奖,目前担任中国自动化学会青年工作委员会委员,控制理论专委会随机学组委员。

 

  1. 报告题目:Necessary Conditions for the Compensation Approach for a Random Walk in the Quarter-plane

报告人:陈燕婷  助理教授, 湖南大学

报告摘要:We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a countably infinite sum of geometric terms which individually satisfy the interior balance equations. We demonstrate that the compensation approach is the only method that may lead to such type of invariant measure. In particular, we show that if a countably infinite sum of geometric terms is an invariant measure, then the geometric terms in an invariant measure must be the union of at most 6 pairwise-coupled sets of infinite cardinality each. We further show that for such invariant measure to be an infinite sum of geometric terms, the random walk cannot have transitions to the north, northeast or east. Finally, we show that for a countably infinite weighted sum of geometric terms to be an invariant measure at least one of the weights must be negative.

 

报告人简介:报告人陈燕婷本科毕业于湖南大学数学与计量经济学院,硕士与博士毕业与荷兰特文特大学(University of Twente)应用数学系,现为湖南大学数学与计量经济学院助理教授,主要研究方向为排队论及其相关应用。

 

 

报告安排II

报告地点:数理楼小报告厅

报告时间: 2018年10月31号(星期三)下午230-530

 

  1. 报告题目:$\beta$-Invariant Measures and Quasi-Stationary

Distributions for Block-Structured Markov Chains

报告人:Yiqiang Q. Zhao 教授

报告摘要:In this talk, we review results of $\beta$-invariant measures and quasi-stationary distributions for block-structured Markov chains, including Markov chains of $M/G/1$ type and $GI/M/1$ type to stimulate further research on other important aspects of properties, such as the uniqueness, domain of attraction problems, and the rate of convergence.

 

Based on joint work with Q-L Li.

 

报告人简介: Yiqiang Q. Zhao, 加拿大卡尔顿(Carleton)大学教授,科学学院副院长。现为《Queueing Systems》、《Operation Research Letters》、《Stochastic Models》、《Advances in Operations Research》等国际期刊的编委。曾担任卡尔顿大学数学与统计系主任和加拿大统计学会概率分会主席。他在应用概率和排队论领域做出了很多开创性的工作,在国际同行里享有很高的声誉。他在《Advances in Applied Probability》、《Operations Research》、《Queueing System》、等国际一流学术刊物上发表论文100余篇,先后应邀多次在国际性的学术会议上作特邀报告。

 

 

 

 

  1. 报告题目:Quasi-stationarity and Quasi-ergodicity of Absorbing Markov

Processes.

报告人:何国满 助理教授, 湖南商学院

报告摘要Quasi-stationary and quasi-ergodic distributions can capture the long term behavior of an absorbing Markov process conditioned on non-extinction. In this talk, we mainly talk about quasi-ergodic distributions of absorbing Markov processes. We give a sufficient condition for the existence of a quasi-ergodic distribution for absorbing Markov processes. Moreover, the quasi-ergodic distribution of birth-death processes and one-dimensional diffusion processes is also studied.

报告人简介:何国满,博士。2017年毕业于湘潭大学,获理学博士学位,现工作于湖南商学院,主要从事马氏过程的拟平稳分布和拟遍历分布的研究,在 Statistics and Probability LettersJournal of Mathematical Analysis and Applications Frontiers of Mathematics in MathematicsComptes Rendus Mathématique 等国际重要刊物上发表SCI学术论文多篇。

 

  1. 报告题目:Transience Classification for Block-structured Markov Chains

    报告人:李文迪 博士生, 中南大学

    报告摘要M/G/1-type and GI/M/1-type Markov chains are level independent matrix analytical models, which have proved very useful for characterizing the phase type queues. Stability properties have been investigated well for M/G/1 and GI/M/1-type Markov chains. In this talk, we will present explicit criteria for classification of instability including geometric transience and algebraic transience for these Markov chains. Possible extensions of the results to continuous-time Markov chains are also considered. The radius of convergence and the expression of quasi-stationary distribution are also examined for some special cases.

     

    报告人简介:李文迪,中南大学在读博士,主要从事马氏过程稳定性及相关领域研究。



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