[1] National Natural Science Foundation of China. Research on black hole effect, multi-stable domain and networking resource loss evaluation of large-scale networks. 2017.01-2020.12.

[2] National Natural Science Foundation of China. Nonlinear Markov process and super-exponential structure of supermarket networks under real-time queuing control. 2015.01-2018.12.

[3] National Natural Science Foundation of China. Research on random load balancing strategy and supermarket models of large-scale parallel queuing network. 2013.01-2016.12.

[4] National Natural Science Foundation of China. Research on multi-level approximation methods of self-similar networks and their performance models. 2009.01- 2011.12.

[5] National Natural Science Foundation of China. Stochastic models in network security and key techniques for performance evaluation. 2007.01-2009.12.

[6] National 973 Program (Tsinghua Sub-project). Stochastic methods in life science and network technologies. 2007.01-2011.12.

[7] National Natural Science Key Fund Project (Tsinghua Sub-project). Design, construction, modeling and analysis of engineering gene regulatory networks. 2008.01-2011.12.

[8] Hebei Natural Science Foundation Project. Research on multi-chain coupled queuing network and medical insurance incentive mechanism of hierarchical diagnosis and treatment and two-way referral. 2018.01-2020.12.

[9] Hebei Higher Education Innovation Team Leading Talent Program. Research on nonlinear calculation of large-scale network and risk           management of port coal supply chain management. 2014.01-2016.12.

[10] Hebei Natural Science Foundation Project. Research on hierarchical calculation and data management technologies for multi-dimensional                 stochastic models in network security. 2012.01-2014.12.

2018

Award Name: Best Paper Award.  The 7th International Conference on Computational Data and Social Networks.

Paper Name: Blockchain Queue Theory

Authors Name: Quan-Lin Li, Jing-Yu Ma, Yan-Xia Chang

2015

Award Name: International INFORMS Paper Award

Paper Name: Operational Performance Evaluation of Reverse Referral Partnership in the Chinese Healthcare System

Authors Name: Na Li, Nan Kong, Quan-Lin Li, Zhibin Jiang

2014

Award Name: The Second Prize of Hebei Science and Technologies (Natural Science)

Project Name: Research on Basic Theory of Numerical Calculation of Multidimensional Stochastic Models

Award Winners: Quan-Lin Li, Chuang Li, Na Li, Nai-shuo Tian

2013

Award Name: The Leading Talents Program of the Innovation Team of Hebei Higher Education Institutions

Project Name: Research on Nonlinear Calculation of Large-Scale Supermarket Network and Risk Management of Port Coal Supply Chain Management

Award Winner: Quan-Lin Li

2007

Award Name: The Second Prize of Beijing Science and Technologies (Natural Science)

Project Name: Basic Research on Computer Network Service Quality (QoS) Evaluation and Control

Award Winners: Chuang Li, Feng-yuan Ren, Hao Yin, Quan-Lin Li 

2005

Award Name: The First Prize of the Ministry of Education Science and Technologies (Natural Science)

Project Name: Stochastic Models and Performance Evaluation of Computer Systems

Award Winners: Chuang Li, Quan-Lin Li, Hao Yin, Feng-yuan Ren, Zhi-guang Shan, Zhang-xi Tan, Ya-ya Wei, Yang Qu

2004

Award Name: New Century Outstanding Talents of the Ministry of Education

Project Name: Research on the Calculation Method of Stochastic Network

Award Winner: Quan-Lin Li

2008

Award Name: Excellent courses in Beijing

Course Name: Operations Research

Award Winners: Xiaobo Zhao (Stochastic models), Hongxuan Huang (Optimal theory), Quan-Lin Li (Decision method)

2012, 2014, The 8, 9th International Conferences on Matrix-Analytic Methods in Stochastic Models. Technical Programme Committee, TPC member　

2007-2019, The 7, 8, 9, 11, 12th International Workshop on Retrial Queues. Technical Programme Committee, TPC Chairman or member　

2015-Now, The 14, 15, 16, 17, 18, 19, 20th International Conference (hosted in Russia) on Information Technology and Mathematical Modeling. International Program Committee, TPC member

2006-2017, The 3th to 12th International Conference on Queueing Theory and Network Applications. Technical Programme Committee, TPC member

1999-Now, The Vice Chairman, the Reliability Society of China Operations Research Society

2008-Now,  The Commentator of the American MathSciNet. Reviewer

The 8th International Workshop on Retrial Queues Conference. Chairman

The 12th International Conference on Queueing Theory and Network Applications Conference. Chairman.

(1)  Stochastic Models

In the study of stochastic models, our works focus on setting up a unified theoretic framwwork through using the RG-factorizations of, such as, Markov processes, Markov reward processes, Markov decision processes, stochastic games, evolutionary game and so on. See Li's 2010 Springer book: Constructive Computation in Stochastic Models with Applications: The RG-Factorizations. For the RG-factorizations, some interesting and useful remarks were given by  V. Vigon (2013):  LU-Factorization Versus Wiener-Hopf Factorization for Markov Chains.

So far, the RG-factorizations have played an important role in performance evaluation, optimization and dynamic decision for many practical stochastic systems. Using the RG-factorizations, we gave several more general and interesting results including the R-measure expression for the stationary probability vector, two types of expressions for the quasi-stationary probability vector, the general  solution to the Poisson equations, numerical methods for Markov processes, the mean-field theory of nonlinear Markov processes, stochastic games and evolutionary games. When applying general Markov processes, the RG-factorizations show a stronger applicable ability, for example, dealing with retrial queues, processor-sharing queues, fluid queues, matched queues; computer networks, manufacturing systems, blockchain systems, sharing economics, healthcare and so on.

(2)  RG-factorizations

Using the censoring technique (also called watched Markov chain given in Lévy [1951, 1952, 1958]), we systematically constructed and devoloped two types of RG-factorizations: 1) UL-type RG-factorization, and 2) LU-type RG-factorization. These RG-factorizations are very useful in the study of, such as, QBD processes, Markov processes, Markov renewal processes, Markov reward processes, Markov decision processes, stochastic game theory and others. Our recent works indicated that the two types of RG-factorizations play a different important role in the study of stochastic models, for example, a) the UL-type RG-factorization is a key to deal with stationary solution to stochastic models,  while LU-type RG-factorization can be used to analyze transient solution to stochastic models. We have an optimistic prediction that the RG-factorizations are very useful for sharpening many important research on stochastic processes, stochastic models, computer networks, manufacturing systems, transportation systems, biological sciences and others.

(3)  QBD processes

QBD processes provided a useful tool in the study of stochastic models, such as queueing systems, manufacturing systems, computer networks and so on. Chapter 3 of Neuts [1981] gave a complete picture of a level independent QBD process. Latouche and Ramaswami [1993] gave a logarithmic reduction algorithm for the rate matrix. Ramaswami [1996] gave an excellent overview for the QBD processes. Bright and Taylor [1995] provided some effective algorithms for computation of level dependent QBD processes. Naoumov [1996] proposed an algebraically matrix-multiplicative approach to study the stationary probability vector of a QBD process. Ramaswami and Taylor [1996] discussed useful properties of the rate operator in a level dependent QBD processes with a countable number of phases. Li and Cao [2004] gave two types of RG-factorizations, which lead to a unified and complete framework to deal with stationary or transient solution to various QBD processes. Li and Liu [2005] provided a sensitivity analysis for a perturbed QBD process. Nielsen and Ramaswami [1997] and Li and Lin [2006] studied QBD processes with continuous phases.

(4)  Quasi-stationary distributions

The study of the quasi-stationary behavior was initiated by Yaglom [33]. Since then, significant advances have been made through the efforts of many researchers, e.g., see a continuously updating overview by Pollett [2011]. For the quasi-stationary distributions of block-structured Markov chains, some preliminary results for Markov chains of GI/M/1 type and of M/G/1 type were obtained by Quan-Lin Li [1997], while a complete work were obtained in Li and Zhao [2002, 2003], and further results in Li's book [2010]. The quasi-stationarity distributions of the QBD processes can be found in Makimoto [1993], Bean, Bright, Latouche, Pearce, Pollett and Taylor [1997], and Bean, Pollett and Taylor [1998, 2000].

(5)  Sensitivity-based optimization theory

Infinitesimal perturbation analysis is a sensitivity-analytic technique for discrete event dynamic systems using single sample path performance measures. The basic approach is to obtain unbiased or strongly consistent estimates for derivatives of the stationary performance measures. For infinitesimal perturbation analysis of Markov chains, Cao, Yuan and Qiu [1996] proposed a novel approach in terms of the realization factor. Perturbation analysis of Markov chains is quite extensive, see Chapter 11 in Li's book: Constructive Computation in Stochastic Models with Applications: RG-Factorizations. Also, he further applied the perturbation analysis of Markov chains to dealing with ESS of stochastic evolutionary games.x

Li et al. applied the sensitivity-based optimization to the optimal energy saving strategy of data center in [2019, 2022], to the optimal dynamic rationing strategy of inventory systems in [2021, 2022], and to the optimal dynamic selfish-mining strategy of blockchain systems in [2022, 2023].

(6)  Mean-field theory, and nonlinear Markov processes

(7)  Sharing economy, and bike-sharing systems

(8)  Platform economy, and medical platform systems

(9)  Stochastic models of blockchain systems

(10)  Machine learning of stochastic models: Performance optimization, and dynamic decision

(11)  Network security

(12)  Multiple classes of queueing systems

Multiple-server queue with server vacation (conditional stochastic decomposition), queues with repairable servers (non-exponential life times), queues with negative customers, processor-sharing queues, fluid queues, matched queues, closed queueing networks.

    Dr. Quan-lin Li has completed the courses as follows:

(1) Service operation management

(2) Risk management

 (3) National Strategies: A Perspective of Chinese History, Culture, Art and Religion