Stochastic Operations Research
Department of Applied Mathematics
University of Twente
P.O. Box 217
7500 AE Enschede, The Netherlands
Phone: (+0031) 534893940
Fax: (+0031) 534894833
Abstract Thesis (download)
“Random walks in the quarter-plane: invariant measures and performance bounds”
This monograph focuses on random walks in the quarter-plane. Such random walks are frequently used to model queueing systems and the invariant measure of a random walk is of major importance in studying the performance of these systems. In special cases the invariant measure of a random walk can be expressed as a geometric product-form and performance measures can readily be obtained. In general, however, no tractable closed-form expressions are available for the invariant measure and exact performance measures are not readily obtained. The aim of this monograph is two-fold. On one hand we consider measures that are a sum of geometric terms. We characterize the random walks in the quarter-plane of which the invariant measure is of this form. This extends the class of random walks for which tractable closed-form results can be obtained. On the other hand we develop approximation schemes that provide analytical upper and lower bounds on performance for the case that no tractable closed-form expressions for the invariant measure are available.
B.S. Mathematics and Applied Mathematics, Hunan University, China, Sep’2004-Jun’2008.
M.S. Applied Mathematics, University of Twente, The Netherlands, Sep’2008-Jul’2010.
Ph.D. candidate, Applied Mathematics, University of Twente, The Netherlands, Sep’2010-present.
Y. Chen, R.J. Boucherie, J. Goseling. The invariant measure of random walks in the quarter-plane: representation in geometric terms. arXiv:1207.5335v4 Accepted by Probability in the Engineering and Informational Sciences.
Y. Chen, R.J. Boucherie, J. Goseling. Necessary conditions for the invariant measure of
a random walk to be a sum of geometric terms. arXiv:1304.3316v2 Submitted for publication.
Conference and Seminar Presentations
The Applied Probability Society Conference, Stockholm, Sweden, July 6-8, 2011.
36th Dutch National OR Conference, Lunteren, The Netherlands, January 17-19, 2012.
Scaling Limits of Random Walks in The Quarter Plane, Eurandom, Eindhoven, The Netherlands, February,13, 2012.
The Applied Probability Society Conference, San Jose, Costa Rica, July 15-17, 2013.
47th Dutch Mathematical Congress, Enschede, The Netherlands, April 14-15, 2011.
3TU.AMI Spring festival, Eindhoven, The Netherlands, May 9, 2011.
CTIT symposium, Enschede, The Netherlands, June 18, 2012.
The Young European Queueing Theorists (YEQT) workshop, VII, November 4-6, 2013.
Teaching assistant. LNMB master course Queueing Theory, Spring 2011.
Teaching assistant. LNMB master course Queueing Theory, Spring 2013.
Honorable mention for the poster contest in 3TU.AMI Spring festival, May 9, 2011.
University of Twente Scholarship. Sep’2008-Aug’2010.