## Stochastic Operations Research

Department of Applied Mathematics

University of TwenteP.O. Box 217

P.O. Box 217

7500 AE Enschede, The Netherlands

Phone: (+0031) 534893940

Fax: (+0031) 534894833

Email: y.chen’at’utwente.nl

Welcome to my homepage. I graduated in Stochastic Operations Research(SOR) at the University of Twente, supervised by Professor Richard Boucherie and Dr Jasper Goseling.

**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.

## Education

- 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.

## Publications

- 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.

## Posters

- 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 activities

- Teaching assistant. LNMB master course Queueing Theory, Spring 2011.
- Teaching assistant. LNMB master course Queueing Theory, Spring 2013.

## Awards

- Honorable mention for the poster contest in 3TU.AMI Spring festival, May 9, 2011.
- University of Twente Scholarship. Sep’2008-Aug’2010.