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Bernd Heidergott
Affiliation
Vrije Universiteit
Faculty of Economics and Business
Administration
Department
of Department of Econometrics and Operations Research
Research fellow
Tinbergen Institute and EURANDOM.
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E-mail: bheidergott [at] feweb [dot] vu
[dot] nl
Phone: 0031 +20 +5986016
Fax: 0031 +20 +5986020
Bernd Heidergott has received the Best Lecturer Award of the faculty of Economics and Business Administration of the VU for the academic year 2008/2009.
Index: Research
Activities, Publications, Career, Grants and Fellowships and Teaching
My main current research
directions are as follows:
Gradient Estimation is concerned with providing unbiased gradient
estimators for stochastic networks. We have worked on the main approaches in
this area such as infinitesimal perturbation analysis (IPA), smoothed
perturbation analysis (SPA), finite perturbation analysis (FPA), rare
perturbation analysis (RPA), score function (SF) and phantom estimators
(originating from measure-valued differentiation). In case studies comparing
the performance of the estimators we could show that phantom estimators have
the potential to outperform single-run gradient estimators like IPA, SPA of SF
(which goes against the common belief in the simulation community). Recently we
obtained first analytical results supporting this finding. This is joint work
with F. Vázquez-Abad.
Differentiation
theory for Markov
chains seeks sufficient conditions for differentiability of performance
characteristics of Markov chains and tries to obtain closed-form analytical
expressions for the derivatives. The research in this area is the driving force
in our attempt to unify gradient estimation and to develop a deeper
understanding of stochastic optimization. We have intensively worked on this
topic and could show that MVD in deed allows for a unified approach to gradient
estimation. A recent breakthrough result is that we could show existence of
derivatives of a particular class of Markov chains (phase-homogeneous random
walks) under substantially weaker conditions than known in the literature.
Furthermore, we have established an important link between differentiation
theory and Banach space theory. This is joint work
with A. Hordijk.
An overview on the state-of-the-art in MVD can be found here (pdf file) .
Max-plus algebra is an algebraic approach to discrete event dynamic
systems, like queuing networks, that are prone to synchronization. Max-plus
algebra has been the main theme of the European research project ALAPEDES. Based on
the weak differentiation approach, we developed a calculus of weak
differentiation for max-plus-linear stochastic systems. Based on this
framework, we established Taylor series expansions for max-plus linear systems. Together with G. J. Olsder and J. van der Woude we have written a
book on deterministic max-plus algebra. Our work on stochastic max-plus algebra
and Taylor series expansions has been published in a monograph. Recent work is concerned
with ergodic theory of stochastic max-plus linear
stochastic systems. For more on max-plus algebra please visit the max-plus web portal. Slides of a tutorial
held on max-plus algebra at the IFORS 2002 conference in Edinburgh, UK, can be
found here (pdf file).
Index
Books:
Max-Plus linear
Stochastic Systems and Perturbation Analysis.
The International Series of Discrete Event Systems 15, Springer,
ISBN: 978-0-387-35206-0 (2007). (contact publisher)
Max Plus at Work - Modeling and Analysis of Synchronized Systems (with G. J. Olsder and J. van der Woude)
Princeton Series in Applied Mathematics, Princeton University Press,
ISBN: 978-0-691-11763-8 (2006). (contact
publisher)
Train
Movement Analysis at Railway Stations: Procedures and Evaluation of Wakob's Approach (with A. de Kort, R.
van Egmond and G. Hooghiemstra)
Studies in
Transport Series No. S99/1,
ISBN: 90-407-1855-5 (1999). (contact publisher)
Sample-Path
Analysis for Stochastic Networks (in German)
Forschungsergebnisse
zur Informatik 10, Verlag Dr. Kovac,
ISBN:
978-3-86064-086-9 (1996). (contact publisher)
Contributions
to books
A paradigm
for derivatives of positive systems.
In Lecture Notes in Control and Information Sciences, vol. 294, pages
312-328, Springer,
ISBN: 3-540-4034206 (2003).
Weak
Differentiation and Gradient Estimation for Discrete Event Processes (with F.
Vázquez-Abad).
In Discrete Event Systems: Analysis and Control, pages 433-440, Kluwer,
ISBN: 0-7923-7897-0 (2000)
GSMP with
discrete lifetime distributions.
In Lecture Notes in Control and Information Sciences vol. 199, pages
456-462. Springer, ISBN: 0-387-19896-2 (1994).
Journal Papers:
Weak differentiability of product measures
(with H. Leahu)
Mathematics of Operations Research (in press)
Gradient estimation for a multi-component maintenance system using measure-valued differentiation (with T. Farenhorst-Yuan) Operations Research (in press)
Series expansions for continuous-time Markov chains (with A. Hordijk and N. Leder) Operations Research (in press)
An Approximation Approach for the Deviation Matrix of Continuous-Time Markov Processes with Application to Markov Decision Theory (with N. Leder and A. Hordijk). Operations Research (in press)
A perturbation analysis approach to phantom estimators for waiting times in the G/G/1 queue (with F. Vázquez-Abad and T. Farenhorst-Yuan). Discrete Event Dynamic Systems (accepted January 2009)
Gradient estimation for discrete-event systems by measure-valued differentiation (with F. Vázquez-Abad, G. Pflug and T. Farenhorst-Yuan). Transactions on Modeling and Computer Simulation (accepted January 2009).
Strong bounds on perturbations (with H. Leahu).
Mathematical Methods of Operations Research
vol. 70, pages 99-127, 2009.
Gradient estimation for a class of systems with bulk arrivals: a problem in public transportation (with F. Vázquez-Abad). Transactions on Modeling and Computer Simulation
vol. 19, issue 3, article 13 (27 pages), 2009. Derivatives of Markov kernels and their Jordan decomposition (with A. Hordijk
and H. Weiβhaupt) Sensitivity Estimation for Gaussian Systems (with F. Vázquez-Abad
and W. Volk-Makarewicz). European Journal of
Operational Research vol. 187, pages 193-207, 2008. A Note on Gradient Estimation for Maintenance Systems (with T. Yuan). IEEE Transactions on Automatic Control vol. 52, pages 2131-2145, 2007.
from 9/2002
until today Department
of Econometrics and Operations Research, Faculty of Economics and Business
Administration, Vrije Universiteit
Amsterdam from
3/2001 to 8/2002 Operations Research and
Statistics, Department of Mathematics and Computer Science, Division of
Mathematics, TU Eindhoven from
8/1999 to 2/2001 EURANDOM from
4/1997 to 7/1999 DIAM,
Department of Information Technology and Systems from
5/1996 to 3/1997 Econometric Institute,
Faculty of Economics, from
3/1992 to 4/1992 Center
of Mathematical Statistics and Stochastic Processes, Department of
Mathematics, University of STW grant for research project Modeling and
Analysis of Operations in Railway Networks: the Influence of Stochasticity. This is a joint project together with F.M. Dekking,
I. Hansen and L. Meester, which will run from October 2003 to September
2007. Deutsche Forschungsgemeinschaft (DFG) Fellowship, from August 1, 1999, to
July 31, 2001. Verein
zur Förderung der Versicherungswissenschaft in Hamburg , Fellowship from October 1, 1995, to May
31, 1996. Wilhelm-Blaschke-Stiftung, travel grants, June 1994 and July 1995. At the Vrije Universiteit Amsterdam I am mainly involved in
teaching mathematics and statistics for economists. In addition, I am teaching
a course on Convex Analysis and Optimization for econometricians.
Journal of Applied Analysis vol. 14, pages 13-26, 2008.
Measure valued differentiation for Markov chains (with F. Vázquez-Abad).
Journal of Optimization and Applications vol. 136, pages 187-209, 2008.
(Web Supplement)
Complexity reduction in MPC for stochastic max-plus-linear
discrete event systems by variability expansion (with T.J.J. van den Boom and B. de Schutter).
Automatica vol. 43, pages 1058-1063, 2007.
Series expansions for finite-state Markov chains (with A. Hordijk
and M. van Uitert).
Probability in Engineering and Informational Sciences vol. 21, pages 381-400, 2007.
Measure-valued differentiation for random horizon problems (with F. Vázquez-Abad).
Measure-valued differentiation for stationary Markov chains (with A. Hordijk
and H. Weiβhaupt)
Mathematics of Operations Research, vol. 31, pages 154-172, 2006.
Single-run gradient estimation via measure-valued differentiation (with A. Hordijk).
IEEE Transactions on Automatic Control , vol. 49, pages 1843-1846, 2004
Advances in Applied Probability, vol. 23, no. 4, pages 1046-1070, 2003.
See also Correction: Taylor series expansions for stationary Markov chains;
Advances in Applied Probability, vol. 36, no. 4, page 1300, 2004.
A probabilistic approach for determining railway
infrastructure capacity (with A. de Kort, and H. Ayhan). European Journal of Operational
Research, vol. 148, pages 644-661, 2003.
A note on the relation between realization probabilities and
weak derivatives (with X.R. Cao ).
IEEE Transactions on Automatic Control, vol. 47, pages 1112-1115, 2002.
Towards a control theory for transportation networks (with R. de Vries).
Discrete Event Dynamic Systems, vol. 11, pages 371-398, 2001.
A differential calculus for random matrices with applications to (max,+)-linear
stochastic systems. Mathematics of Operations Research, vol. 26,
pages 679-699, 2001.
Option
pricing via Monte Carlo Simulation: A weak derivative approach.
Probability in Engineering and Informational Sciences, vol. 15, pages
335-349, 2001.
A weak
derivative approach to optimization of threshold parameters in a
multi-component maintenance system.
Journal of Applied Probability, vol. 38, pages 386-406, 2001.
Analyzing sojourn times in queuing networks: a structural approach.
Mathematical Methods of Operations Research, vol. 52, pages 115-132,
2000.
A characterization for (max,+)-linear queuing systems.
Queuing Systems: Theory and Applications, vol. 35, pages 237-262, 2000.
Customer-oriented finite perturbation analysis for queuing networks.
Discrete Event Dynamic Systems, pages 201-232, 2000.
Optimization
of a single-component maintenance system: a smoothed perturbation analysis
approach.
European Journal of Operations Research, pages 181-190, 1999.
Infinitesimal perturbation analysis for queuing networks with general service
time distributions Queuing Systems: Theory and Applications, pages
43-58, 1999.
The zero utility principle for scale families of risk distributions ( with D.
Pfeifer).
Deutsche Gesellschaft fürVersicherungsmathematik,
pages 711-722, 1996.
Sensitivity
analysis of a manufacturing workstation using perturbation analysis techniques.
International Journal of Production Research, vol. 33, pages 611-622,
1995.
Conferences with Refereed Proceedings:
Railway timetable stability analysis using stochastic max-plus linear systems
(with R. Goverde, and G. Merlet).
Proceedings 3rd International Seminar on Railway Operations Modelling and Analysis, Zürich, Switzerland, pages 1-18, 2009.
Perturbation analysis of Markov chains.
International Workshop on DES (WODES' 08), Göteborg, Sweden,
pages 99-104, 2008.
Stochastic optimization for control for maintenance systems (with T. Farenhorst-Yuan).
International Workshop on DES (WODES' 08), Göteborg, Sweden, pages 93-98, 2008.
A fast approximation algorithm for the Lyapunov exponent of stochastic max-plus systems
(with R. Goverde and G. Merlet).
International Workshop on DES (WODES' 08), Göteborg, Sweden, pages 49-54, 2008.
Bounds on Perturbations for DES (with A. Hordijk and H. Leahu)
International Workshop on DES (WODES 06), Ann Arbor,
USA, pages 378-383, 2006.
Asymptotic growth rate of stochastic max-plus systems that with a positive
probability have a sunflower-like support (with J. van der Woude).
International Workshop on DES(WODES 06),
Ann Arbor, USA, pages 451-456, 2006.
Series Expansions of Generalized Matrix Products (with H. Leahu).
Proceedings of the CDC, Seville, Spain, pages 7793-7798,
2005.
On choosing the right gradient estimator.
5th St. Petersburg Workshop on Simulation, St. Petersburg, Russia, June
26 - July 2, pages 313-318, 2005.
An ergodic theorem for stochastic max-plus
linear systems (with J. van der Woude and G. J. Olsder).
International Workshop on DES (WODES'04), Reims,
France, pages 97-102, 2004.
Gradient estimation for a problem in public transportation: A comparison of
SPA, SF and MVD (with F. Vázquez-Abad).
International Workshop on DES (WODES'04), Reims,
France, pages 241-246, 2004.
A paradigm for derivatives of positive systems.
Lecture Notes in Control and Information Sciences, vol. 294, Springer,
pages 312-328, 2003.
Complexity reduction in MPC for stochastic max-plus-linear
systems by variability expansion (with T.J.J. van den Boom and B. de Schutter).
Proceedings of the CDC, Las Vegas, Nevada, USA, pages 3567-3572, 2002.
Variability expansion for performance characteristics of (max,plus)-linear
systems.
International Workshop on DES (WODES'02), Zaragoza,
Spain, pages 245-250, 2002.
Sensitivity
analysis of joint characteristics of (max,+)-linear queuing networks.
IFAC satellite workshop on (max,+) algebra, Prague, Czech Republic,
pages 221-226, 2001.
Bounding
the Coupling Time of (Max,+)-Linear Systems (with Soto y Koelemeijer).
Transport, Infrastructure and Logistics, 6th TRAIL annual congress, The
Hague, the Netherlands, 2000.
Weak
differentiation and gradient estimation for discrete event processes (with F. Vázquez-Abad).
Discrete Event Systems: Analysis and Control, Kluwer
Academic Publisher, proceedings of the WODES (WODES'00), Gent, Belgium, pages
433-440, Kluwer, Boston, 2000.
Optimization
of synchronization constraints via weak derivatives.
International Workshop on DES (WODES'98), Cagliari,
Italy, pages 261-266. IEE, London, 1998.
Modeling
and Analysis of queuing processes at railway stations: a case study (with R.-J.
van Egmond, A. de Kort, and G. Hooghiemstra).
Transport, Infrastructure and Logistics, 4th TRAIL annual
congress, The Hague, the Netherlands, 1998.
An overview
of waiting time approximations for single server queues (with R.-J. van Egmond, A. de Kort, and G. Hooghiemstra).
Transport, Infrastructure and Logistics, 4th TRAIL annual
congress, The Hague, the Netherlands, 1998.
A stochastic minimal headway model for trains (with R.-J. van Egmond, A. de Kort, and G. Hooghiemstra).
Transport, Infrastructure and Logistics, 4th TRAIL annual
congress, The Hague, the Netherlands, 1998.
GSMP with
discrete lifetime distributions.
Lecture Notes in Control and Information Sciences, vol. 199, Springer,
London, pages 456-462, 1994.
Sensitivitätsanalyse eines Fertigungssystems mit Hilfe der infinitesimalen Perturbationsanalyse (Sensitivity analysis for a
manufacturing system using IPA).
ASIM91, Hagen, Germany, 1991.
Infinitesimal
perturbation analysis: an overview.
Methods of OR, vol. 64, Vienna, Austria, pages 163-172, 1990.
Perturbation
analysis, concept of an implementation.
SCS European Simulation Multiconference, Erlangen-Nürnberg, Germany, pages 192-197, 1990.