Tijms, Prof. dr H.C. (emeritus professor)

1. General

Name:Henk Tijms
born:23 April 1944 in Beverwijk (Wijk aan Duin), The Netherlands
work address:Dept of Econometrics
Vrije University
De Boelelaan 1105
1081 HV Amsterdam, The Netherlands
home address:Duinweg 20, 2082 CB Santpoort, The Netherlands

2. Education

1961HBS-B Diplom, Rijks HBS in IJmuiden.
1967Master Degree in Mathematics and Statistics, University of Amsterdam.
1972PhD Degree in Operations Research, University of Amsterdam.

3. Professional Experience

1967-1976Senior Researcher at the Center for Mathematics and Computer Science, Amsterdam.
1976-2009Full professor in Operations Research, Vrije University, Amsterdam.
1976-1983Advisor at the Center for Mathematics and Computer Science, Amsterdam.
1988-2000Advisor at the Shell Reseach Laboratorium, Amsterdam.
1988-2001Dutch Member of The International Advisory Board of the Teletraffic Congresses.

4. Miscellaneous

5. Awards

6. Recent Papers

  1. Optimal Control of a Queueing System with Heterogeneous Servers and Setup Costs (with R.D. Nobel), IEEE Transactions on Automatic Control, 45, 780 - 784, 2000.
  2. A Fast Algorithm for the Transient Reward Distribution in Continuous-Time Markov Chains (with R. Veldman), Operations Research Letters, 26, 155-158, 2000.
  3. Markov Processes on a Semi-infinite Strip and the Geometric Tail Algorithm (with D.J. van Vuuren), book series Annals of Operations Research 113 (ed. J. Artalejo), 133-140, 2002.
  4. A real-world stochastic two-person game (with J. van der Wal), Probability in the Engineering and Informational Sciences, 20, 599-608, 2006.
  5. Waiting-time probabilities in the M/G/1 retrial queue (with R. D. Nobel), Statistica Neerlandica, 60, 73-79, 2006.
  6. Negative probabilities at work in the M/D/1 queue (with Koen Staats), Probability in the Engineering and Informational Sciences, 21, 1-7, 2007.
  7. Dice games and stochastic dynamic programming, Morfismos (Mexican student journal), 11, 1-14, 2007.
  8. Bayesiaanse kansrekening (in Dutch), Euclides 4, 154-156, 2008.
  9. Stochastic games and dynamic programming, Asia Pacific Mathematics Newsletter, Vol. 2, No.3, 6-10, 2012, see pdf file.
  10. Devil's penny puzzle, New York Times, March 3, 2014.
  11. Dropping balls into bins, New York Times, February 9, 2015.
  12. Boys and girls in new clothes , New York Times, May 11, 2015.
  13. The gift exchange , New York Times, December 28, 2015.
Complete list of publications.

7. MCQueue: educational software for Markov Chains and Queues (non-commercial use)

This software package contains two modules. The first module is for the transient and steady-analysis of discrete-time and continuous-time Markov chains up to 100 states. The other module calculates performance measures including queue-length probabilities and waiting-time probabilities for basic queueing models (M/G/1 queue, M/M/c queue, M/D/c queue, G/M/c queue, M/M/c/c+N queue, the transient M/M/1 queue). The algorithms in this software package are based on methods discussed in the book H.C. Tijms, A First Course in Stochastic Models, Wiley, 2003. Download here the zip-file.

8. Orstat2000: educational software for applied probability and operations research

This software package is a polished and extended English version of software that was originally developed to promote probability and operations research in the senior forms of Dutch high schools (and early college). The software package contains modules for coin-tossing, roulette, Buffon's needle problem, central limit theorem, simulation of queues, traveling salesman problem, dynamic programming, linear programming, and integer programming amongst others. For non-commercial use, the full version of the software package ORSTAT2000 can be downloaded free of charge: Download here the zip-file.

9. Probability, A Lively Introduction, Cambridge University Press, 2017

There is no book I have written with more enthusiasm and dedication than this introductory textbook on probability. The students are the focal point, and much effort has been taken to make the book truly readable for them. Inessential technicalities are avoided wherever possible. There are some 750 problems and 150 examples, all carefully selected for being both appealing and illuminating. An important difference from other introductory probability books is the section of detailed solutions to all odd numbered problems, with the goal of actively engaging the student in the learning process.

A solutions manual with solutions to all problems is available to qualified university instructors who have adopted the book as a required text for their course. When sending a request for the solutions manual, please provide a syllabus and/or webpage for the course.

Available from Amazon

Review 1
Review 2
Review 3

10. New Probability Books

1. Surprises in Probability- Seventeen Short Stories, Chapman and Hall/CRC Press, 2018,


This book is appropriate for many different audiences, including students who want 'behind the scene' examples of probability to complement what they learn in class and teachers who want an easy source of instructive fun material for their students.

2. Basic Probability, What Every Math Student Should Know, World Scientific Press, 2019,

Basic Probability

This book has grown out of my activities to modernize and popularize the teaching of probability at Dutch high schools. It is a short book of 132 pages, but it covers all the essentials of probability for high school and college students learning about probability for the first time. In particular, the book gives much attention to conditional probability and Bayesian thinking and to the interface of probability and computer simulation.

11. Other Books

12. Kansrekening in Werking - een moderne aanpak

Dit Zebraboekje is een pleidooi voor de invoering van kansrekening als volwaardig wiskunde vak in de hogere klassen van het VWO. In het boekje wordt uitgewerkt hoe het vak op een moderne wijze ingevuld zou kunnen worden. Conditionele kansen met daaraan gekoppeld de Bayesiaanse denkwijze en de combinatie kansrekening en computer simulatie staan centraal. Het boekje is verschenen bij uitgeverij Epsilon in Amsterdam

13. Wiskunde-D module Optimalisering in Netwerken

Deze wiskunde-D module is een avontuurlijke reis langs niet-aangeharkte paden door het gebied van de optimalisering in netwerken en richt zich op leerlingen in 5 en 6 VWO. De module bevat uitdagende stof voor zowel leerling als leraar en laat zien welke boeiende toepassingen de wiskunde in de praktijk heeft. Vele praktische problemen in uiteenlopende gebieden kunnen worden geformuleerd als een optimaliseringsprobleem op een netwerk: kortste-pad probleem, handelsreizigersprobleem, routeringsproblemen, etc.
Om de pdf file van deze module te downloaden klik hier.

Click here for a cartoon on the Lotto.