Berkhout, J.

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Topics in Markov Chain Theory and Simulation Optimisation

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VU Research PortalTopics in Markov Chain Theory and Simulation OptimisationBerkhout, J.2016document versionPublisher's PDF, also known as Version of recordLink to publication in VU Research Portalcitation for published version (APA)Berkhout, J. (2016). Topics in Markov Chain Theory and Simulation Optimisation. Amsterdam BusinessResearch Institute.General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.E-mail address:vuresearchportal.ub@vu.nlDownload date: 23. May. 2021JOOST BERKHOUTTOPICS IN MARKOV CHAIN THEORY AND SIMULATION OPTIMISATION  AMSTERDAM IN SCIENCE,BUSINESS AND SOCIETY ABRI AMSTERDAM BUSINESS RESEARCH INSTITUTEWWW.ABRI.VU.NLTOPICS IN MARKOV CHAIN THEORY AND SIMULATION OPTIMISATIONThis thesis covers an improvement of a general purpose simulation optimisation algorithm and the following topics from Markov chains: • Parameter insecurity analysis of Jackson networks which allow simultaneous breakdowns and repairs of nodes. • Existing perturbation bounds found in literature are compared and analysed. A novelty is that the relative error of these bounds is considered. A new perturbation bound is introduced that has the attractive feature that this relative error vanishes as the size of the perturbation tends to zero. Existing bounds such as the condition number bounds lack this feature in general.• An efficient approximation method for the ergodic projector of Markov multi-chains is introduced and analysed which ensures a ‘jump start’ towards ergodicity using a power method alike approach, it is therefore called the jump start power method.• The techniques from the jump start power method are further developed into an efficient approximation framework for the, in Markov chain theory fundamental, deviation matrix. The approximation is applied to community detection in social networks and statistical cluster analysis.• A generalized ranking methodology based on Markov multi-chain structures is proposed that ensures more careful rankings of nodes in networks compared to the acclaimed Google PageRank.JOOST BERKHOUT Joost Berkhout (1990) obtained his BSc and MSc (Cum Laude) degrees in the field of Econometrics and Operations Research at the Vrije Universiteit Amsterdam (in 2011 and 2012, resp.). In 2012 he joined the Amsterdam Business Research Institute (ABRI) Junior Research Programme which allowed him to enter the three-year ABRI PhD program in 2013. During his PhD Joost was awarded with the Student Best Paper Award at the International Workshop on Discrete Event Systems (WODES) 2016 in Xi’an (China). In September 2016 Joost started as a post-doctoral researcher at the Centrum Wiskunde & Informatica (CWI). ISBN: 978 90 5170 831 8TOPICS IN MARKOV CHAIN THEORY AND SIMULATION OPTIMISATION17 JOOST BERKHOUT

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JOOST BERKHOUT
TOPICS IN MARKOV CHAIN 
THEORY AND SIMULATION 
OPTIMISATION
  
AMSTERDAM 
IN SCIENCE,
BUSINESS 
AND SOCIETY 
ABRI 
AMSTERDAM BUSINESS RESEARCH INSTITUTE
WWW.ABRI.VU.NL
TOPICS IN MARKOV CHAIN 
THEORY AND SIMULATION 
OPTIMISATION
This thesis covers an improvement of a general purpose simulation optimisation algorithm and the following topics 
from Markov chains: 
• Parameter insecurity analysis of Jackson networks which allow simultaneous breakdowns and repairs of nodes. 
• Existing perturbation bounds found in literature are compared and analysed. A novelty is that the relative 
error of these bounds is considered. A new perturbation bound is introduced that has the attractive feature 
that this relative error vanishes as the size of the perturbation tends to zero. Existing bounds such as the 
condition number bounds lack this feature in general.
• An efficient approximation method for the ergodic projector of Markov multi-chains is introduced 
and analysed which ensures a ‘jump start’ towards ergodicity using a power method alike approach, 
it is therefore called the jump start power method.
• The techniques from the jump start power method are further developed into an efficient 
approximation framework for the, in Markov chain theory fundamental, deviation matrix. The 
approximation is applied to community detection in social networks and statistical cluster 
analysis.
• A generalized ranking methodology based on Markov multi-chain structures is 
proposed that ensures more careful rankings of nodes in networks compared to the 
acclaimed Google PageRank.
JOOST BERKHOUT 
Joost Berkhout (1990) obtained his BSc and MSc (Cum Laude) degrees in 
the field of Econometrics and Operations Research at the Vrije Universiteit 
Amsterdam (in 2011 and 2012, resp.). In 2012 he joined the Amsterdam 
Business Research Institute (ABRI) Junior Research Programme 
which allowed him to enter the three-year ABRI PhD program in 
2013. During his PhD Joost was awarded with the Student Best 
Paper Award at the International Workshop on Discrete Event 
Systems (WODES) 2016 in Xi’an (China). In September 2016 
Joost started as a post-doctoral researcher at the Centrum 
Wiskunde & Informatica (CWI). 
ISBN: 978 90 5170 831 8
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