Multilevel Approximations of Markovian Jump Processes with Applications in Communication Networks

Handle URI:
http://hdl.handle.net/10754/552664
Title:
Multilevel Approximations of Markovian Jump Processes with Applications in Communication Networks
Authors:
Vilanova, Pedro ( 0000-0001-6620-6261 )
Abstract:
This thesis focuses on the development and analysis of efficient simulation and inference techniques for Markovian pure jump processes with a view towards applications in dense communication networks. These techniques are especially relevant for modeling networks of smart devices —tiny, abundant microprocessors with integrated sensors and wireless communication abilities— that form highly complex and diverse communication networks. During 2010, the number of devices connected to the Internet exceeded the number of people on Earth: over 12.5 billion devices. By 2015, Cisco’s Internet Business Solutions Group predicts that this number will exceed 25 billion. The first part of this work proposes novel numerical methods to estimate, in an efficient and accurate way, observables from realizations of Markovian jump processes. In particular, hybrid Monte Carlo type methods are developed that combine the exact and approximate simulation algorithms to exploit their respective advantages. These methods are tailored to keep a global computational error below a prescribed global error tolerance and within a given statistical confidence level. Indeed, the computational work of these methods is similar to the one of an exact method, but with a smaller constant. Finally, the methods are extended to systems with a disparity of time scales. The second part develops novel inference methods to estimate the parameters of Markovian pure jump process. First, an indirect inference approach is presented, which is based on upscaled representations and does not require sampling. This method is simpler than dealing directly with the likelihood of the process, which, in general, cannot be expressed in closed form and whose maximization requires computationally intensive sampling techniques. Second, a forward-reverse Monte Carlo Expectation-Maximization algorithm is provided to approximate a local maximum or saddle point of the likelihood function of the parameters given a set of observations. The third part is devoted to applications in communication networks where also mean field or fluid approximations techniques, to substantially reduce the computational work of simulating large communication networks are explored. These methods aim to capture the global behaviour of systems with large state spaces by using an aggregate approximation, which is often described by means of a non-linear dynamical system.
Advisors:
Tempone, Raul ( 0000-0003-1967-4446 )
Committee Member:
Keyes, David E. ( 0000-0002-4052-7224 ) ; Gomes, Diogo; Shihada, Basem ( 0000-0003-4434-4334 ) ; Djehiche, Boualem
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
4-May-2015
Type:
Thesis
Appears in Collections:
Applied Mathematics and Computational Science Program; Theses; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorTempone, Raulen
dc.contributor.authorVilanova, Pedroen
dc.date.accessioned2015-05-12T13:22:51Zen
dc.date.available2015-05-12T13:22:51Zen
dc.date.issued2015-05-04en
dc.identifier.urihttp://hdl.handle.net/10754/552664en
dc.description.abstractThis thesis focuses on the development and analysis of efficient simulation and inference techniques for Markovian pure jump processes with a view towards applications in dense communication networks. These techniques are especially relevant for modeling networks of smart devices —tiny, abundant microprocessors with integrated sensors and wireless communication abilities— that form highly complex and diverse communication networks. During 2010, the number of devices connected to the Internet exceeded the number of people on Earth: over 12.5 billion devices. By 2015, Cisco’s Internet Business Solutions Group predicts that this number will exceed 25 billion. The first part of this work proposes novel numerical methods to estimate, in an efficient and accurate way, observables from realizations of Markovian jump processes. In particular, hybrid Monte Carlo type methods are developed that combine the exact and approximate simulation algorithms to exploit their respective advantages. These methods are tailored to keep a global computational error below a prescribed global error tolerance and within a given statistical confidence level. Indeed, the computational work of these methods is similar to the one of an exact method, but with a smaller constant. Finally, the methods are extended to systems with a disparity of time scales. The second part develops novel inference methods to estimate the parameters of Markovian pure jump process. First, an indirect inference approach is presented, which is based on upscaled representations and does not require sampling. This method is simpler than dealing directly with the likelihood of the process, which, in general, cannot be expressed in closed form and whose maximization requires computationally intensive sampling techniques. Second, a forward-reverse Monte Carlo Expectation-Maximization algorithm is provided to approximate a local maximum or saddle point of the likelihood function of the parameters given a set of observations. The third part is devoted to applications in communication networks where also mean field or fluid approximations techniques, to substantially reduce the computational work of simulating large communication networks are explored. These methods aim to capture the global behaviour of systems with large state spaces by using an aggregate approximation, which is often described by means of a non-linear dynamical system.en
dc.language.isoenen
dc.subjectinference for continuous-timeen
dc.subjectMarkov Chainsen
dc.subjecterror controlen
dc.subjectweak approximationen
dc.subjectmultilevel monte carloen
dc.subjectchernoff tau-leapen
dc.titleMultilevel Approximations of Markovian Jump Processes with Applications in Communication Networksen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberKeyes, David E.en
dc.contributor.committeememberGomes, Diogoen
dc.contributor.committeememberShihada, Basemen
dc.contributor.committeememberDjehiche, Boualemen
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id102008en
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