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Continuum limits of Markov chains with application to wireless network modeling and control

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dc.contributor.authorZhang, Yang, author
dc.contributor.authorChong, Edwin K. P., advisor
dc.contributor.authorEstep, Donald, committee member
dc.contributor.authorLuo, J. Rockey, committee member
dc.contributor.authorPezeshki, Ali, committee member
dc.date.accessioned2007-01-03T06:39:02Z
dc.date.available2007-01-03T06:39:02Z
dc.date.issued2014
dc.description.abstractWe investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model networks with a very large number of nodes. We show that a sequence of such Markov chains indexed by N , the number of components in the system that they model, converges in a certain sense to its continuum limit, which is the solution of a partial differential equation (PDE), as N goes to infinity. We provide sufficient conditions for the convergence and characterize the rate of convergence. As an application we approximate Markov chains modeling large wireless networks by PDEs. We first describe PDE models for networks with uniformly located nodes, and then generalize to networks with nonuniformly located, and possibly mobile, nodes. While traditional Monte Carlo simulation for very large networks is practically infeasible, PDEs can be solved with reasonable computation overhead using well-established mathematical tools. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierZhang_colostate_0053A_12175.pdf
dc.identifier.urihttp://hdl.handle.net/10217/82486
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectpartial differential equations
dc.subjectnetwork modeling
dc.subjectmodeling
dc.subjectMarkov processes
dc.titleContinuum limits of Markov chains with application to wireless network modeling and control
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineElectrical and Computer Engineering
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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