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On successive lumping of large scale systems

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TitleInfo
Title
On successive lumping of large scale systems
Name (type = personal)
NamePart (type = family)
Smit
NamePart (type = given)
Laurens C.
NamePart (type = date)
1986-
DisplayForm
Laurens Smit
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Katehakis
NamePart (type = given)
Michael N
DisplayForm
Michael N Katehakis
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Yang
NamePart (type = given)
Jian
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Jian Yang
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Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Ruszczyński
NamePart (type = given)
Andrzej
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Andrzej Ruszczyński
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Papayanopoulos
NamePart (type = given)
Lee
DisplayForm
Lee Papayanopoulos
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Perry
NamePart (type = given)
Ohad
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Ohad Perry
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = personal)
NamePart (type = family)
Spieksma
NamePart (type = given)
Flora
DisplayForm
Flora Spieksma
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - Newark
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2014
DateOther (qualifier = exact); (type = degree)
2014-05
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
The general area of research of this dissertation concerns large systems with random aspects to their behavior that can be modeled and studied in terms of the stationary distribution of Markov chains. As the state spaces of such systems become large, their behavior gets hard to analyze, either via mathematical theory, computational algorithms or via computer simulation. In this dissertation a class of Markov chains that we call successively lumpable is specified for which we show that the stationary probabilities can be obtained by successively computing the stationary probabilities of a propitiously constructed se- quence of Markov chains. Each of the latter chains has a (typically much) smaller state space and this yields significant computational improvements. In a successively lumpable Markov chain, we denote the states by tuples of the form (m,i), where m represents the “current” level of the state and i the current phase of the state. A Markov process is called quasi skip free (QSF) when its transition probability matrix does not permit one step transitions to states that are two or more levels away from the current state in one direction of the level variable m. We study the class of QSF processes for which in all levels m transitions from level m can only go “down” to a single state in level m − 1 while “upward” transitions are not restricted. Furthermore, we study the class of QSF processes for which in all level m transitions from level m can go “down” to any state in level m − 1 while “upward” transitions go only to one state in the highest level. We derive explicit solutions and bounds for the steady state probabilities for both classes of processes, when the process is ergodic. These two classes of QSF processes have applications in many areas of applied proba- bility comprising computer science, queueing theory, inventory theory, reliability and the theory of branching processes. To elaborate the applicability of the method we present explicit solutions for well known queueing models. In addition we will give examples of inventory models and restart models that also fit in the framework of successively lumpable QSF processes.
Subject (authority = RUETD)
Topic
Management
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_5569
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
vii, 84 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = vita)
Includes vita
Note (type = statement of responsibility)
by Laurens C. Smit
Subject (authority = ETD-LCSH)
Topic
Markov processes
Subject (authority = ETD-LCSH)
Topic
Stationary processes
Subject (authority = ETD-LCSH)
Topic
Probabilities
RelatedItem (type = host)
TitleInfo
Title
Graduate School - Newark Electronic Theses and Dissertations
Identifier (type = local)
rucore10002600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3QZ288X
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Smit
GivenName
Laurens
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2014-04-23 09:56:25
AssociatedEntity
Name
Laurens Smit
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - Newark
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
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Copyright protected
Availability
Status
Open
Reason
Permission or license
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RULTechMD (ID = TECHNICAL1)
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ETD
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windows xp
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