Analysis of large Markov chains using stochastic automata networks

Simple item page
buir.advisorDayar, Tuğrul
dc.contributor.authorOleg, Gusak
dc.date.accessioned2017-12-12T11:56:49Z
dc.date.available2017-12-12T11:56:49Z
dc.date.copyright2001-07
dc.date.issued2001-07
dc.date.submitted2001-07
dc.departmentDepartment of Computer Engineeringen_US
dc.descriptionCataloged from PDF version of article.en_US
dc.descriptionThesis (Ph.D.): Bilkent University, Department of Computer Engineering, İhsan Doğramacı Bilkent University, 2001.en_US
dc.descriptionIncludes bibliographical references (leaves 94-100).en_US
dc.description.abstractThis work contributes to the existing research in the area of analysis of finite Markov chains (MCs) modeled as stochastic automata networks (SANs). First, this thesis extends the near complete decomposability concept of Markov chains to SANs so that the inherent difficulty associated with solving the underlying MC car! be forecasted and solution techniques based on this concept car! be investigated. A straightforward approach to finding a nearly completely decomposable (NCD) partitioning of the MC underlying a SAN requires the computation of the nonzero elements of its global generator. This is not feasible for very large systems ever! in sparse matrix representation due to memory and execution time constraints. In this thesis, an efficient decompositional solution algorithm to this problem that is based on analyzing the NCD structure of each component of a giver! SAN is introduced. Numerical results show that the giver! algorithm performs much better than the straightforward approach. Second, this work specifies easy to check lumpability conditions for the generator of a SAN. When there exists a lumpable partitioning induced by the tensor representation of the generator, it is shown that an efficient iterative aggregation-disaggregation algorithm (IAD) may be employed to compute the steady state distribution of the MC underlying the SAN model. The results of experiments with continuous-time arid discrete-time SAN models show that the proposed algorithm performs better than the highly competitive block Gauss- Seidel (BGS) in terms of both the number of iterations arid the time to converge to the solution. having relatively large blocks in lurnpable partitionings is investigated. To overcome difficulties associated with solving large diagonal blocks at each iteration of the IAD algorithm, the recursive implementation of BGS for SANs is employed. The performance of IAD is compared with that of BGS. The results of experiments show that it is possible to tune IAD so that it outperforms BGS.en_US
dc.description.degreePh.D.en_US
dc.description.statementofresponsibilityby Oleg Gusak.en_US
dc.format.extentxv, 119 leaves ; 30 cmen_US
dc.identifier.itemidBILKUTUPB057974
dc.identifier.urihttp://hdl.handle.net/11693/35669
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectMarkov chainen_US
dc.subjectStochastic automata networken_US
dc.subjectNear complete decomposabilityen_US
dc.subjectLumpabilityen_US
dc.subjectIterative aggregation-disaggregationen_US
dc.subject.lccQA274.7 .G87 2001en_US
dc.titleAnalysis of large Markov chains using stochastic automata networksen_US
dc.title.alternativeBüyük Markov zincirlerinin rassal özdevinimli ağ kullanılarak çözümlemesien_US
dc.typeThesisen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
0001715.pdf
Size:
1.26 MB
Format:
Adobe Portable Document Format
Description:
Full printable version
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.71 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
Dept. of Computer Engineering - Ph.D. / Sc.D.