A Perturbation and Reduction Based Algorithm
We present a new algorithm for solving discrete-time Markov chains where transition probabilities have several orders of magnitude. Our method combines the decomposition by perturbation and the reduction approaches. In the decomposition phase, we remove from the chain some transitions with very smal...
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| creator | Fourneau, J. -M. Mokdad, L. |
| description | We present a new algorithm for solving discrete-time Markov chains where transition probabilities have several orders of magnitude. Our method combines the decomposition by perturbation and the reduction approaches. In the decomposition phase, we remove from the chain some transitions with very small probabilities. But we assume that the reduced graph is still strongly connected after the deletion. A transversal (a cut set of the directed cycles) is then obtained and the reduction method is used to compute the first approximation of the steady-state distribution. Further approximations may be computed iteratively to obtain the desirable accuracy. We prove the algorithm and present some examples. |
| doi_str_mv | 10.1007/3-540-68061-6_12 |
| format | Conference Proceeding |
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Our method combines the decomposition by perturbation and the reduction approaches. In the decomposition phase, we remove from the chain some transitions with very small probabilities. But we assume that the reduced graph is still strongly connected after the deletion. A transversal (a cut set of the directed cycles) is then obtained and the reduction method is used to compute the first approximation of the steady-state distribution. Further approximations may be computed iteratively to obtain the desirable accuracy. We prove the algorithm and present some examples.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540649496</identifier><identifier>ISBN: 3540649492</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540680611</identifier><identifier>EISBN: 3540680616</identifier><identifier>DOI: 10.1007/3-540-68061-6_12</identifier><identifier>OCLC: 958523495</identifier><identifier>LCCallNum: QA76.9.E94QA76.758</identifier><language>eng</language><publisher>Germany: Springer Berlin / Heidelberg</publisher><subject>Algorithmics. Computability. Computer arithmetics ; Applied sciences ; Computer Science ; Computer science; control theory; systems ; Computer systems performance. Reliability ; Data Packet ; Direct Algorithm ; Directed Cycle ; Exact sciences and technology ; Leaky Bucket ; Markov Chain ; Software ; Theoretical computing</subject><ispartof>Computer Performance Evaluation, 1998, Vol.1469, p.142-153</ispartof><rights>Springer-Verlag Berlin Heidelberg 1998</rights><rights>1998 INIST-CNRS</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0002-6182-4869</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttps://ebookcentral.proquest.com/covers/3073300-l.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/3-540-68061-6_12$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/3-540-68061-6_12$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,779,780,784,789,790,793,885,4050,4051,27925,38255,41442,42511</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=2291500$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.u-pec.fr/hal-04044805$$DView record in HAL$$Hfree_for_read</backlink></links><search><contributor>Carbonell, Jaime G</contributor><contributor>Siekmann, Jörg</contributor><contributor>Goos, Gerhard</contributor><contributor>Puigjaner, Ramon</contributor><contributor>Serra, Bartomeu</contributor><contributor>Savino, Nunzio N.</contributor><creatorcontrib>Fourneau, J. -M.</creatorcontrib><creatorcontrib>Mokdad, L.</creatorcontrib><title>A Perturbation and Reduction Based Algorithm</title><title>Computer Performance Evaluation</title><description>We present a new algorithm for solving discrete-time Markov chains where transition probabilities have several orders of magnitude. Our method combines the decomposition by perturbation and the reduction approaches. In the decomposition phase, we remove from the chain some transitions with very small probabilities. But we assume that the reduced graph is still strongly connected after the deletion. A transversal (a cut set of the directed cycles) is then obtained and the reduction method is used to compute the first approximation of the steady-state distribution. Further approximations may be computed iteratively to obtain the desirable accuracy. We prove the algorithm and present some examples.</description><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Applied sciences</subject><subject>Computer Science</subject><subject>Computer science; control theory; systems</subject><subject>Computer systems performance. Reliability</subject><subject>Data Packet</subject><subject>Direct Algorithm</subject><subject>Directed Cycle</subject><subject>Exact sciences and technology</subject><subject>Leaky Bucket</subject><subject>Markov Chain</subject><subject>Software</subject><subject>Theoretical computing</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540649496</isbn><isbn>3540649492</isbn><isbn>9783540680611</isbn><isbn>3540680616</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>1998</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNpFUE1PGzEQNYVWRCH3HnPoBYmlMx7bax8DagtSJBCCs-X1epNtl93U3iDx7-t8qMxlNG_ee6N5jH1FuEaA8jsVUkChNCgslEV-wmam1JTBPYaf2ARzK4iEOf3YCSOMOmMTIOCFKQV9YRMjteSZJs_ZLKXfkIs4R1ATdrWYP4Y4bmPlxnbo566v50-h3vr9dONSqOeLbjXEdly_XrDPjetSmB37lL38_PF8e1csH37d3y6WxZqj4oVv8imPzqtacs0rAbwWXHHpq8ZjGYTUWGFVOzRO6tKoGqEiSaGpiLRwNGWXB9-16-wmtq8uvtvBtfZusbQ7DAQIoUG-YeZ-O3A3LnnXNdH1vk3_VZwblPndKbs-0FLe9KsQbTUMf5JFsLu0Ldkcnt0na3dpZwEdfePwdxvSaMNO4UM_Rtf5tduMISZLUBJBNtEWpaB_Nkx5GQ</recordid><startdate>1998</startdate><enddate>1998</enddate><creator>Fourneau, J. -M.</creator><creator>Mokdad, L.</creator><general>Springer Berlin / Heidelberg</general><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>FFUUA</scope><scope>IQODW</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-6182-4869</orcidid></search><sort><creationdate>1998</creationdate><title>A Perturbation and Reduction Based Algorithm</title><author>Fourneau, J. -M. ; Mokdad, L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-h2162-cf495c1ac6d5282b402d42625cbfc17e4581b1bda19a58796d10b353efb3384a3</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>1998</creationdate><topic>Algorithmics. Computability. Computer arithmetics</topic><topic>Applied sciences</topic><topic>Computer Science</topic><topic>Computer science; control theory; systems</topic><topic>Computer systems performance. Reliability</topic><topic>Data Packet</topic><topic>Direct Algorithm</topic><topic>Directed Cycle</topic><topic>Exact sciences and technology</topic><topic>Leaky Bucket</topic><topic>Markov Chain</topic><topic>Software</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fourneau, J. -M.</creatorcontrib><creatorcontrib>Mokdad, L.</creatorcontrib><collection>ProQuest Ebook Central - Book Chapters - Demo use only</collection><collection>Pascal-Francis</collection><collection>Hyper Article en Ligne (HAL)</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fourneau, J. -M.</au><au>Mokdad, L.</au><au>Carbonell, Jaime G</au><au>Siekmann, Jörg</au><au>Goos, Gerhard</au><au>Puigjaner, Ramon</au><au>Serra, Bartomeu</au><au>Savino, Nunzio N.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>A Perturbation and Reduction Based Algorithm</atitle><btitle>Computer Performance Evaluation</btitle><date>1998</date><risdate>1998</risdate><volume>1469</volume><spage>142</spage><epage>153</epage><pages>142-153</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540649496</isbn><isbn>3540649492</isbn><eisbn>9783540680611</eisbn><eisbn>3540680616</eisbn><abstract>We present a new algorithm for solving discrete-time Markov chains where transition probabilities have several orders of magnitude. Our method combines the decomposition by perturbation and the reduction approaches. In the decomposition phase, we remove from the chain some transitions with very small probabilities. But we assume that the reduced graph is still strongly connected after the deletion. A transversal (a cut set of the directed cycles) is then obtained and the reduction method is used to compute the first approximation of the steady-state distribution. Further approximations may be computed iteratively to obtain the desirable accuracy. We prove the algorithm and present some examples.</abstract><cop>Germany</cop><pub>Springer Berlin / Heidelberg</pub><doi>10.1007/3-540-68061-6_12</doi><oclcid>958523495</oclcid><tpages>12</tpages><orcidid>https://orcid.org/0000-0002-6182-4869</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Computer Performance Evaluation, 1998, Vol.1469, p.142-153 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_2291500 |
| source | Springer Books |
| subjects | Algorithmics. Computability. Computer arithmetics Applied sciences Computer Science Computer science control theory systems Computer systems performance. Reliability Data Packet Direct Algorithm Directed Cycle Exact sciences and technology Leaky Bucket Markov Chain Software Theoretical computing |
| title | A Perturbation and Reduction Based Algorithm |
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