BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery
Identifieur interne : 001032 ( Istex/Corpus ); précédent : 001031; suivant : 001033BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery
Auteurs : A. N. Dudin ; A. V. KarolikSource :
- Performance Evaluation [ 0166-5316 ] ; 2001.
Abstract
We consider a BMAP/SM/1 system which is exposed to disasters’ arrivals. A disaster causes all customers to leave the system instantaneously. After a disaster appearance the system is recovering during some random time interval. The variants of accumulating and losing customers during the recover period are considered. The embedded and arbitrary time queue length distributions as well as the average output rate and loss probability are calculated. The results are illustrated by numerical examples.
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DOI: 10.1016/S0166-5316(00)00063-8
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title>BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery</title><author><name sortKey="Dudin, A N" sort="Dudin, A N" uniqKey="Dudin A" first="A. N." last="Dudin">A. N. Dudin</name><affiliation><mods:affiliation>Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. Skorina Ave., 220050 Minsk 50, Byelorussia</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: dudin@fpm.bsu.unibel.by</mods:affiliation></affiliation></author><author><name sortKey="Karolik, A V" sort="Karolik, A V" uniqKey="Karolik A" first="A. V." last="Karolik">A. V. Karolik</name><affiliation><mods:affiliation>Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. 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Dudin</name><affiliation><mods:affiliation>Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. Skorina Ave., 220050 Minsk 50, Byelorussia</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: dudin@fpm.bsu.unibel.by</mods:affiliation></affiliation></author><author><name sortKey="Karolik, A V" sort="Karolik, A V" uniqKey="Karolik A" first="A. V." last="Karolik">A. V. Karolik</name><affiliation><mods:affiliation>Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. Skorina Ave., 220050 Minsk 50, Byelorussia</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Performance Evaluation</title><title level="j" type="abbrev">PEVA</title><idno type="ISSN">0166-5316</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="2001">2001</date><biblScope unit="volume">45</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="19">19</biblScope><biblScope unit="page" to="32">32</biblScope></imprint><idno type="ISSN">0166-5316</idno></series><idno type="istex">60801374B1CDD2C63439602FE9B3A7469A93E9E4</idno><idno type="DOI">10.1016/S0166-5316(00)00063-8</idno><idno type="PII">S0166-5316(00)00063-8</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0166-5316</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We consider a BMAP/SM/1 system which is exposed to disasters’ arrivals. A disaster causes all customers to leave the system instantaneously. After a disaster appearance the system is recovering during some random time interval. The variants of accumulating and losing customers during the recover period are considered. The embedded and arbitrary time queue length distributions as well as the average output rate and loss probability are calculated. The results are illustrated by numerical examples.</div></front></TEI><istex><corpusName>elsevier</corpusName><author><json:item><name>A.N. Dudin</name><affiliations><json:string>Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. Skorina Ave., 220050 Minsk 50, Byelorussia</json:string><json:string>E-mail: dudin@fpm.bsu.unibel.by</json:string></affiliations></json:item><json:item><name>A.V. Karolik</name><affiliations><json:string>Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. Skorina Ave., 220050 Minsk 50, Byelorussia</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Negative arrivals</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>BMAP/SM/1 queue</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Markovian arrival process of disasters</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Recovering</value></json:item></subject><language><json:string>eng</json:string></language><originalGenre><json:string>Full-length article</json:string></originalGenre><abstract>We consider a BMAP/SM/1 system which is exposed to disasters’ arrivals. A disaster causes all customers to leave the system instantaneously. After a disaster appearance the system is recovering during some random time interval. The variants of accumulating and losing customers during the recover period are considered. The embedded and arbitrary time queue length distributions as well as the average output rate and loss probability are calculated. The results are illustrated by numerical examples.</abstract><qualityIndicators><score>5.758</score><pdfVersion>1.2</pdfVersion><pdfPageSize>612 x 792 pts (letter)</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>4</keywordCount><abstractCharCount>501</abstractCharCount><pdfWordCount>4870</pdfWordCount><pdfCharCount>23498</pdfCharCount><pdfPageCount>14</pdfPageCount><abstractWordCount>74</abstractWordCount></qualityIndicators><title>BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery</title><pii><json:string>S0166-5316(00)00063-8</json:string></pii><refBibs><json:item><author><json:item><name>J. 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Appl.</title></host><title>Stochastic clearing systems</title></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>45</volume><pii><json:string>S0166-5316(00)X0058-2</json:string></pii><pages><last>32</last><first>19</first></pages><issn><json:string>0166-5316</json:string></issn><issue>1</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><title>Performance Evaluation</title><publicationDate>2001</publicationDate></host><categories><wos><json:string>science</json:string><json:string>computer science, theory & methods</json:string><json:string>computer science, hardware & architecture</json:string></wos><scienceMetrix><json:string>applied sciences</json:string><json:string>information & communication technologies</json:string><json:string>networking & telecommunications</json:string></scienceMetrix></categories><publicationDate>2001</publicationDate><copyrightDate>2001</copyrightDate><doi><json:string>10.1016/S0166-5316(00)00063-8</json:string></doi><id>60801374B1CDD2C63439602FE9B3A7469A93E9E4</id><score>0.019784834</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/60801374B1CDD2C63439602FE9B3A7469A93E9E4/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/60801374B1CDD2C63439602FE9B3A7469A93E9E4/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/60801374B1CDD2C63439602FE9B3A7469A93E9E4/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>ELSEVIER</publisher><availability><p>©2001 Elsevier Science B.V.</p></availability><date>2001</date></publicationStmt><notesStmt><note type="content">Fig. 1: Dependence of the mean queue length on the traffic load.</note><note type="content">Fig. 2: Dependence of the mean queue length on the traffic load in cases of increasing the traffic by accelerating the input and by slowing the service.</note><note type="content">Fig. 3: Dependence of the mean queue length on the disaster intensity.</note><note type="content">Fig. 4: Dependence of the mean queue length on the mean recovery time.</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery</title><author xml:id="author-1"><persName><forename type="first">A.N.</forename><surname>Dudin</surname></persName><email>dudin@fpm.bsu.unibel.by</email><note type="correspondence"><p>Corresponding author.</p></note><affiliation>Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. Skorina Ave., 220050 Minsk 50, Byelorussia</affiliation></author><author xml:id="author-2"><persName><forename type="first">A.V.</forename><surname>Karolik</surname></persName><affiliation>Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. Skorina Ave., 220050 Minsk 50, Byelorussia</affiliation></author></analytic><monogr><title level="j">Performance Evaluation</title><title level="j" type="abbrev">PEVA</title><idno type="pISSN">0166-5316</idno><idno type="PII">S0166-5316(00)X0058-2</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="2001"></date><biblScope unit="volume">45</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="19">19</biblScope><biblScope unit="page" to="32">32</biblScope></imprint></monogr><idno type="istex">60801374B1CDD2C63439602FE9B3A7469A93E9E4</idno><idno type="DOI">10.1016/S0166-5316(00)00063-8</idno><idno type="PII">S0166-5316(00)00063-8</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2001</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>We consider a BMAP/SM/1 system which is exposed to disasters’ arrivals. A disaster causes all customers to leave the system instantaneously. After a disaster appearance the system is recovering during some random time interval. The variants of accumulating and losing customers during the recover period are considered. The embedded and arbitrary time queue length distributions as well as the average output rate and loss probability are calculated. The results are illustrated by numerical examples.</p></abstract><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>Negative arrivals</term></item><item><term>BMAP/SM/1 queue</term></item><item><term>Markovian arrival process of disasters</term></item><item><term>Recovering</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2000-10-19">Modified</change><change when="2001">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/60801374B1CDD2C63439602FE9B3A7469A93E9E4/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: ce:floats; body; tail"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"><istex:entity SYSTEM="gr1" NDATA="IMAGE" name="gr1"></istex:entity><istex:entity SYSTEM="gr2" NDATA="IMAGE" name="gr2"></istex:entity><istex:entity SYSTEM="gr3" NDATA="IMAGE" name="gr3"></istex:entity><istex:entity SYSTEM="gr4" NDATA="IMAGE" name="gr4"></istex:entity><istex:entity SYSTEM="fx1" NDATA="IMAGE" name="fx1"></istex:entity><istex:entity SYSTEM="fx2" NDATA="IMAGE" name="fx2"></istex:entity></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>PEVA</jid><aid>895</aid><ce:pii>S0166-5316(00)00063-8</ce:pii><ce:doi>10.1016/S0166-5316(00)00063-8</ce:doi><ce:copyright type="full-transfer" year="2001">Elsevier Science B.V.</ce:copyright></item-info><head><ce:title>BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery</ce:title><ce:author-group><ce:author biographyid="VT1"><ce:given-name>A.N.</ce:given-name><ce:surname>Dudin</ce:surname><ce:cross-ref refid="CORR1">*</ce:cross-ref><ce:e-address>dudin@fpm.bsu.unibel.by</ce:e-address></ce:author><ce:author biographyid="VT2"><ce:given-name>A.V.</ce:given-name><ce:surname>Karolik</ce:surname></ce:author><ce:affiliation><ce:textfn>Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. Skorina Ave., 220050 Minsk 50, Byelorussia</ce:textfn></ce:affiliation><ce:correspondence id="CORR1"><ce:label>*</ce:label><ce:text>Corresponding author.</ce:text></ce:correspondence></ce:author-group><ce:date-received day="1" month="3" year="2000"></ce:date-received><ce:date-revised day="19" month="10" year="2000"></ce:date-revised><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>We consider a BMAP/SM/1 system which is exposed to disasters’ arrivals. A disaster causes all customers to leave the system instantaneously. After a disaster appearance the system is recovering during some random time interval. The variants of accumulating and losing customers during the recover period are considered. The embedded and arbitrary time queue length distributions as well as the average output rate and loss probability are calculated. The results are illustrated by numerical examples.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords class="keyword"><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>Negative arrivals</ce:text></ce:keyword><ce:keyword><ce:text>BMAP/SM/1 queue</ce:text></ce:keyword><ce:keyword><ce:text>Markovian arrival process of disasters</ce:text></ce:keyword><ce:keyword><ce:text>Recovering</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery</title></titleInfo><name type="personal"><namePart type="given">A.N.</namePart><namePart type="family">Dudin</namePart><affiliation>Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. Skorina Ave., 220050 Minsk 50, Byelorussia</affiliation><affiliation>E-mail: dudin@fpm.bsu.unibel.by</affiliation><description>Corresponding author.</description><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.V.</namePart><namePart type="family">Karolik</namePart><affiliation>Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. Skorina Ave., 220050 Minsk 50, Byelorussia</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">2001</dateIssued><dateModified encoding="w3cdtf">2000-10-19</dateModified><copyrightDate encoding="w3cdtf">2001</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">We consider a BMAP/SM/1 system which is exposed to disasters’ arrivals. A disaster causes all customers to leave the system instantaneously. After a disaster appearance the system is recovering during some random time interval. The variants of accumulating and losing customers during the recover period are considered. The embedded and arbitrary time queue length distributions as well as the average output rate and loss probability are calculated. The results are illustrated by numerical examples.</abstract><note type="content">Fig. 1: Dependence of the mean queue length on the traffic load.</note><note type="content">Fig. 2: Dependence of the mean queue length on the traffic load in cases of increasing the traffic by accelerating the input and by slowing the service.</note><note type="content">Fig. 3: Dependence of the mean queue length on the disaster intensity.</note><note type="content">Fig. 4: Dependence of the mean queue length on the mean recovery time.</note><subject><genre>Keywords</genre><topic>Negative arrivals</topic><topic>BMAP/SM/1 queue</topic><topic>Markovian arrival process of disasters</topic><topic>Recovering</topic></subject><relatedItem type="host"><titleInfo><title>Performance Evaluation</title></titleInfo><titleInfo type="abbreviated"><title>PEVA</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">200105</dateIssued></originInfo><identifier type="ISSN">0166-5316</identifier><identifier type="PII">S0166-5316(00)X0058-2</identifier><part><date>200105</date><detail type="volume"><number>45</number><caption>vol.</caption></detail><detail type="issue"><number>1</number><caption>no.</caption></detail><extent unit="issue pages"><start>1</start><end>76</end></extent><extent unit="pages"><start>19</start><end>32</end></extent></part></relatedItem><identifier type="istex">60801374B1CDD2C63439602FE9B3A7469A93E9E4</identifier><identifier type="DOI">10.1016/S0166-5316(00)00063-8</identifier><identifier type="PII">S0166-5316(00)00063-8</identifier><accessCondition type="use and reproduction" contentType="copyright">©2001 Elsevier Science B.V.</accessCondition><recordInfo><recordContentSource>ELSEVIER</recordContentSource><recordOrigin>Elsevier Science B.V., ©2001</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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