{"id":"https://openalex.org/W2160247693","doi":"https://doi.org/10.1109/qest.2006.36","title":"On Single-Class Load-Dependent Normalizing Constant Equations","display_name":"On Single-Class Load-Dependent Normalizing Constant Equations","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2160247693","doi":"https://doi.org/10.1109/qest.2006.36","mag":"2160247693"},"language":"en","primary_location":{"id":"doi:10.1109/qest.2006.36","is_oa":false,"landing_page_url":"https://doi.org/10.1109/qest.2006.36","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Third International Conference on the Quantitative Evaluation of Systems - (QEST'06)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045967404","display_name":"Giuliano Casale","orcid":"https://orcid.org/0000-0003-4548-7951"},"institutions":[{"id":"https://openalex.org/I143544115","display_name":"Snam (Italy)","ror":"https://ror.org/04g2nab09","country_code":"IT","type":"company","lineage":["https://openalex.org/I143544115"]},{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Giuliano Casale","raw_affiliation_strings":["Neptuny R&D, Milan","Neptuny R&D, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Neptuny R&D, Milan","institution_ids":["https://openalex.org/I189158943"]},{"raw_affiliation_string":"Neptuny R&D, Milan, Italy","institution_ids":["https://openalex.org/I143544115"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045967404"],"corresponding_institution_ids":["https://openalex.org/I143544115","https://openalex.org/I189158943"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"1","issue":null,"first_page":"333","last_page":"342"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11195","display_name":"Simulation Techniques and Applications","score":0.98089998960495,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9661999940872192,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6517268419265747},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6454883813858032},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5914672613143921},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5563833117485046},{"id":"https://openalex.org/keywords/queue","display_name":"Queue","score":0.5398603677749634},{"id":"https://openalex.org/keywords/queueing-theory","display_name":"Queueing theory","score":0.511685848236084},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5073830485343933},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.502098798751831},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4600546061992645},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4328807592391968},{"id":"https://openalex.org/keywords/mean-value-analysis","display_name":"Mean value analysis","score":0.41885846853256226},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.41369596123695374},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.4104885458946228},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33092379570007324},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27093565464019775},{"id":"https://openalex.org/keywords/layered-queueing-network","display_name":"Layered queueing network","score":0.23706361651420593},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19850018620491028},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10612982511520386},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09135660529136658},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.07182922959327698}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6517268419265747},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6454883813858032},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5914672613143921},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5563833117485046},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.5398603677749634},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.511685848236084},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5073830485343933},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.502098798751831},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4600546061992645},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4328807592391968},{"id":"https://openalex.org/C129978463","wikidata":"https://www.wikidata.org/wiki/Q6803663","display_name":"Mean value analysis","level":4,"score":0.41885846853256226},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.41369596123695374},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4104885458946228},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33092379570007324},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27093565464019775},{"id":"https://openalex.org/C33891772","wikidata":"https://www.wikidata.org/wiki/Q6505536","display_name":"Layered queueing network","level":3,"score":0.23706361651420593},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19850018620491028},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10612982511520386},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09135660529136658},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.07182922959327698},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/qest.2006.36","is_oa":false,"landing_page_url":"https://doi.org/10.1109/qest.2006.36","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Third International Conference on the Quantitative Evaluation of Systems - (QEST'06)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.61.7773","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.7773","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.elet.polimi.it/upload/casale/casale06onsingle.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W175437267","https://openalex.org/W1964081384","https://openalex.org/W1966517285","https://openalex.org/W1967379724","https://openalex.org/W1978006658","https://openalex.org/W1978746287","https://openalex.org/W1983946005","https://openalex.org/W2005002355","https://openalex.org/W2009621954","https://openalex.org/W2014028771","https://openalex.org/W2015379135","https://openalex.org/W2021900251","https://openalex.org/W2023980590","https://openalex.org/W2035428815","https://openalex.org/W2044576707","https://openalex.org/W2058155782","https://openalex.org/W2060840612","https://openalex.org/W2066866933","https://openalex.org/W2094055697","https://openalex.org/W2104110349","https://openalex.org/W2115525458","https://openalex.org/W3025560576","https://openalex.org/W4234416551"],"related_works":["https://openalex.org/W2483576841","https://openalex.org/W4390603192","https://openalex.org/W2168047232","https://openalex.org/W2036729104","https://openalex.org/W2914116015","https://openalex.org/W1532067004","https://openalex.org/W1967163829","https://openalex.org/W2593077298","https://openalex.org/W2600727783","https://openalex.org/W1975917392"],"abstract_inverted_index":{"Normalizing":[0],"constant":[1,57],"recurrence":[2,43],"equations":[3],"play":[4],"an":[5],"important":[6],"role":[7],"in":[8],"the":[9,25,67,84,99,111],"exact":[10,117],"analysis":[11,102],"of":[12,42,52,70,83,103,110],"load-independent":[13],"(LI)":[14],"product-form":[15],"queueing":[16],"networks.":[17],"However,":[18],"they":[19],"have":[20],"not":[21,90],"been":[22],"extended":[23],"to":[24,78],"load-dependent":[26],"(LD)":[27],"case,":[28],"and":[29,115],"this":[30,46],"is":[31],"a":[32,80,96,108],"limitation":[33],"for":[34,98,119],"new":[35,68,116],"solution":[36],"techniques":[37],"based":[38],"on":[39],"linear":[40],"systems":[41],"equations.":[44,58],"In":[45],"paper,":[47],"we":[48,94],"define":[49],"LD":[50,81],"generalizations":[51],"existing":[53],"LI":[54,120],"single-class":[55],"normalizing":[56],"We":[59],"first":[60],"extend":[61],"Buzen\u2019s":[62],"convolution":[63],"expression":[64],"by":[65],"introducing":[66],"concept":[69],"station":[71],"rate":[72],"shift.":[73],"This":[74],"also":[75],"leads":[76],"us":[77],"derive":[79],"extension":[82],"MVA":[85],"queue-length":[86],"recursion":[87],"that":[88],"does":[89],"involve":[91],"probabilities.":[92],"Moreover,":[93],"propose":[95],"technique":[97],"mean":[100],"value":[101],"queue-dependent":[104],"functions,":[105],"which":[106],"provides":[107],"generalization":[109],"network":[112],"population":[113],"constraint":[114],"formulas":[118],"models.":[121]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
