{"id":"https://openalex.org/W2040294627","doi":"https://doi.org/10.1007/bf01158903","title":"Busy period distribution in state-dependent queues","display_name":"Busy period distribution in state-dependent queues","publication_year":1987,"publication_date":"1987-09-01","ids":{"openalex":"https://openalex.org/W2040294627","doi":"https://doi.org/10.1007/bf01158903","mag":"2040294627"},"language":"en","primary_location":{"id":"doi:10.1007/bf01158903","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01158903","pdf_url":null,"source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","1572-9443"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"},"type":"article","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/A5038794095","display_name":"Charles Knessl","orcid":"https://orcid.org/0000-0001-8106-8880"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C. Knessl","raw_affiliation_strings":["Department of Engineering Sciences and Applied Mathematics, Northwestern University, 60201, Evanston, Illinois, USA","Northwestern University Evanston IL"],"affiliations":[{"raw_affiliation_string":"Department of Engineering Sciences and Applied Mathematics, Northwestern University, 60201, Evanston, Illinois, USA","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Northwestern University Evanston IL","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000956173","display_name":"B. J. Matkowsky","orcid":null},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. J. Matkowsky","raw_affiliation_strings":["Department of Engineering Sciences and Applied Mathematics, Northwestern University, 60201, Evanston, Illinois, USA","Northwestern University Evanston IL"],"affiliations":[{"raw_affiliation_string":"Department of Engineering Sciences and Applied Mathematics, Northwestern University, 60201, Evanston, Illinois, USA","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Northwestern University Evanston IL","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072194007","display_name":"Z. Schuss","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Z. Schuss","raw_affiliation_strings":["Department of Mathematics, Tel-Aviv University, Tel-Aviv, Israel","Tel Aviv University, Tel Aviv, Israel,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel,","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042966516","display_name":"Charles Tier","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Tier","raw_affiliation_strings":["Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 60680, Chicago, Illinois, USA","University of Illinois , at Chicago, Chicago"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 60680, Chicago, Illinois, USA","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"University of Illinois , at Chicago, Chicago","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5038794095"],"corresponding_institution_ids":["https://openalex.org/I111979921"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.21837349,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2","issue":"3","first_page":"285","last_page":"305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9021999835968018,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/queue","display_name":"Queue","score":0.7011374235153198},{"id":"https://openalex.org/keywords/instant","display_name":"Instant","score":0.6795698404312134},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.576007068157196},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5070786476135254},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.48418620228767395},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.47779589891433716},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.43740078806877136},{"id":"https://openalex.org/keywords/period","display_name":"Period (music)","score":0.4238680899143219},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.41384631395339966},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40080639719963074},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3706310987472534},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36382877826690674},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23020967841148376},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.17865648865699768},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16743820905685425},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.157512366771698},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14640745520591736}],"concepts":[{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.7011374235153198},{"id":"https://openalex.org/C2779432360","wikidata":"https://www.wikidata.org/wiki/Q16963779","display_name":"Instant","level":2,"score":0.6795698404312134},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.576007068157196},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5070786476135254},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.48418620228767395},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.47779589891433716},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.43740078806877136},{"id":"https://openalex.org/C2781291010","wikidata":"https://www.wikidata.org/wiki/Q178580","display_name":"Period (music)","level":2,"score":0.4238680899143219},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.41384631395339966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40080639719963074},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3706310987472534},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36382877826690674},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23020967841148376},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.17865648865699768},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16743820905685425},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.157512366771698},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14640745520591736},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01158903","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01158903","pdf_url":null,"source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","1572-9443"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1657347807","https://openalex.org/W1982710373","https://openalex.org/W2008872817","https://openalex.org/W2019171317","https://openalex.org/W2047077063","https://openalex.org/W2086715755","https://openalex.org/W2120062331","https://openalex.org/W2322480514","https://openalex.org/W2751862591","https://openalex.org/W2986057930","https://openalex.org/W4239608788"],"related_works":["https://openalex.org/W2356370096","https://openalex.org/W2794694000","https://openalex.org/W2094154142","https://openalex.org/W2350999733","https://openalex.org/W2392387319","https://openalex.org/W2067732275","https://openalex.org/W1953762007","https://openalex.org/W2089165037","https://openalex.org/W2146625955","https://openalex.org/W4200518464"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}