{"id":"https://openalex.org/W2104091453","doi":"https://doi.org/10.1080/03461238.1970.10405658","title":"On the transient behaviour of the GI/G/1 waiting-times","display_name":"On the transient behaviour of the GI/G/1 waiting-times","publication_year":1970,"publication_date":"1970-07-01","ids":{"openalex":"https://openalex.org/W2104091453","doi":"https://doi.org/10.1080/03461238.1970.10405658","mag":"2104091453"},"language":"en","primary_location":{"id":"doi:10.1080/03461238.1970.10405658","doi":"https://doi.org/10.1080/03461238.1970.10405658","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03461238.1970.10405658","pdf_url":null,"source":{"id":"https://openalex.org/S125980181","display_name":"Scandinavian Actuarial Journal","issn_l":"0346-1238","issn":["0346-1238","1651-2030"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scandinavian Actuarial Journal","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5014173287","display_name":"Nils Blomqvist","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nils Blomqvist","raw_affiliation_strings":["Gothenburg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Gothenburg","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5014173287"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.33635988,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"1970","issue":"3-4","first_page":"118","last_page":"129"},"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/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"}},"topics":[{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9994999766349792,"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/T11720","display_name":"Probability and Risk Models","score":0.00019999999494757503,"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/T13500","display_name":"Probability and Statistical Research","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gi-g-1-queue","display_name":"GI/G/1 queue","score":0.9520000219345093},{"id":"https://openalex.org/keywords/waiting-time","display_name":"waiting time","score":0.7170000076293945},{"id":"https://openalex.org/keywords/transient-response","display_name":"transient response","score":0.8569999933242798},{"id":"https://openalex.org/keywords/single-server-queue","display_name":"single-server queue","score":0.8320000171661377},{"id":"https://openalex.org/keywords/service-time","display_name":"service time","score":0.9869999885559082},{"id":"https://openalex.org/keywords/average-waiting-time","display_name":"average waiting time","score":0.5370000004768372}],"concepts":[{"id":"https://openalex.org/C16320812","wikidata":"https://www.wikidata.org/wiki/Q1812200","display_name":"Idle","level":2,"score":0.671000599861145},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5647162795066833},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.5331992506980896},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.5196565389633179},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49857449531555176},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4885476529598236},{"id":"https://openalex.org/C2986422491","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing system","level":3,"score":0.4823717176914215},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.4710374176502228},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4475034475326538},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.4359095096588135},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4256875514984131},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.4127095341682434},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.364470899105072},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.23466312885284424},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.15439081192016602},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08648329973220825},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.06423678994178772},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03461238.1970.10405658","doi":"https://doi.org/10.1080/03461238.1970.10405658","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03461238.1970.10405658","pdf_url":null,"source":{"id":"https://openalex.org/S125980181","display_name":"Scandinavian Actuarial Journal","issn_l":"0346-1238","issn":["0346-1238","1651-2030"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scandinavian Actuarial Journal","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W14515589","https://openalex.org/W1480723515","https://openalex.org/W1577556259","https://openalex.org/W1981060282","https://openalex.org/W1991962848","https://openalex.org/W1996466655","https://openalex.org/W2015840019","https://openalex.org/W2098169676","https://openalex.org/W2107435280","https://openalex.org/W2119557964","https://openalex.org/W2327285397","https://openalex.org/W2505010025","https://openalex.org/W2978954154","https://openalex.org/W4230707513"],"related_works":["https://openalex.org/W2218075354","https://openalex.org/W2001583298","https://openalex.org/W789238537","https://openalex.org/W2042490604","https://openalex.org/W360574729","https://openalex.org/W4243961788","https://openalex.org/W85152629","https://openalex.org/W3014748244","https://openalex.org/W1990974689","https://openalex.org/W4239999567"],"abstract_inverted_index":{"Consider":[0],"a":[1],"single-server":[2],"queuing":[3],"system,":[4],"where":[5],"the":[6,11,33,52,55,61,66,80,88],"arrival":[7],"intervals":[8],"Ti":[9],"and":[10,23,39,58,92],"service-times":[12],"Ui":[13],"of":[14,21,47,54,90],"consecutive":[15],"customers":[16,30],"form":[17],"two":[18],"independent":[19,22],"sequences":[20],"equally":[24],"distributed":[25],"random":[26],"variables.":[27],"Assume":[28],"that":[29,40,60],"arriving":[31],"when":[32,79],"server":[34,62],"is":[35,63],"busy":[36],"line":[37],"up":[38],"they":[41],"are":[42],"then":[43],"served":[44],"in":[45],"order":[46],"arrival.":[48],"Let":[49],"Wn":[50,78,91],"be":[51,87],"waiting-time":[53],"nth":[56],"customer":[57],"suppose":[59],"idle":[64],"at":[65],"start,":[67],"i.e.":[68],"W1":[69],"=":[70,74],"0.":[71],"Put":[72],"W":[73],"lim":[75],"n":[76,96],"\u221e":[77],"limit":[81],"exists.":[82],"Furthermore,":[83],"let":[84],"Fn":[85],"(\u22c5)":[86],"c.d.f.":[89],"put":[93],"EWn":[94],"=\u03c9":[95],".":[97]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
