{"id":"https://openalex.org/W2474140803","doi":"https://doi.org/10.1007/s11134-014-9420-z","title":"Service-time ages, residuals, and lengths in an $$M/GI/\\infty $$ M / G I / \u221e service system","display_name":"Service-time ages, residuals, and lengths in an $$M/GI/\\infty $$ M / G I / \u221e service system","publication_year":2014,"publication_date":"2014-10-04","ids":{"openalex":"https://openalex.org/W2474140803","doi":"https://doi.org/10.1007/s11134-014-9420-z","mag":"2474140803"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-014-9420-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11134-014-9420-z.pdf","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_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11134-014-9420-z.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030111068","display_name":"Tomasz Rolski","orcid":"https://orcid.org/0000-0002-9835-9681"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"funder","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"T. Rolski","raw_affiliation_strings":["Mathematical Institute, University of Wroc\u0142aw, Wroc\u0142aw, Poland"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Wroc\u0142aw, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003761238","display_name":"Richard F. Serfozo","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"funder","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Serfozo","raw_affiliation_strings":["School of Industrial and System Engineering, Georgia Tech, Atlanta, USA"],"affiliations":[{"raw_affiliation_string":"School of Industrial and System Engineering, Georgia Tech, Atlanta, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034213683","display_name":"Dietrich Stoyan","orcid":"https://orcid.org/0000-0001-8934-7702"},"institutions":[{"id":"https://openalex.org/I61893789","display_name":"TU Bergakademie Freiberg","ror":"https://ror.org/031vc2293","country_code":"DE","type":"funder","lineage":["https://openalex.org/I61893789"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"D. Stoyan","raw_affiliation_strings":["Institute of Stochastics, TU Bergakademie Freiberg, Freiberg, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Stochastics, TU Bergakademie Freiberg, Freiberg, Germany","institution_ids":["https://openalex.org/I61893789"]}]}],"institution_assertions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030111068"],"corresponding_institution_ids":["https://openalex.org/I219388962"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.511,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":3,"citation_normalized_percentile":{"value":0.755829,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":76,"max":79},"biblio":{"volume":"79","issue":"2","first_page":"173","last_page":"181"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9984,"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":0.9984,"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/T11720","display_name":"Probability and Risk Models","score":0.9799,"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9753,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/statistic","display_name":"Statistic","score":0.48004568}],"concepts":[{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.701627},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.6743182},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.63730043},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.48004568},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4474056},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.44483796},{"id":"https://openalex.org/C133338972","wikidata":"https://www.wikidata.org/wiki/Q2055750","display_name":"Compound Poisson process","level":4,"score":0.4191624},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.36726674},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3221925},{"id":"https://openalex.org/C166144826","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson process","level":3,"score":0.26524696},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12169564},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.08208096},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-014-9420-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11134-014-9420-z.pdf","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_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-014-9420-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11134-014-9420-z.pdf","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_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.54,"display_name":"Life on land"}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":14,"referenced_works":["https://openalex.org/W1970381033","https://openalex.org/W1977398917","https://openalex.org/W2015840019","https://openalex.org/W2049844434","https://openalex.org/W2050952069","https://openalex.org/W2052197092","https://openalex.org/W2103071636","https://openalex.org/W2248670831","https://openalex.org/W2334369124","https://openalex.org/W2525528836","https://openalex.org/W4233064940","https://openalex.org/W4242808910","https://openalex.org/W4254338057","https://openalex.org/W649673299"],"related_works":["https://openalex.org/W4245457074","https://openalex.org/W4240383795","https://openalex.org/W2605475288","https://openalex.org/W2387184232","https://openalex.org/W2347893880","https://openalex.org/W2347733609","https://openalex.org/W2292976891","https://openalex.org/W2128683635","https://openalex.org/W2066502241","https://openalex.org/W2008809748"],"abstract_inverted_index":{"Important":[0],"supplementary":[1],"variables":[2],"of":[3,17,52,58,74,88,109,130],"a":[4,32,40,97,105,120,133],"stationary":[5,33],"$$M/GI/\\infty":[6,111],"$$":[7,112],"service":[8],"system":[9,23,34],"are":[10,65],"the":[11,18,22,48,55,59,79,82,110],"service-time":[12,60],"ages,":[13,61],"residuals,":[14,62],"and":[15,63,67,94],"lengths":[16,64],"customers":[19],"present":[20],"in":[21,96,132],"at":[24],"time":[25],"$$0$$":[26],".":[27,45],"Our":[28],"main":[29],"result":[30,116],"for":[31,119],"is":[35,78,102,117,124],"that":[36],"these":[37,75],"times":[38,77],"form":[39],"Poisson":[41,53,107],"processes":[42],"on":[43,104],"$$R_+^3$$":[44],"Thus,":[46],"by":[47],"order":[49],"statistic":[50],"property":[51],"processes,":[54],"three-dimensional":[56],"vectors":[57],"independent":[66],"identically":[68],"distributed.":[69],"The":[70,100],"joint":[71,84],"distribution":[72,86],"function":[73,87],"three":[76],"same":[80],"as":[81],"respective":[83],"limiting":[85],"an":[89,125],"inter-renewal":[90],"time\u2019s":[91],"age,":[92],"residual,":[93],"length":[95],"renewal":[98],"process.":[99],"proof":[101],"based":[103],"space-time":[106],"representation":[108],"system.":[113,122],"A":[114],"similar":[115],"presented":[118],"non-stationary":[121],"Included":[123],"ecological":[126],"application":[127],"concerning":[128],"ages":[129],"trees":[131],"forest.":[134]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2474140803","counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-03-16T23:34:11.620970","created_date":"2016-07-22"}