{"id":"https://openalex.org/W2024508584","doi":"https://doi.org/10.2478/v10065-010-0040-x","title":"On departure process in the batch arrival queue with single vacation and setup time","display_name":"On departure process in the batch arrival queue with single vacation and setup time","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2024508584","doi":"https://doi.org/10.2478/v10065-010-0040-x","mag":"2024508584"},"language":"en","primary_location":{"id":"doi:10.2478/v10065-010-0040-x","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10065-010-0040-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210184648","display_name":"Annales Universitatis Mariae Curie-Sklodowska sectio AI \u2013 Informatica","issn_l":"1732-1360","issn":["1732-1360","2083-3628"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales UMCS, Informatica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.2478/v10065-010-0040-x","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087810785","display_name":"Wojciech M. Kempa","orcid":"https://orcid.org/0000-0001-9476-2070"},"institutions":[{"id":"https://openalex.org/I119004910","display_name":"Silesian University of Technology","ror":"https://ror.org/02dyjk442","country_code":"PL","type":"education","lineage":["https://openalex.org/I119004910"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Wojciech Kempa","raw_affiliation_strings":["Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, Gliwice, Poland#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, Gliwice, Poland#TAB#","institution_ids":["https://openalex.org/I119004910"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5087810785"],"corresponding_institution_ids":["https://openalex.org/I119004910"],"apc_list":null,"apc_paid":null,"fwci":1.55903807,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.84889168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"10","issue":"1","first_page":null,"last_page":null},"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/T11720","display_name":"Probability and Risk Models","score":0.96670001745224,"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/T13601","display_name":"Urban Transport Systems Analysis","score":0.9373999834060669,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/probability-generating-function","display_name":"Probability-generating function","score":0.6495456099510193},{"id":"https://openalex.org/keywords/renewal-theory","display_name":"Renewal theory","score":0.6312242746353149},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.6288512945175171},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6170361042022705},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5888822078704834},{"id":"https://openalex.org/keywords/queue","display_name":"Queue","score":0.5799705982208252},{"id":"https://openalex.org/keywords/queueing-theory","display_name":"Queueing theory","score":0.5353963971138},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5112729072570801},{"id":"https://openalex.org/keywords/queueing-system","display_name":"Queueing system","score":0.49951672554016113},{"id":"https://openalex.org/keywords/markovian-arrival-process","display_name":"Markovian arrival process","score":0.4802260994911194},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4750416576862335},{"id":"https://openalex.org/keywords/moment-generating-function","display_name":"Moment-generating function","score":0.4555432200431824},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4532431960105896},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.4323287904262543},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4128292500972748},{"id":"https://openalex.org/keywords/real-time-computing","display_name":"Real-time computing","score":0.3760010898113251},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36977413296699524},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2519071400165558},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17992550134658813},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.15605363249778748},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.08452555537223816}],"concepts":[{"id":"https://openalex.org/C187825244","wikidata":"https://www.wikidata.org/wiki/Q372071","display_name":"Probability-generating function","level":4,"score":0.6495456099510193},{"id":"https://openalex.org/C110507122","wikidata":"https://www.wikidata.org/wiki/Q1356856","display_name":"Renewal theory","level":2,"score":0.6312242746353149},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.6288512945175171},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6170361042022705},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5888822078704834},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.5799705982208252},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.5353963971138},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5112729072570801},{"id":"https://openalex.org/C2986422491","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing system","level":3,"score":0.49951672554016113},{"id":"https://openalex.org/C192163390","wikidata":"https://www.wikidata.org/wiki/Q612061","display_name":"Markovian arrival process","level":3,"score":0.4802260994911194},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4750416576862335},{"id":"https://openalex.org/C101796028","wikidata":"https://www.wikidata.org/wiki/Q535587","display_name":"Moment-generating function","level":3,"score":0.4555432200431824},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4532431960105896},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.4323287904262543},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4128292500972748},{"id":"https://openalex.org/C79403827","wikidata":"https://www.wikidata.org/wiki/Q3988","display_name":"Real-time computing","level":1,"score":0.3760010898113251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36977413296699524},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2519071400165558},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17992550134658813},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.15605363249778748},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.08452555537223816},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2478/v10065-010-0040-x","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10065-010-0040-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210184648","display_name":"Annales Universitatis Mariae Curie-Sklodowska sectio AI \u2013 Informatica","issn_l":"1732-1360","issn":["1732-1360","2083-3628"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales UMCS, Informatica","raw_type":"journal-article"},{"id":"pmh:oai:ojs.umcsd.home.net.pl:article/3272","is_oa":true,"landing_page_url":"http://journals.umcs.pl/ai/article/view/3272","pdf_url":null,"source":{"id":"https://openalex.org/S4306402290","display_name":"Studia Iuridica Lublinensia (Uniwersytet Marii Curie-Sk\u0142odowskiej w Lublinie)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I174183983","host_organization_name":"Maria Curie-Sk\u0142odowska University","host_organization_lineage":["https://openalex.org/I174183983"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Annales Universitatis Mariae Curie-Sklodowska, sectio AI \u00e2\u0080\u0093 Informatica; Vol 10, No 1 (2010); 93-102","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.2478/v10065-010-0040-x","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10065-010-0040-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210184648","display_name":"Annales Universitatis Mariae Curie-Sklodowska sectio AI \u2013 Informatica","issn_l":"1732-1360","issn":["1732-1360","2083-3628"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales UMCS, Informatica","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.44999998807907104,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W118388751","https://openalex.org/W182392954","https://openalex.org/W577991167","https://openalex.org/W1886160976","https://openalex.org/W1967401610","https://openalex.org/W1967433614","https://openalex.org/W1980093303","https://openalex.org/W1989585328","https://openalex.org/W1989931905","https://openalex.org/W1992897018","https://openalex.org/W2005098937","https://openalex.org/W2005851980","https://openalex.org/W2007864759","https://openalex.org/W2114540359","https://openalex.org/W2734644343"],"related_works":["https://openalex.org/W2184541843","https://openalex.org/W2130433141","https://openalex.org/W2047138165","https://openalex.org/W4388297545","https://openalex.org/W2167220663","https://openalex.org/W2064985096","https://openalex.org/W2067078302","https://openalex.org/W2974585908","https://openalex.org/W2902773392","https://openalex.org/W4231953960"],"abstract_inverted_index":{"A":[0],"single-server":[1],"queueing":[2],"system":[3,15,139,175,185],"of":[4,28,34,52,55,77,104,116,120,130,132,137,142,158,183,191],"MX/G/1":[5],"type":[6],"with":[7,148],"unlimited":[8],"buffer":[9],"size":[10],"is":[11,26,41,123],"considered.":[12],"Whenever":[13],"the":[14,18,29,35,39,53,56,59,64,74,81,85,102,138,155,178,181,184,189,197],"becomes":[16],"empty,":[17],"server":[19],"takes":[20,95],"a":[21,44,97,143,168,202],"single":[22,169],"compulsory":[23],"vacation":[24,40,65,170],"that":[25,89],"independent":[27],"arrival":[30],"process.":[31],"The":[32,150],"service":[33],"first":[36,75,162],"customer":[37],"after":[38,63],"preceded":[42],"by":[43,128],"random":[45,98],"setup":[46,60],"time.":[47],"We":[48],"distinguish":[49],"two":[50,159],"cases":[51],"evolution":[54],"system:":[57],"when":[58,73],"time":[61],"begins":[62,70],"only,":[66],"or":[67],"if":[68],"it":[69],"at":[71,90],"once":[72],"group":[76],"customers":[78,105],"enters.":[79],"In":[80],"paper":[82],"we":[83,163,195],"investigate":[84],"departure":[86,121,165],"process":[87,122,166],"h(t)":[88],"any":[91],"fixed":[92],"moment":[93],"t":[94],"on":[96,167],"value":[99],"equal":[100],"to":[101,180,200],"number":[103],"completely":[106],"served":[107],"before":[108],"t.":[109],"An":[110],"explicit":[111],"representation":[112],"for":[113,172],"Laplace":[114],"Transform":[115],"probability":[117],"generating":[118],"function":[119],"derived":[124],"and":[125,140,176],"written":[126],"down":[127],"means":[129],"transforms":[131],"four":[133],"crucial":[134],"input":[135],"distributions":[136],"factors":[141],"certain":[144],"factorization":[145],"identity":[146],"connected":[147],"them.":[149],"results":[151],"are":[152],"obtained":[153],"using":[154],"method":[156],"consisting":[157],"main":[160],"stages:":[161],"study":[164],"cycle":[171],"an":[173],"auxiliary":[174],"direct":[177],"analysis":[179],"case":[182],"without":[186],"vacations,":[187],"applying":[188],"formula":[190],"total":[192],"probability;":[193],"next":[194],"use":[196],"renewal-theory":[198],"approach":[199],"obtain":[201],"general":[203],"formula.":[204]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}