{"id":"https://openalex.org/W2017101037","doi":"https://doi.org/10.1155/2013/834731","title":"A Discrete-Time<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mi>G</mml:mi><mml:mi>e</mml:mi><mml:mi>o</mml:mi><mml:mo>/</mml:mo><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mn>1</mml:mn></mml:math>Retrial Queue with<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"><mml:mrow><mml:mi>J</mml:mi></mml:mrow></mml:math>Vacations and Two Types of Breakdowns","display_name":"A Discrete-Time<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mi>G</mml:mi><mml:mi>e</mml:mi><mml:mi>o</mml:mi><mml:mo>/</mml:mo><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mn>1</mml:mn></mml:math>Retrial Queue with<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"><mml:mrow><mml:mi>J</mml:mi></mml:mrow></mml:math>Vacations and Two Types of Breakdowns","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2017101037","doi":"https://doi.org/10.1155/2013/834731","mag":"2017101037"},"language":"en","primary_location":{"id":"doi:10.1155/2013/834731","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/834731","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/834731.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/834731.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101859337","display_name":"Feng Zhang","orcid":"https://orcid.org/0000-0002-4374-8532"},"institutions":[{"id":"https://openalex.org/I135714990","display_name":"North University of China","ror":"https://ror.org/047bp1713","country_code":"CN","type":"education","lineage":["https://openalex.org/I135714990"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Feng Zhang","raw_affiliation_strings":["College of Science, North University of China, Taiyuan 030051, China"],"raw_orcid":"https://orcid.org/0000-0002-4374-8532","affiliations":[{"raw_affiliation_string":"College of Science, North University of China, Taiyuan 030051, China","institution_ids":["https://openalex.org/I135714990"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100951395","display_name":"Zhifeng Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I135714990","display_name":"North University of China","ror":"https://ror.org/047bp1713","country_code":"CN","type":"education","lineage":["https://openalex.org/I135714990"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhifeng Zhu","raw_affiliation_strings":["College of Science, North University of China, Taiyuan 030051, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, North University of China, Taiyuan 030051, China","institution_ids":["https://openalex.org/I135714990"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101859337"],"corresponding_institution_ids":["https://openalex.org/I135714990"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.0733,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.80937847,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"11"},"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9607999920845032,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11773","display_name":"Healthcare Operations and Scheduling Optimization","score":0.9193000197410583,"subfield":{"id":"https://openalex.org/subfields/3604","display_name":"Emergency Medical Services"},"field":{"id":"https://openalex.org/fields/36","display_name":"Health Professions"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7023075819015503},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5784149169921875},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.4002458453178406}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7023075819015503},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5784149169921875},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.4002458453178406}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2013/834731","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/834731","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/834731.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808204","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808204","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:fb44b06c8b96430ebf58bb7152562755","is_oa":true,"landing_page_url":"https://doaj.org/article/fb44b06c8b96430ebf58bb7152562755","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/834731","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/834731","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/834731.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2017101037.pdf","grobid_xml":"https://content.openalex.org/works/W2017101037.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1485087921","https://openalex.org/W1968663063","https://openalex.org/W1990057380","https://openalex.org/W2008028953","https://openalex.org/W2009261453","https://openalex.org/W2027342815","https://openalex.org/W2028145630","https://openalex.org/W2059809123","https://openalex.org/W2067464175","https://openalex.org/W2076442016","https://openalex.org/W2077273886","https://openalex.org/W2077391908","https://openalex.org/W2078528393","https://openalex.org/W2080000082","https://openalex.org/W2082913267","https://openalex.org/W2085176157","https://openalex.org/W2090189565","https://openalex.org/W2091619852","https://openalex.org/W2105071299","https://openalex.org/W2137997684","https://openalex.org/W2145432703","https://openalex.org/W2157261855","https://openalex.org/W2170852456","https://openalex.org/W4230270705"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,22,47,52,61],"concerned":[3],"with":[4],"a":[5,44],"discrete-time<mml:math":[6],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[7,12,29],"id=\"M3\"><mml:mi>G</mml:mi><mml:mi>e</mml:mi><mml:mi>o</mml:mi><mml:mo>/</mml:mo><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mn>1</mml:mn></mml:math>retrial":[8],"queueing":[9,74,118],"model":[10],"with<mml:math":[11],"id=\"M4\"><mml:mrow><mml:mi>J</mml:mi></mml:mrow></mml:math>vacations":[13],"and":[14,60,76,88,114,134],"two":[15,55],"types":[16,56],"of":[17,57,95,132,140],"breakdowns.":[18],"If":[19],"the":[20,24,39,50,68,72,78,85,89,106,110,115,130,141],"orbit":[21,40,86],"empty,":[23],"server":[25,51],"takes":[26],"at":[27,33],"most<mml:math":[28],"id=\"M5\"><mml:mrow><mml:mi>J</mml:mi></mml:mrow></mml:math>vacations":[30],"repeatedly":[31],"until":[32],"least":[34],"one":[35],"customer":[36],"appears":[37],"in":[38,93],"upon":[41],"returning":[42],"from":[43],"vacation.":[45],"It":[46],"assumed":[48],"that":[49],"subject":[53],"to":[54,128],"different":[58],"breakdowns":[59,135],"sent":[62],"immediately":[63],"for":[64],"repair.":[65],"We":[66],"analyze":[67],"Markov":[69],"chain":[70],"underlying":[71],"considered":[73],"system":[75,79,90,119],"derive":[77],"state":[80],"distribution":[81],"as":[82,84],"well":[83],"size":[87,91],"distributions":[92],"terms":[94],"their":[96],"generating":[97,107],"functions.":[98,108],"Then,":[99],"we":[100],"obtain":[101],"some":[102,123],"performance":[103,138],"measures":[104,139],"through":[105],"Moreover,":[109],"stochastic":[111],"decomposition":[112],"property":[113],"corresponding":[116],"continuous-time":[117],"are":[120,126],"investigated.":[121],"Finally,":[122],"numerical":[124],"examples":[125],"provided":[127],"illustrate":[129],"effect":[131],"vacations":[133],"on":[136],"several":[137],"system.":[142]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}