{"id":"https://openalex.org/W3179697346","doi":"https://doi.org/10.1016/j.orl.2021.06.014","title":"Busy periods of discrete-time queues using the Lagrange implicit function theorem","display_name":"Busy periods of discrete-time queues using the Lagrange implicit function theorem","publication_year":2021,"publication_date":"2021-07-08","ids":{"openalex":"https://openalex.org/W3179697346","doi":"https://doi.org/10.1016/j.orl.2021.06.014","mag":"3179697346"},"language":"en","primary_location":{"id":"doi:10.1016/j.orl.2021.06.014","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.orl.2021.06.014","pdf_url":null,"source":{"id":"https://openalex.org/S27769002","display_name":"Operations Research Letters","issn_l":"0167-6377","issn":["0167-6377","1872-7468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research Letters","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/A5039624815","display_name":"Geoffrey W. Brown","orcid":"https://orcid.org/0000-0003-2614-6174"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Geoffrey W. Brown","raw_affiliation_strings":["Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada","institution_ids":["https://openalex.org/I98251732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039956503","display_name":"N. Balakrishnan","orcid":"https://orcid.org/0000-0001-5842-8892"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Narayanaswamy Balakrishnan","raw_affiliation_strings":["Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada","institution_ids":["https://openalex.org/I98251732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039624815"],"corresponding_institution_ids":["https://openalex.org/I98251732"],"apc_list":{"value":2760,"currency":"USD","value_usd":2760},"apc_paid":null,"fwci":0.2116,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55603132,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"49","issue":"5","first_page":"650","last_page":"654"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9988999962806702,"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":0.9988999962806702,"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/T11716","display_name":"Random Matrices and Applications","score":0.9865000247955322,"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/queue","display_name":"Queue","score":0.6919645071029663},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.6232709288597107},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5770764350891113},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.570353090763092},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5332908630371094},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5037826895713806},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5036348700523376},{"id":"https://openalex.org/keywords/bernoulli-process","display_name":"Bernoulli process","score":0.4841350018978119},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.4688122272491455},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44901227951049805},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4478604793548584},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.28383782505989075},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24669033288955688},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10620149970054626}],"concepts":[{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.6919645071029663},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.6232709288597107},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5770764350891113},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.570353090763092},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5332908630371094},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5037826895713806},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5036348700523376},{"id":"https://openalex.org/C23990920","wikidata":"https://www.wikidata.org/wiki/Q518831","display_name":"Bernoulli process","level":3,"score":0.4841350018978119},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.4688122272491455},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44901227951049805},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4478604793548584},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28383782505989075},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24669033288955688},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10620149970054626},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.orl.2021.06.014","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.orl.2021.06.014","pdf_url":null,"source":{"id":"https://openalex.org/S27769002","display_name":"Operations Research Letters","issn_l":"0167-6377","issn":["0167-6377","1872-7468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W2005804192","https://openalex.org/W2399991609","https://openalex.org/W2905199852","https://openalex.org/W2911361414","https://openalex.org/W4212799367","https://openalex.org/W4241257365","https://openalex.org/W4299490515"],"related_works":["https://openalex.org/W1965445247","https://openalex.org/W2614254025","https://openalex.org/W1532661502","https://openalex.org/W2057070106","https://openalex.org/W4206788352","https://openalex.org/W2129020938","https://openalex.org/W4236327034","https://openalex.org/W265990816","https://openalex.org/W2011912538","https://openalex.org/W2974666701"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}