{"id":"https://openalex.org/W2020116653","doi":"https://doi.org/10.1109/tcom.1981.1095145","title":"Asymptotic Expansion for Erlang Loss Function and Its Derivative","display_name":"Asymptotic Expansion for Erlang Loss Function and Its Derivative","publication_year":1981,"publication_date":"1981-09-01","ids":{"openalex":"https://openalex.org/W2020116653","doi":"https://doi.org/10.1109/tcom.1981.1095145","mag":"2020116653"},"language":"en","primary_location":{"id":"doi:10.1109/tcom.1981.1095145","doi":"https://doi.org/10.1109/tcom.1981.1095145","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcom.1981.1095145","pdf_url":null,"source":{"id":"https://openalex.org/S4210170832","display_name":"IRE Transactions on Communications Systems","issn_l":"0096-2244","issn":["0096-2244","2162-2132"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Communications","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/A5054415818","display_name":"Haruo Akimaru","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I136259955","display_name":"Toyohashi University of Technology","ror":"https://ror.org/04ezg6d83","country_code":"JP","type":"education","lineage":["https://openalex.org/I136259955"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"H. Akimaru","raw_affiliation_strings":["School of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Japan","institution_ids":["https://openalex.org/I136259955"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113830498","display_name":"Haruna Takahashi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I136259955","display_name":"Toyohashi University of Technology","ror":"https://ror.org/04ezg6d83","country_code":"JP","type":"education","lineage":["https://openalex.org/I136259955"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"H. Takahashi","raw_affiliation_strings":["School of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Japan","institution_ids":["https://openalex.org/I136259955"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I136259955"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.24368687,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"9","first_page":"1257","last_page":"1260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.7949000000953674,"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":0.7949000000953674,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.1388999968767166,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.01640000008046627,"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/asymptotic-expansion","display_name":"asymptotic expansion","score":0.9869999885559082},{"id":"https://openalex.org/keywords/truncation-error-estimation","display_name":"truncation error estimation","score":0.9639999866485596},{"id":"https://openalex.org/keywords/switching-systems","display_name":"switching systems","score":0.753000020980835},{"id":"https://openalex.org/keywords/queueing-systems","display_name":"queueing systems","score":0.5329999923706055}],"concepts":[{"id":"https://openalex.org/C82484044","wikidata":"https://www.wikidata.org/wiki/Q334879","display_name":"Erlang (programming language)","level":3,"score":0.8699378967285156},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.7103944420814514},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6539642810821533},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6209163665771484},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.580802321434021},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.5785625576972961},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5272882580757141},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.41646426916122437},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3301927149295807},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2960270643234253},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25055646896362305},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2319069802761078},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1219506561756134},{"id":"https://openalex.org/C42383842","wikidata":"https://www.wikidata.org/wiki/Q193076","display_name":"Functional programming","level":2,"score":0.06606444716453552},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcom.1981.1095145","doi":"https://doi.org/10.1109/tcom.1981.1095145","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcom.1981.1095145","pdf_url":null,"source":{"id":"https://openalex.org/S4210170832","display_name":"IRE Transactions on Communications Systems","issn_l":"0096-2244","issn":["0096-2244","2162-2132"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Communications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W1978197837"],"related_works":["https://openalex.org/W1978197837","https://openalex.org/W2058504321","https://openalex.org/W2600662797","https://openalex.org/W2772593575","https://openalex.org/W2092570475","https://openalex.org/W2027476515","https://openalex.org/W2009081824","https://openalex.org/W7100598850","https://openalex.org/W2036916166","https://openalex.org/W7064599693"],"abstract_inverted_index":{"This":[0],"paper":[1],"reveals":[2],"the":[3,7,11,22,25,40,49,61,65,73],"general":[4],"structure":[5],"of":[6,31,39,76],"asymptotic":[8],"expansion":[9,26,41],"for":[10,21,46,72],"Erlang":[12],"loss":[13],"function":[14],"and":[15,29,44,68,79],"its":[16],"derivative.":[17],"A":[18],"recursive":[19],"formula":[20,59],"coefficients":[23],"in":[24],"is":[27,42,70],"given":[28],"some":[30],"numerical":[32],"examples":[33],"are":[34,55],"presented.":[35],"The":[36,57],"truncation":[37],"error":[38,50],"estimated":[43],"charts":[45],"calculation":[47,62],"with":[48],"less":[51],"than":[52],"0.1":[53],"percent":[54],"shown.":[56],"present":[58],"facilitates":[60],"by":[63],"saving":[64],"computation":[66],"time,":[67],"it":[69],"useful":[71],"optimization":[74],"problems":[75],"switching":[77],"systems":[78],"other":[80],"applications.":[81]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}