{"id":"https://openalex.org/W2143720727","doi":"https://doi.org/10.1007/s11134-009-9118-9","title":"Monotonicity and error bounds for networks of Erlang loss queues","display_name":"Monotonicity and error bounds for networks of Erlang loss queues","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2143720727","doi":"https://doi.org/10.1007/s11134-009-9118-9","mag":"2143720727"},"language":"en","primary_location":{"id":"doi:10.1007/s11134-009-9118-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-009-9118-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11134-009-9118-9.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_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11134-009-9118-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003550171","display_name":"Richard J. Boucherie","orcid":"https://orcid.org/0000-0002-1046-2044"},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Richard J. Boucherie","raw_affiliation_strings":["Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands","Department of Applied Mathematics, University of Twente, Enschede, The Netherlands 7500 AE"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands","institution_ids":["https://openalex.org/I94624287"]},{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Enschede, The Netherlands 7500 AE","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109486072","display_name":"N.M. van Dijk","orcid":null},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]},{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Nico M. van Dijk","raw_affiliation_strings":["Department of Operations Research, Universiteit van Amsterdam, Roetersstraat 11, 1018 WB, Amsterdam, The Netherlands","Department of Operations Research, Universiteit van Amsterdam, Amsterdam, The Netherlands 1018 WB#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Operations Research, Universiteit van Amsterdam, Roetersstraat 11, 1018 WB, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I865915315","https://openalex.org/I887064364"]},{"raw_affiliation_string":"Department of Operations Research, Universiteit van Amsterdam, Amsterdam, The Netherlands 1018 WB#TAB#","institution_ids":["https://openalex.org/I887064364"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003550171"],"corresponding_institution_ids":["https://openalex.org/I94624287"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.9804,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.81748451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"62","issue":"1-2","first_page":"159","last_page":"193"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9986000061035156,"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":0.9986000061035156,"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/T10575","display_name":"Wireless Communication Networks Research","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9776999950408936,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/erlang","display_name":"Erlang (programming language)","score":0.821324348449707},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6773974895477295},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6201225519180298},{"id":"https://openalex.org/keywords/queue","display_name":"Queue","score":0.5411940813064575},{"id":"https://openalex.org/keywords/queueing-theory","display_name":"Queueing theory","score":0.5165599584579468},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5163854360580444},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.47920140624046326},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46789276599884033},{"id":"https://openalex.org/keywords/erlang-distribution","display_name":"Erlang distribution","score":0.46296998858451843},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4584881663322449},{"id":"https://openalex.org/keywords/dimensioning","display_name":"Dimensioning","score":0.4577535390853882},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.44791021943092346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43324345350265503},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.20432749390602112},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.10897931456565857},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0980643630027771}],"concepts":[{"id":"https://openalex.org/C82484044","wikidata":"https://www.wikidata.org/wiki/Q334879","display_name":"Erlang (programming language)","level":3,"score":0.821324348449707},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6773974895477295},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6201225519180298},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.5411940813064575},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.5165599584579468},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5163854360580444},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.47920140624046326},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46789276599884033},{"id":"https://openalex.org/C145437242","wikidata":"https://www.wikidata.org/wiki/Q762448","display_name":"Erlang distribution","level":3,"score":0.46296998858451843},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4584881663322449},{"id":"https://openalex.org/C89714869","wikidata":"https://www.wikidata.org/wiki/Q2280470","display_name":"Dimensioning","level":2,"score":0.4577535390853882},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.44791021943092346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43324345350265503},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.20432749390602112},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.10897931456565857},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0980643630027771},{"id":"https://openalex.org/C42383842","wikidata":"https://www.wikidata.org/wiki/Q193076","display_name":"Functional programming","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s11134-009-9118-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-009-9118-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11134-009-9118-9.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_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"},{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/2c1b36ae-afd1-4b9b-aa0d-bfd208408ac1","is_oa":false,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/monotonicity-and-error-bounds-for-networks-of-erlang-loss-queues(2c1b36ae-afd1-4b9b-aa0d-bfd208408ac1).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boucherie, R J & van Dijk, N M 2009, 'Monotonicity and error bounds for networks of Erlang loss queues', Queueing Systems, vol. 62, no. 1-2, pp. 159-193. https://doi.org/10.1007/s11134-009-9118-9","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:ris.utwente.nl:openaire/5245be1e-a0fd-43f5-a883-ddb2bb9f0e09","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/5245be1e-a0fd-43f5-a883-ddb2bb9f0e09","pdf_url":"https://ris.utwente.nl/ws/files/6728100/2009-XBoucherieDijk.pdf","source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Boucherie, R J & van Dijk, N M 2009, 'Monotonicity and error bounds for networks of Erlang loss queues', Queueing systems, vol. 62, no. 1-2, pp. 159-193. https://doi.org/10.1007/s11134-009-9118-9","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:dare.uva.nl:publications/2c1b36ae-afd1-4b9b-aa0d-bfd208408ac1","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/monotonicity-and-error-bounds-for-networks-of-erlang-loss-queues(2c1b36ae-afd1-4b9b-aa0d-bfd208408ac1).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Boucherie, R J & van Dijk, N M 2009, 'Monotonicity and error bounds for networks of Erlang loss queues', Queueing Systems, vol. 62, no. 1-2, pp. 159-193. https://doi.org/10.1007/s11134-009-9118-9","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:ris.utwente.nl:publications/a73fd3e6-4655-4afa-b0cb-e13f19f0a326","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1007/s11134-009-9118-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-009-9118-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11134-009-9118-9.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_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2143720727.pdf","grobid_xml":"https://content.openalex.org/works/W2143720727.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1508506372","https://openalex.org/W1512866443","https://openalex.org/W1526512085","https://openalex.org/W1576140702","https://openalex.org/W1963622809","https://openalex.org/W1964876833","https://openalex.org/W1984801914","https://openalex.org/W2004133013","https://openalex.org/W2038661399","https://openalex.org/W2067911502","https://openalex.org/W2075259347","https://openalex.org/W2080727337","https://openalex.org/W2096594845","https://openalex.org/W2098964917","https://openalex.org/W2104884130","https://openalex.org/W2118564187","https://openalex.org/W2121227824","https://openalex.org/W2126760772","https://openalex.org/W2137919757","https://openalex.org/W2139028252","https://openalex.org/W2142795817","https://openalex.org/W2143280922","https://openalex.org/W2160959619","https://openalex.org/W2317872868","https://openalex.org/W2319980604","https://openalex.org/W2325495270","https://openalex.org/W4232461091","https://openalex.org/W4244375800","https://openalex.org/W4252040407"],"related_works":["https://openalex.org/W2594392289","https://openalex.org/W830184964","https://openalex.org/W4380886430","https://openalex.org/W2613997428","https://openalex.org/W2322385984","https://openalex.org/W4327524501","https://openalex.org/W1999178477","https://openalex.org/W4233259071","https://openalex.org/W2162800547","https://openalex.org/W2063143196"],"abstract_inverted_index":{"Networks":[0],"of":[1,21,84,114,140,159],"Erlang":[2],"loss":[3,25],"queues":[4],"naturally":[5],"arise":[6],"when":[7],"modelling":[8],"finite":[9],"communication":[10],"systems":[11],"without":[12],"delays,":[13],"among":[14],"which,":[15],"most":[16],"notably":[17],"are":[18,73,78,139,147,158],"Performance":[19],"measures":[20],"interest":[22,141,161],"such":[23,178],"as":[24,128,179],"probabilities":[26,171],"or":[27],"throughputs":[28],"can":[29],"be":[30,103],"obtained":[31,79],"from":[32],"the":[33,50,61,86,94],"steady":[34,40],"state":[35,41,87],"distribution.":[36],"However,":[37],"while":[38],"this":[39],"distribution":[42],"has":[43],"a":[44,81,90,175],"closed":[45],"product":[46,107],"form":[47,71,108],"expression":[48],"in":[49,60],"first":[51],"case":[52,63],"(loss":[53],"networks),":[54],"it":[55],"does":[56],"not":[57,173],"have":[58],"one":[59],"second":[62],"due":[64],"to":[65,111,167],"blocked":[66],"(and":[67],"lost)":[68],"handovers.":[69],"Product":[70],"approximations":[72,77,109],"therefore":[74],"suggested.":[75],"These":[76],"by":[80,142],"combined":[82],"modification":[83],"both":[85,119],"space":[88],"(by":[89,97],"hypercubic":[91],"expansion)":[92],"and":[93,122,136,150],"transition":[95],"rates":[96],"extra":[98],"redial":[99],"rates).":[100],"It":[101],"will":[102],"shown":[104],"that":[105,169],"these":[106,115],"lead":[110],"The":[112,144,156],"proofs":[113],"results":[116,121,157],"rely":[117],"upon":[118],"monotonicity":[120],"an":[123],"analytic":[124],"error":[125],"bound":[126],"method":[127],"based":[129],"on":[130],"Markov":[131],"reward":[132],"theory.":[133],"This":[134],"combination":[135],"its":[137],"technicalities":[138],"themselves.":[143],"technical":[145],"conditions":[146],"worked":[148],"out":[149],"verified":[151],"for":[152,162,180],"two":[153],"specific":[154],"applications:":[155],"practical":[160],"computational":[163],"simplifications":[164],"and,":[165],"particularly,":[166],"guarantee":[168],"blocking":[170],"do":[172],"exceed":[174],"given":[176],"threshold":[177],"network":[181],"dimensioning.":[182]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}