{"id":"https://openalex.org/W4236500573","doi":"https://doi.org/10.1017/s0021900200013176","title":"Computing Stationary Expectations in Level-Dependent QBD Processes","display_name":"Computing Stationary Expectations in Level-Dependent QBD Processes","publication_year":2013,"publication_date":"2013-03-01","ids":{"openalex":"https://openalex.org/W4236500573","doi":"https://doi.org/10.1017/s0021900200013176"},"language":"en","primary_location":{"id":"doi:10.1017/s0021900200013176","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0021900200013176","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","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/A5090016931","display_name":"Hendrik Baumann","orcid":"https://orcid.org/0000-0001-5050-0976"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hendrik Baumann","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5012212299","display_name":"Werner Sandmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Werner Sandmann","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090016931"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0526,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.83767315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"50","issue":"01","first_page":"151","last_page":"165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9995999932289124,"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":0.9995999932289124,"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/T11195","display_name":"Simulation Techniques and Applications","score":0.9789000153541565,"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/T11773","display_name":"Healthcare Operations and Scheduling Optimization","score":0.9283000230789185,"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/mathematics","display_name":"Mathematics","score":0.720430314540863},{"id":"https://openalex.org/keywords/queueing-theory","display_name":"Queueing theory","score":0.7008708119392395},{"id":"https://openalex.org/keywords/stationary-distribution","display_name":"Stationary distribution","score":0.6426613330841064},{"id":"https://openalex.org/keywords/cumulant","display_name":"Cumulant","score":0.540397584438324},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5315900444984436},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5115271806716919},{"id":"https://openalex.org/keywords/stationary-process","display_name":"Stationary process","score":0.4912077784538269},{"id":"https://openalex.org/keywords/stationary-state","display_name":"Stationary state","score":0.4539797008037567},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36384376883506775},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2497909665107727},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1646365523338318},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.16163182258605957}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.720430314540863},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.7008708119392395},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.6426613330841064},{"id":"https://openalex.org/C172686274","wikidata":"https://www.wikidata.org/wiki/Q746007","display_name":"Cumulant","level":2,"score":0.540397584438324},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5315900444984436},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5115271806716919},{"id":"https://openalex.org/C110405555","wikidata":"https://www.wikidata.org/wiki/Q1192209","display_name":"Stationary process","level":2,"score":0.4912077784538269},{"id":"https://openalex.org/C47458137","wikidata":"https://www.wikidata.org/wiki/Q911951","display_name":"Stationary state","level":2,"score":0.4539797008037567},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36384376883506775},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2497909665107727},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1646365523338318},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.16163182258605957},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0021900200013176","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0021900200013176","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1987886940","https://openalex.org/W2046439604","https://openalex.org/W2053217384","https://openalex.org/W2090542186","https://openalex.org/W2093550427","https://openalex.org/W2135987490","https://openalex.org/W2168739325"],"related_works":["https://openalex.org/W2033050283","https://openalex.org/W1964237502","https://openalex.org/W2801640167","https://openalex.org/W2066988799","https://openalex.org/W2549861624","https://openalex.org/W3129662985","https://openalex.org/W1532813632","https://openalex.org/W2082649263","https://openalex.org/W2508315671","https://openalex.org/W2313379943"],"abstract_inverted_index":{"Stationary":[0],"expectations":[1,45],"corresponding":[2],"to":[3],"long-run":[4,18],"averages":[5],"of":[6,26,52,81,90],"additive":[7],"functionals":[8],"on":[9],"level-dependent":[10],"quasi-birth-and-death":[11],"processes":[12],"are":[13,85],"considered.":[14],"Special":[15],"cases":[16],"include":[17],"average":[19],"costs":[20],"or":[21],"rewards,":[22],"moments":[23],"and":[24,32,87],"cumulants":[25],"steady-state":[27],"queueing":[28,97],"network":[29,98],"performance":[30],"measures,":[31],"many":[33],"others.":[34],"We":[35],"provide":[36],"a":[37,96],"matrix-analytic":[38],"scheme":[39],"for":[40,66],"numerically":[41],"computing":[42,48],"such":[43],"stationary":[44,50,67],"without":[46],"explicitly":[47],"the":[49,53,79,88,91],"distribution":[51],"process,":[54],"which":[55],"yields":[56],"an":[57],"algorithm":[58,92],"that":[59],"is":[60,93],"as":[61,63],"quick":[62],"its":[64],"counterparts":[65],"distributions":[68],"but":[69],"requires":[70],"far":[71],"less":[72],"computer":[73],"storage.":[74],"Specific":[75],"problems":[76],"arising":[77],"in":[78],"case":[80],"infinite":[82],"state":[83],"spaces":[84],"discussed":[86],"application":[89],"demonstrated":[94],"by":[95],"example.":[99]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}