{"id":"https://openalex.org/W1998878945","doi":"https://doi.org/10.1007/bf01245323","title":"Linear independence of root equations forM/G/1 type Markov chains","display_name":"Linear independence of root equations forM/G/1 type Markov chains","publication_year":1995,"publication_date":"1995-09-01","ids":{"openalex":"https://openalex.org/W1998878945","doi":"https://doi.org/10.1007/bf01245323","mag":"1998878945"},"language":"en","primary_location":{"id":"doi:10.1007/bf01245323","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01245323","pdf_url":null,"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":null,"license_id":null,"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":"green","oa_url":"https://hdl.handle.net/2027.42/47619","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037512392","display_name":"H. Richard Gail","orcid":null},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]},{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. R. Gail","raw_affiliation_strings":["IBM Thomas J. Watson Research Center, 10598, Yorktown Heights, NY, USA","IBM\u2014Thomas J. Watson Research Center, Yorktown Heights, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Thomas J. Watson Research Center, 10598, Yorktown Heights, NY, USA","institution_ids":["https://openalex.org/I4210114115"]},{"raw_affiliation_string":"IBM\u2014Thomas J. Watson Research Center, Yorktown Heights, USA","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050001689","display_name":"S. L. Hantler","orcid":null},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]},{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. L. Hantler","raw_affiliation_strings":["IBM Thomas J. Watson Research Center, 10598, Yorktown Heights, NY, USA","IBM\u2014Thomas J. Watson Research Center, Yorktown Heights, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Thomas J. Watson Research Center, 10598, Yorktown Heights, NY, USA","institution_ids":["https://openalex.org/I4210114115"]},{"raw_affiliation_string":"IBM\u2014Thomas J. Watson Research Center, Yorktown Heights, USA","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103098664","display_name":"Maawiya Ould Sidi","orcid":"https://orcid.org/0000-0002-0034-5661"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"M. Sidi","raw_affiliation_strings":["Technion, IIT, 32000, Haifa, Israel","Technion (IIT), Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technion, IIT, 32000, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Technion (IIT), Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109534991","display_name":"B. A. Taylor","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. A. Taylor","raw_affiliation_strings":["The University of Michigan, 48109, Ann Arbor, MI, USA","the University of Michigan, Ann Arbor, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Michigan, 48109, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"the University of Michigan, Ann Arbor, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.8524,"has_fulltext":true,"cited_by_count":35,"citation_normalized_percentile":{"value":0.849039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"20","issue":"3-4","first_page":"321","last_page":"339"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.8819000124931335,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.8819000124931335,"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"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.857200026512146,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10044","display_name":"Protein Structure and Dynamics","score":0.8493000268936157,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.776850163936615},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7683372497558594},{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.6363773345947266},{"id":"https://openalex.org/keywords/balance-equation","display_name":"Balance equation","score":0.5799782872200012},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.565037190914154},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.561040997505188},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.493068665266037},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4857671558856964},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4320584833621979},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4214402139186859},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3863622844219208},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.25659871101379395},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08053997159004211}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.776850163936615},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7683372497558594},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.6363773345947266},{"id":"https://openalex.org/C158917313","wikidata":"https://www.wikidata.org/wiki/Q4849964","display_name":"Balance equation","level":4,"score":0.5799782872200012},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.565037190914154},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.561040997505188},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.493068665266037},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4857671558856964},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4320584833621979},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4214402139186859},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3863622844219208},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.25659871101379395},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08053997159004211},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bf01245323","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01245323","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"},{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/47619","is_oa":true,"landing_page_url":"http://hdl.handle.net/2027.42/47619>","pdf_url":"https://hdl.handle.net/2027.42/47619","source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/47619","is_oa":true,"landing_page_url":"http://hdl.handle.net/2027.42/47619>","pdf_url":"https://hdl.handle.net/2027.42/47619","source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1998878945.pdf"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1538639190","https://openalex.org/W1584847367","https://openalex.org/W1981651576","https://openalex.org/W2324715883","https://openalex.org/W2610857016","https://openalex.org/W2905326196","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2391646062","https://openalex.org/W2070152949","https://openalex.org/W2895561605","https://openalex.org/W2365817010","https://openalex.org/W13375693","https://openalex.org/W3099350264","https://openalex.org/W185427221","https://openalex.org/W1989625169","https://openalex.org/W2113019827","https://openalex.org/W2379651310"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}