{"id":"https://openalex.org/W4281735717","doi":"https://doi.org/10.3390/sym14061167","title":"On the Exiting Patterns of Multivariate Renewal-Reward Processes with an Application to Stochastic Networks","display_name":"On the Exiting Patterns of Multivariate Renewal-Reward Processes with an Application to Stochastic Networks","publication_year":2022,"publication_date":"2022-06-06","ids":{"openalex":"https://openalex.org/W4281735717","doi":"https://doi.org/10.3390/sym14061167"},"language":"en","primary_location":{"id":"doi:10.3390/sym14061167","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14061167","pdf_url":"https://www.mdpi.com/2073-8994/14/6/1167/pdf?version=1654515766","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/6/1167/pdf?version=1654515766","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053279009","display_name":"Ryan T. White","orcid":"https://orcid.org/0000-0002-5524-629X"},"institutions":[{"id":"https://openalex.org/I106959904","display_name":"Florida Institute of Technology","ror":"https://ror.org/04atsbb87","country_code":"US","type":"education","lineage":["https://openalex.org/I106959904"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ryan T. White","raw_affiliation_strings":["Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA"],"raw_orcid":"https://orcid.org/0000-0002-5524-629X","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA","institution_ids":["https://openalex.org/I106959904"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053279009"],"corresponding_institution_ids":["https://openalex.org/I106959904"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1689,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51692308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"6","first_page":"1167","last_page":"1167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9962999820709229,"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/T11720","display_name":"Probability and Risk Models","score":0.9962999820709229,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9932000041007996,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9815000295639038,"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/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.8203120231628418},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5745418667793274},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.5485672354698181},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.5300725698471069},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5103721022605896},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.4997086524963379},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4742621183395386},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.46424400806427},{"id":"https://openalex.org/keywords/renewal-theory","display_name":"Renewal theory","score":0.4638436436653137},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4570711553096771},{"id":"https://openalex.org/keywords/stochastic-ordering","display_name":"Stochastic ordering","score":0.44438016414642334},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.4172244071960449},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36708855628967285},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36584246158599854},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3357086777687073},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.165768563747406},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.12275511026382446},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0647447407245636}],"concepts":[{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.8203120231628418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5745418667793274},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.5485672354698181},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5300725698471069},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5103721022605896},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.4997086524963379},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4742621183395386},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.46424400806427},{"id":"https://openalex.org/C110507122","wikidata":"https://www.wikidata.org/wiki/Q1356856","display_name":"Renewal theory","level":2,"score":0.4638436436653137},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4570711553096771},{"id":"https://openalex.org/C32645036","wikidata":"https://www.wikidata.org/wiki/Q475164","display_name":"Stochastic ordering","level":2,"score":0.44438016414642334},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.4172244071960449},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36708855628967285},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36584246158599854},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3357086777687073},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.165768563747406},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.12275511026382446},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0647447407245636},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14061167","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14061167","pdf_url":"https://www.mdpi.com/2073-8994/14/6/1167/pdf?version=1654515766","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1e9df57483644782a03b955d3049e1e3","is_oa":true,"landing_page_url":"https://doaj.org/article/1e9df57483644782a03b955d3049e1e3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 6, p 1167 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/6/1167/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14061167","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14061167","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14061167","pdf_url":"https://www.mdpi.com/2073-8994/14/6/1167/pdf?version=1654515766","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4281735717.pdf"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W1659890402","https://openalex.org/W1968850438","https://openalex.org/W1972370506","https://openalex.org/W1972441125","https://openalex.org/W1990233169","https://openalex.org/W1990753149","https://openalex.org/W1995453571","https://openalex.org/W1995922652","https://openalex.org/W1998637290","https://openalex.org/W2003432780","https://openalex.org/W2005910253","https://openalex.org/W2010624285","https://openalex.org/W2016586635","https://openalex.org/W2024610598","https://openalex.org/W2035394851","https://openalex.org/W2035490465","https://openalex.org/W2047615370","https://openalex.org/W2048058897","https://openalex.org/W2060699057","https://openalex.org/W2062126404","https://openalex.org/W2064962060","https://openalex.org/W2065501141","https://openalex.org/W2065640593","https://openalex.org/W2067613733","https://openalex.org/W2077642920","https://openalex.org/W2080505067","https://openalex.org/W2086458537","https://openalex.org/W2104759269","https://openalex.org/W2111074574","https://openalex.org/W2116653060","https://openalex.org/W2135094424","https://openalex.org/W2165834468","https://openalex.org/W2264658725","https://openalex.org/W2523140505","https://openalex.org/W2793173952","https://openalex.org/W2800437611","https://openalex.org/W2913947510","https://openalex.org/W2921268006","https://openalex.org/W2949286879","https://openalex.org/W2950225623","https://openalex.org/W2952913929","https://openalex.org/W2992645009","https://openalex.org/W2994698584","https://openalex.org/W3113807548","https://openalex.org/W3123240089","https://openalex.org/W3190639977","https://openalex.org/W3194296281","https://openalex.org/W4233879328","https://openalex.org/W6667446125","https://openalex.org/W6677144511","https://openalex.org/W6758568772","https://openalex.org/W6759110286","https://openalex.org/W6799693528"],"related_works":["https://openalex.org/W4387367109","https://openalex.org/W4384447705","https://openalex.org/W4200006019","https://openalex.org/W4213236634","https://openalex.org/W4233709816","https://openalex.org/W2744141321","https://openalex.org/W283926992","https://openalex.org/W4239925015","https://openalex.org/W2374815698","https://openalex.org/W10119213"],"abstract_inverted_index":{"This":[0],"article":[1],"is":[2],"a":[3,41,54,70],"study":[4],"of":[5,13,32,43,50,76,81,89,100,119],"vector-valued":[6],"renewal-reward":[7],"processes":[8],"on":[9],"Rd.":[10],"The":[11,84],"jumps":[12],"the":[14,51,74,90,98,120],"process":[15,52],"are":[16,66,92,109],"assumed":[17],"to":[18,64,68,97,111],"be":[19,35],"independent":[20],"and":[21,45,60,86,103],"identically":[22],"distributed":[23],"nonnegative":[24],"random":[25],"vectors":[26],"with":[27,62,113],"mutually":[28],"dependent":[29],"components,":[30],"each":[31],"which":[33],"may":[34],"either":[36],"discrete":[37,44],"or":[38],"continuous":[39,46],"(or":[40],"mixture":[42],"components).":[47],"Each":[48],"component":[49],"has":[53],"fixed":[55],"threshold.":[56],"Operational":[57],"calculus":[58],"techniques":[59],"symmetries":[61],"respect":[63],"permutations":[65],"used":[67],"find":[69],"general":[71],"result":[72,91],"for":[73],"probability":[75],"an":[77,95],"arbitrary":[78],"weak":[79],"ordering":[80],"threshold":[82],"crossings.":[83],"analytic":[85],"numerical":[87],"tractability":[88],"demonstrated":[93],"by":[94],"application":[96],"reliability":[99],"stochastic":[101],"networks":[102],"some":[104],"other":[105],"special":[106],"cases.":[107],"Results":[108],"shown":[110],"agree":[112],"empirical":[114],"probabilities":[115],"generated":[116],"through":[117],"simulation":[118],"process.":[121]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
