{"id":"https://openalex.org/W7225642113","doi":"https://doi.org/10.5281/zenodo.24069918","title":"The time-stationary and Palm inter-arrival times of a Markov-modulated Poisson process need not be ordered","display_name":"The time-stationary and Palm inter-arrival times of a Markov-modulated Poisson process need not be ordered","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225642113","doi":"https://doi.org/10.5281/zenodo.24069918"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24069918","doi":"https://doi.org/10.5281/zenodo.24069918","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069918","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24069918","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041315596","display_name":"Yitzchak Shmalo","orcid":"https://orcid.org/0000-0002-2886-3049","observed_orcids":["https://orcid.org/0000-0002-2886-3049"]},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Shmalo, Yitzchak","raw_affiliation_strings":["Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041315596"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.4713999927043915,"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":0.4713999927043915,"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/T13500","display_name":"Probability and Statistical Research","score":0.39259999990463257,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.07440000027418137,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-modulated-poisson-process","display_name":"Markov modulated Poisson process","score":0.9990000128746033},{"id":"https://openalex.org/keywords/interarrival-times","display_name":"interarrival times","score":0.9150000214576721},{"id":"https://openalex.org/keywords/palm-distribution","display_name":"palm distribution","score":0.7549999952316284},{"id":"https://openalex.org/keywords/stationary-distribution","display_name":"stationary distribution","score":0.5609999895095825},{"id":"https://openalex.org/keywords/stochastic-orders","display_name":"stochastic ordering","score":0.6980000138282776},{"id":"https://openalex.org/keywords/hazard-function","display_name":"hazard function","score":0.6349999904632568},{"id":"https://openalex.org/keywords/cox-process","display_name":"Cox process","score":0.9079999923706055},{"id":"https://openalex.org/keywords/phase-type-distributions","display_name":"phase-type distributions","score":0.8289999961853027},{"id":"https://openalex.org/keywords/mean-convexity","display_name":"mean convexity","score":0.6650000214576721},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.8659999966621399}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7340999841690063},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6438999772071838},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.6031000018119812},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5317999720573425},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4878000020980835},{"id":"https://openalex.org/C155051063","wikidata":"https://www.wikidata.org/wiki/Q1290919","display_name":"Cox process","level":4,"score":0.4731999933719635},{"id":"https://openalex.org/C3017552255","wikidata":"https://www.wikidata.org/wiki/Q4135208","display_name":"Arrival time","level":2,"score":0.4668999910354614},{"id":"https://openalex.org/C110507122","wikidata":"https://www.wikidata.org/wiki/Q1356856","display_name":"Renewal theory","level":2,"score":0.4562000036239624},{"id":"https://openalex.org/C133338972","wikidata":"https://www.wikidata.org/wiki/Q2055750","display_name":"Compound Poisson process","level":4,"score":0.4542999863624573},{"id":"https://openalex.org/C166144826","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson process","level":3,"score":0.45159998536109924},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4246000051498413},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4077000021934509},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4032000005245209},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3781000077724457},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.3630000054836273},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3603000044822693},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3546999990940094},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3447999954223633},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.34279999136924744},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.32989999651908875},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2973000109195709},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C149717495","wikidata":"https://www.wikidata.org/wiki/Q117806","display_name":"Gamma distribution","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.26759999990463257}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24069918","doi":"https://doi.org/10.5281/zenodo.24069918","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069918","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24069919","doi":"https://doi.org/10.5281/zenodo.24069919","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069919","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24069918","doi":"https://doi.org/10.5281/zenodo.24069918","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069918","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2943080170","https://openalex.org/W2066906122","https://openalex.org/W7097371994","https://openalex.org/W2061500975","https://openalex.org/W2034075882","https://openalex.org/W576867945","https://openalex.org/W2788775423","https://openalex.org/W1993836657","https://openalex.org/W2094503683","https://openalex.org/W7099930669"],"abstract_inverted_index":{"For":[0,80,101,140],"an":[1,24,123],"irreducible":[2],"Markov-modulated":[3],"Poisson":[4],"process,":[5],"let":[6],"$T^\\pi$":[7,39,74],"be":[8,158],"the":[9,16,21,27,31,48,55,70,77,102,105,143,150,161],"time":[10,22],"from":[11,23],"a":[12,81,86,96],"stationary":[13],"instant":[14],"to":[15,26,69],"next":[17,28],"arrival":[18,25,78,109],"and":[19,35,45,122],"$T^\\alpha$":[20],"one":[29],"in":[30,136,160],"event-stationary":[32],"version.":[33],"Asanjarani":[34],"Nazarathy":[36],"conjectured":[37],"that":[38,149],"is":[40,63,67],"stochastically":[41],"larger":[42],"than":[43],"$T^\\alpha$,":[44],"He":[46],"listed":[47],"same":[49],"property":[50],"among":[51],"open":[52],"questions":[53],"on":[54,95,104],"MMPP":[56,103,126],"class":[57],"of":[58,73,98,152,163],"phase-type":[59],"distributions.":[60],"The":[61,65],"conjecture":[62],"false.":[64],"order":[66,144],"equivalent":[68],"hazard":[71],"rate":[72],"never":[75],"exceeding":[76],"rate.":[79],"Cox":[82],"process":[83],"driven":[84],"by":[85],"non-constant":[87],"periodic":[88],"intensity":[89],"with":[90,108,127],"uniform":[91],"phase":[92],"this":[93],"fails":[94,114],"set":[97],"positive":[99,128],"measure.":[100],"directed":[106],"$n$-cycle":[107],"rates":[110,130],"$\\varepsilon(1+b\\cos(2\\pi":[111],"j/n))$":[112],"it":[113],"for":[115],"all":[116],"small":[117],"$\\varepsilon>0$":[118],"whenever":[119],"$n\\ge":[120],"12$,":[121],"explicit":[124],"twelve-state":[125],"rational":[129,138],"has":[131],"$\\mathbb":[132],"P(T^\\pi>19/2)-\\mathbb":[133],"P(T^\\alpha>19/2)<-1/300000$,":[134],"proved":[135],"exact":[137],"arithmetic.":[139],"reversible":[141],"modulators":[142],"holds.":[145],"We":[146],"also":[147],"show":[148],"mean":[151],"He's":[153],"MMPP-type":[154],"distribution":[155],"need":[156],"not":[157],"convex":[159],"speed":[162],"modulation.":[164]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
