{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T11:50:47Z","timestamp":1648727447144},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2016,7,14]],"date-time":"2016-07-14T00:00:00Z","timestamp":1468454400000},"content-version":"unspecified","delay-in-days":4153,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Probability"],"published-print":{"date-parts":[[2005,3]]},"abstract":"<jats:p>As proposed by Irle and Gani in 2001, a process <jats:italic>X<\/jats:italic> is said to be slower in level crossing than a process <jats:italic>Y<\/jats:italic> if it takes <jats:italic>X<\/jats:italic> stochastically longer to exceed any given level than it does <jats:italic>Y<\/jats:italic>. In this paper, we extend a result of Irle (2003), relative to the level crossing ordering of uniformizable skip-free-to-the-right continuous-time Markov chains, to derive a new set of sufficient conditions for the level crossing ordering of these processes. We apply our findings to birth-death processes with and without catastrophes, and M\/M\/<jats:italic>s<\/jats:italic>\/<jats:italic>c<\/jats:italic> systems.<\/jats:p>","DOI":"10.1239\/jap\/1110381370","type":"journal-article","created":{"date-parts":[[2005,3,11]],"date-time":"2005-03-11T15:45:49Z","timestamp":1110555949000},"page":"52-60","source":"Crossref","is-referenced-by-count":3,"title":["Level Crossing Ordering of Skip-Free-to-the-Right Continuous-Time Markov Chains"],"prefix":"10.1017","volume":"42","author":[{"given":"F\u00e1tima","family":"Ferreira","sequence":"first","affiliation":[]},{"given":"Ant\u00f3nio","family":"Pacheco","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,7,14]]},"reference":[{"key":"S002190020000005X_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S0269964803171057"},{"key":"S002190020000005X_ref8","volume-title":"Modeling and Analysis of Stochastic Systems","author":"Kulkarni","year":"1995"},{"key":"S002190020000005X_ref4","volume-title":"Fundamentals of Queueing Theory","author":"Gross","year":"1998"},{"key":"S002190020000005X_ref9","volume-title":"Comparison Methods for Stochastic Models and Risks","author":"M\u00fcller","year":"2002"},{"key":"S002190020000005X_ref6","first-page":"66","volume-title":"Probability, Statistics and Seismology","volume":"38A","author":"Irle","year":"2001"},{"key":"S002190020000005X_ref7","doi-asserted-by":"publisher","DOI":"10.1080\/02331887608801286"},{"key":"S002190020000005X_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(02)00465-4"},{"key":"S002190020000005X_ref11","volume-title":"Stochastic Orders and Their Applications","author":"Shaked","year":"1994"},{"key":"S002190020000005X_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0001867800020784"},{"key":"S002190020000005X_ref10","volume-title":"Adventures in Stochastic Processes","author":"Resnick","year":"1992"},{"key":"S002190020000005X_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0021900200019355"},{"key":"S002190020000005X_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0001867800018929"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002190020000005X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T21:16:07Z","timestamp":1556918167000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002190020000005X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2005,3]]}},"alternative-id":["S002190020000005X"],"URL":"https:\/\/doi.org\/10.1239\/jap\/1110381370","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,3]]}}}