{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T03:49:30Z","timestamp":1759117770790},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p>In this paper we show that fractional Brownian motion with <jats:italic>H<\/jats:italic> &amp;lt; \u00bd can arise as a limit of a simple class of traffic processes that we call \u2018scheduled traffic models\u2019. To our knowledge, this paper provides the first simple traffic model leading to fractional Brownnian motion with <jats:italic>H<\/jats:italic> &amp;lt; \u00bd. We also discuss some immediate implications of this result for queues fed by scheduled traffic, including a heavy-traffic limit theorem.<\/jats:p>","DOI":"10.1017\/s0021900200009487","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:49:46Z","timestamp":1459262986000},"page":"710-718","source":"Crossref","is-referenced-by-count":3,"title":["Fractional Brownian Motion with H &lt; 1\/2 as a Limit of Scheduled Traffic"],"prefix":"10.1017","volume":"49","author":[{"given":"Victor F.","family":"Araman","sequence":"first","affiliation":[]},{"given":"Peter W.","family":"Glynn","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"S0021900200009487_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2006.02.003"},{"key":"S0021900200009487_ref8","first-page":"1385","volume":"18","year":"2009","journal-title":"Ann. Appl. Prob."},{"key":"S0021900200009487_ref7","first-page":"119","volume-title":"Stochastic Networks: Theory and Applications","year":"1996"},{"key":"S0021900200009487_ref1","volume-title":"Convergence of Probability Measures","year":"1999"},{"key":"S0021900200009487_ref6","first-page":"383","volume-title":"In and Out of Equilibrium 2","year":"2008"},{"key":"S0021900200009487_ref10","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1015961155"},{"key":"S0021900200009487_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(99)00041-1"},{"key":"S0021900200009487_ref2","volume-title":"Queues","year":"1961"},{"key":"S0021900200009487_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/BF00532868"},{"key":"S0021900200009487_ref11","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1077544606"},{"key":"S0021900200009487_ref5","first-page":"199","volume-title":"Fractals in Engineering, New Trends in Theory and Applications","year":"2005"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200009487","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T07:08:12Z","timestamp":1682492892000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200009487\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":11,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2012,9]]}},"alternative-id":["S0021900200009487"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200009487","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9]]}}}