{"65187":{"#nid":"65187","#data":{"type":"event","title":"Stochastic Systems Seminar","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETITLE:\u0026nbsp; \u003C\/strong\u003EStochastic Systems Seminar\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003ESPEAKER:\u003C\/strong\u003E\u0026nbsp; Masakiyo Miyazawa\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EABSTRACT:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003EWe are concerned with the stationary distributions of reflecting random \nwalks on the multidimensional nonnegative orthant and other related \nprocesses, provided they exist. Such stationary distributions arise in \nperformance evaluation for various queueing systems and their networks. \nHowever, it is very hard to obtain them analytically in general, so our \ninterest is directed to analytically tractable characteristics. For \nthis, we consider tail asymptotics of the stationary distributions.\n\u003C\/p\u003E\u003Cp\u003E\u003Cbr \/\u003EThe purpose of this talk is twofold. In the first part, we discuss why \nwe need a reflecting random walk for a queueing network. This includes \nintroducing a new class called a generalized reflecting random walk. In \nthe second part, we overview the current approaches to attack the tail \nasymptotic problem from a unified viewpoint. Among them, we focus on an \nanalytic function approach, which is recently developed by the author \nand his colleagues. We like to show its key ideas, and demonstrate how \nthey work. We here mainly consider the tail asymptotics for two \ndimensional reflecting random walks, but also discuss how we can \napproach the case of more than two dimensions. We finally note that a \nsimilar approach has been and is being studied for a semimartingale \nreflecting Brownian motion.\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Stochastic Systems Seminar"}],"uid":"27187","created_gmt":"2011-03-28 14:25:21","changed_gmt":"2016-10-08 01:54:38","author":"Anita Race","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2011-03-31T12:00:00-04:00","event_time_end":"2011-03-31T13:00:00-04:00","event_time_end_last":"2011-03-31T13:00:00-04:00","gmt_time_start":"2011-03-31 16:00:00","gmt_time_end":"2011-03-31 17:00:00","gmt_time_end_last":"2011-03-31 17:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[],"keywords":[],"core_research_areas":[],"news_room_topics":[],"event_categories":[],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}