{"id":50,"date":"2018-10-18T18:46:01","date_gmt":"2018-10-18T16:46:01","guid":{"rendered":"https:\/\/pole-acs.lis-lab.fr\/?p=50"},"modified":"2019-03-31T09:39:18","modified_gmt":"2019-03-31T07:39:18","slug":"stephane-gaubert","status":"publish","type":"post","link":"https:\/\/pole-acs.lis-lab.fr\/?p=50","title":{"rendered":"St\u00e9phane Gaubert (CMAP, \u00c9cole Polytechnique)"},"content":{"rendered":"<h3><a href=\"http:\/\/www.cmap.polytechnique.fr\/~gaubert\/\"><span style=\"color: #0b2161;\">St\u00e9phane Gaubert<\/span><\/a><br \/>\n<span style=\"color: #0b2161;\"><a style=\"color: #0b2161;\" href=\"https:\/\/portail.polytechnique.edu\/cmap\/fr\">CMAP UMR CNRS 7641<\/a><\/span><br \/>\n<span style=\"color: #0b2161;\">\u00c9cole Polytechnique<\/span><\/h3>\n<p><span style=\"color: #0b2161;\">21 Juin 2018, 14.00<\/span><br \/>\n<span style=\"color: #0b2161;\">salle des commissions, b\u00e2t Polytech<\/span><br \/>\n<span style=\"color: #0b2161;\">Campus de St. J\u00e9r\u00f4me<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"color: #0b2161;\"><em>Tropical analysis of timed Petri nets with priorities and application to performance evaluation of an emergency call center<\/em><\/span><\/h3>\n<p><em><span style=\"color: #0b2161;\">We analyze a timed Petri net model of an emergency call center which processes calls with different levels of priority. The counter variables of the Petri net represent the cumulated number of events as a function of time. We show that these variables are determined by a piecewise linear dynamical system. We also prove that computing the stationary regimes of the associated uid dynamics reduces to the problem of computing a tropical prevariety, i.e., to solving a polynomial system over a tropical (min-plus) semifield. This leads to explicit formulae expressing the throughput of the uid system as a piecewise linear function of the resources, revealing the existence of different congestion phases. Numerical experiments show that the analysis of the fluid dynamics yields a good approximation of the real throughput. In this way, tropical geometry allows one to identify bottleneck resources. This works originates from a case study, concerning the analysis of the new organization of reception of the 17-18-112 emergency calls in the Paris area, currently deployed by Pr\u00e9fecture de Police. This is a joint work with Xavier Allamigeon and Vianney Boeuf.<\/span> <\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>St\u00e9phane Gaubert CMAP UMR CNRS 7641 \u00c9cole Polytechnique 21 Juin 2018, 14.00 salle des commissions, b\u00e2t Polytech Campus de St. J\u00e9r\u00f4me &nbsp; Tropical analysis of timed Petri nets with priorities and application to performance evaluation of an emergency call center We analyze a timed Petri net model of an emergency call center which processes calls &hellip; <a href=\"https:\/\/pole-acs.lis-lab.fr\/?p=50\" class=\"more-link\">Continuer la lecture de <span class=\"screen-reader-text\">St\u00e9phane Gaubert (CMAP, \u00c9cole Polytechnique)<\/span><\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,6],"tags":[3],"class_list":["post-50","post","type-post","status-publish","format-standard","hentry","category-2","category-st-jerome","tag-3"],"_links":{"self":[{"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/posts\/50","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=50"}],"version-history":[{"count":3,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/posts\/50\/revisions"}],"predecessor-version":[{"id":56,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/posts\/50\/revisions\/56"}],"wp:attachment":[{"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=50"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=50"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=50"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}