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UID:150@lincs.fr
DTSTART;TZID=Europe/Paris:20140430T140000
DTEND;TZID=Europe/Paris:20140430T150000
DTSTAMP:20170313T171308Z
URL:https://www.lincs.fr/events/tandem-jackson-networks-asymmetric-inclusi
 on-processes-catalan-numbers/
SUMMARY:Tandem Jackson Networks\, Asymmetric Inclusion Processes and
 Catalan Numbers
DESCRIPTION:The Tandem Jackson Networkis a system of n sites (queues)in
 series\, where single particles (customers\, jobs\, packets\, etc.) move\,
 one by one anduni-directionally\,from one site to the next until they leave
 the system. (Think\, for example\, on aproduction line\, or on a line in a
 cafeteria).When each site is a M/M/1 queue\, the Tandem Jackson Network is
 famous for its product-form solution of the multi-dimensional Probability
 Generating Function of the site occupancies. In contrast\, the Asymmetric
 Inclusion Process (ASIP) is a series of n Markovian queues (sites)\, each
 with unbounded capacity\, but with unlimited-size batch service. That is\,
 when service is completed at site k\, all particles present there move
 simultaneously to sitek+1\,and form a cluster with the particles present in
 the latter site. We analyze the ASIP and show that its multi-dimensional
 Probability Generating Function(PGF) does notposses a product-form
 solution. We then present a method to calculate this PGF. We further show
 that homogeneous systems are optimal and derive limit laws (when the number
 of sites becomes large) for various variables (e.g. busy period\, draining
 time\, etc.). Considering the occupancies of the sites (queue sizes) we
 show that occupation probabilities in the ASIP obey a discrete
 two-dimensional boundary value problem. Solving this problem we find
 explicit expressions for the probability that site k is occupied by m
 particles (m=0\,1\,2\,..).Catalan's numbersare shown to naturally arise in
 the context of these occupation probabilities. This is a joint work with
 ShlomiReuveni and Iddo Eiazar.
CATEGORIES:Seminars,Youtube
LOCATION:LINCS Meeting Room 40\, 23\, avenue d'Italie\, Paris\, 75013\,
 France
GEO:48.8283983;2.3568972000000485
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 40:geo:48.8283983,2.3568972000000485
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TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:DAYLIGHT
DTSTART:20140330T030000
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
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