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X-ORIGINAL-URL:https://www.eurandom.tue.nl
X-WR-CALDESC:Events for Eurandom
BEGIN:VTIMEZONE
TZID:UTC
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TZOFFSETFROM:+0000
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DTSTART:20190101T000000
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BEGIN:VEVENT
DTSTART;TZID=UTC:20191216T154500
DTEND;TZID=UTC:20191216T164500
DTSTAMP:20200803T231727
CREATED:20191213T190447Z
LAST-MODIFIED:20191216T081554Z
UID:3274-1576511100-1576514700@www.eurandom.tue.nl
SUMMARY:Eindhoven Stochastics Seminar
DESCRIPTION:Gianmarco Bet (University of Florence) \nWeighted Dyck pathsÂ for non stationary queues \nWe consider a model for a transitory queue in which only a fixed number $N$ of customers can join. Each customer joins the queue independently of the other ones at a random time\, which we assume to be exponentially distributed. Assuming further that the service times also follow an exponential distribution\, this system can be described as a two-dimensional Markov process on a triangular subset of $\mathbb Z^2$. The resulting random walk with state-dependent transition rates has a rich but intricate combinatorial structure which we study by introducing appropriate generating functions that exploit the recursive structure of the model. We derive a fully explicit expression for the probability density function of the number of customers served in the first busy period (and thus in any busy period) in terms of a certain balls-in-urns combinatorial scheme. This formula can be interpreted as a decomposition of weighted Dyck paths. We also derive an explicit expression for the joint probability distribution of the maximum queue length and the number of customers served during a busy period. \n
URL:https://www.eurandom.tue.nl/event/eindhoven-stochastics-seminar-15/
LOCATION:MF 11-12 (4th floor MetaForum Building\, TU/e)
CATEGORIES:STO Seminar
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