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Exponential concentration for first passage percolation through modified Poincaré inequalities

Michel Benaïm, Raphaël Rossignol (2008)

Annales de l'I.H.P. Probabilités et statistiques

We provide a new exponential concentration inequality for first passage percolation valid for a wide class of edge times distributions. This improves and extends a result by Benjamini, Kalai and Schramm (Ann. Probab.31 (2003)) which gave a variance bound for Bernoulli edge times. Our approach is based on some functional inequalities extending the work of Rossignol (Ann. Probab.35 (2006)), Falik and Samorodnitsky (Combin. Probab. Comput.16 (2007)).

Finite buffer GI/Geo/ 1 batch servicing queue with multiple working vacations

P. Vijaya Laxmi, Kanithi Jyothsna (2014)

RAIRO - Operations Research - Recherche Opérationnelle

This paper analyzes a discrete-time finite buffer renewal input queue with multiple working vacations where services are performed in batches of maximum size “b”. The service times both during a regular service period and vacation period and vacation times are geometrically distributed. Employing the supplementary variable and imbedded Markov chain techniques, we derive the steady-state queue length distributions at pre-arrival, arbitrary and outside observer’s observation epochs. Based on the queue...

Fires on trees

Jean Bertoin (2012)

Annales de l'I.H.P. Probabilités et statistiques

We consider random dynamics on the edges of a uniform Cayley tree with n vertices, in which edges are either flammable, fireproof, or burnt. Every flammable edge is replaced by a fireproof edge at unit rate, while fires start at smaller rate n - α on each flammable edge, then propagate through the neighboring flammable edges and are only stopped at fireproof edges. A vertex is called fireproof when all its adjacent edges are fireproof. We show that as n , the terminal density of fireproof vertices converges...

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