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6 papers · 2 filters
A functional central limit theorem for the M/GI/ queue
Laurent Decreusefond, Pascal Moyal
In this paper, we present a functional fluid limit theorem and a functional central limit theorem for a queue with an infinity of servers M/GI/. The system is represented b…
The ODE method for stability of skip-free Markov chains with applications to MCMC
Gersende Fort, Sean Meyn, Eric Moulines +1
Fluid limit techniques have become a central tool to analyze queueing networks over the last decade, with applications to performance analysis, simulation and optimization. In this…
Hitting times for Gaussian processes
Laurent Decreusefond, David Nualart
We establish a general formula for the Laplace transform of the hitting times of a Gaussian process. Some consequences are derived, and particular cases like the fractional Brownia…
Wasserstein distance on configuration space
L. Decreusefond
We investigate here the optimal transportation problem on configuration space for the quadratic cost. It is shown that, as usual, provided that the corresponding Wasserstein is fin…
Bounds on Regeneration Times and Limit Theorems for Subgeometric Markov Chains
Randal Douc, Arnaud Guillin, Eric Moulines
This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate de…
Fluid limit of a heavily loaded EDF queue with impatient customers
Laurent Decreusefond, Pascal Moyal
In this paper we present the fluid limit of an heavily loaded Earliest Deadline First queue with impatient customers, represented by a measure-valued process keeping track of resid…