Pascal Moyal

Large graph limit for an SIR process in random network with heterogeneous connectivity

We consider an SIR epidemic model propagating on a Configuration Model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. As a corollary, this provides a rigorous proof of the equations obtained by Volz (2008).

A functional central limit theorem for the M/GI/infinity queue

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/

On queues with impatience: stability, and the optimality of Earliest Deadline First

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Stability of the stochastic matching model

. The system is represented by a point-measure valued process keeping track of the remaining processing times of the customers in service. The convergence in law of a sequence of such processes is proved by compactness-uniqueness methods, and the deterministic fluid limit is the solution of an integrated equation in the space

Convex comparison of service disciplines in real time queues

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Stability of a processor-sharing queue with varying throughput

of tempered distributions. We then establish the corresponding central limit theorem, i.e. the approximation of the normalized error process by a

Estimating the Transmission Probability in Wireless Networks with Configuration Models

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A pathwise comparison of parallel queues

-valued diffusion.

Fluid Limit of the M/M/1+GI-EDF Queue

In this paper, we consider a queue with impatient customers, under general assumptions. We introduce a convenient representation of the system by a stochastic recursive sequence keeping track of the remaining service and patience times of the customers. This description allows us (i) to provide a comprehensive stability condition in the general case, (ii) to give a rigorous proof of the optimality of the Earliest Deadline First (EDF) service discipline in several cases, and (iii) to show that the abandonment probability of the system follows inversely the stochastic ordering of the generic patience time distribution.

On the stability of a class of non-monotonic systems of parallel queues

We introduce and study a new model that we call the {\em matching model}. Items arrive one by one in a buffer and depart from it as soon as possible but by pairs. The items of a departing pair are said to be {\em matched}. There is a finite set of classes