G. Latouche

activity

20122021

collaborators

8 papers

math.NA2021

Numerical solution of a matrix integral equation arising in Markov Modulated Lévy processes

Dario A. Bini, Guy Latouche, Beatrice Meini

Markov-modulated Lévy processes lead to matrix integral equations of the kind $A_{0} + A_{1} X + A_{2} X^{2} + A_{3} (X) = 0$ where $A_{0}$ , $A_{1}$ , $A_{2}$ are given matrix coefficients, while $A_{3} (X)$ …

math.NA2020

A family of fast fixed point iterations for M/G/1-type Markov chains

Dario Andrea Bini, Guy Latouche, Beatrice Meini

We consider the problem of computing the minimal nonnegative solution $G$ of the nonlinear matrix equation $X = \sum_{i = - 1}^{\infty} A_{i} X^{i + 1}$ where $A_{i}$ , for $i \geq - 1$ , are nonnega…

math.PR2019

Traffic lights, clumping and QBDs

Steven Finch, Guy Latouche, Guy Louchard +1

In discrete time, $ℓ$ -blocks of red lights are separated by $ℓ$ -blocks of green lights. Cars arrive at random. \ We seek the distribution of maximum line length of idle cars,…

math.PR2018

Analysis of fluid flow models

Guy Latouche, Giang Nguyen

Markov-modulated fluids have a long history. They form a simple class of Markov additive processes, and were initially developed in the 1950s as models for dams and reservoirs, bef…

math.PR2017

The time-dependent expected reward and deviation matrix of a finite QBD process

Sarah Dendievel, Sophie Hautphenne, Guy Latouche +1

Deriving the time-dependent expected reward function associated with a continuous-time Markov chain involves the computation of its transient deviation matrix. In this paper we foc…

math.PR2017

Perturbation analysis of Markov modulated fluid models

Sarah Dendievel, Guy Latouche

We consider perturbations of positive recurrent Markov modulated fluid models. In addition to the infinitesimal generator of the phases, we also perturb the rate matrix, and analyz…