11 citations · 32 across the 19 of their papers we have counts for
22 papers
Cut-edge centralities in an undirected graph
Dario Bini, Steve Kirkland, Guy Latouche +1
A centrality measure of the cut-edges of an undirected graph, given in [Altafini et al.~SIMAX 2023] and based on Kemeny's constant, is revisited. A numerically more stable expressi…
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 where , , are given matrix coefficients, while …
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 of the nonlinear matrix equation where , for , are nonnega…
Traffic lights, clumping and QBDs
Steven Finch, Guy Latouche, Guy Louchard +1
In discrete time, -blocks of red lights are separated by -blocks of green lights. Cars arrive at random. \ We seek the distribution of maximum line length of idle cars,…
Strong convergence to two-dimensional alternating Brownian motion processes
Guy Latouche, Giang T. Nguyen, Oscar Peralta
Flip-flop processes refer to a family of stochastic fluid processes which converge to either a standard Brownian motion (SBM) or to a Markov modulated Brownian motion (MMBM). In re…
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…
Why is Kemeny's constant a constant?
Dario Bini, Jeffrey J. Hunter, Guy Latouche +2
In their 1960 book on finite Markov chains, Kemeny and Snell established that a certain sum is invariant. The value of this sum has become known as {\it Kemeny's constant}. Various…
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…
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…
General solution of the Poisson equation for Quasi-Birth-and-Death processes
Dario A. Bini, Sarah Dendievel, Guy Latouche +1
We consider the Poisson equation , where is the transition matrix of a Quasi-Birth-and-Death (QBD) process with infinitely many levels, $\bm…
Feedback control: two-sided Markov-modulated Brownian motion with instantaneous change of phase at boundaries
Guy Latouche, Giang T. Nguyen
We consider a Markov-modulated Brownian motion with two boundaries at and , and allow for the controlling Markov chain to instantaneously und…
Shift techniques for Quasi-Birth and Death processes: canonical factorizations and matrix equations
Dario A. Bini, Guy Latouche, Beatrice Meini
We revisit the shift technique applied to Quasi-Birth and Death (QBD) processes (He, Meini, Rhee, SIAM J. Matrix Anal. Appl., 2001) by bringing the attention to the existence and p…
Slowing time: Markov-modulated Brownian motion with a sticky boundary
Guy Latouche, Giang T. Nguyen
We analyze the stationary distribution of regulated Markov modulated Brownian motions (MMBM) modified so that their evolution is slowed down when the process reaches level zero ---…
Computing the Exponential of Large Block-Triangular Block-Toeplitz Matrices Encountered in Fluid Queues
D. A. Bini, S. Dendievel, G. Latouche +1
The Erlangian approximation of Markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block-triangular, block-Toeplitz structure…
Lyapunov exponents for branching processes in a random environment: The effect of information
Sophie Hautphenne, Guy Latouche
We consider multitype Markovian branching processes evolving in a Markovian random environment. To determine whether or not the branching process becomes extinct almost surely is a…
Approximations for time-dependent distributions in Markovian fluid models
Sarah Dendievel, Guy Latouche
In this paper we study the distribution of the level at time of Markovian fluid queues and Markovian continuous time random walks, the maximum (and minimum) level over ,…
Two-dimensional fluid queues with temporary assistance
Guy Latouche, Giang T. Nguyen, Zbigniew Palmowski
We consider a two-dimensional stochastic fluid model with ON-OFF inputs and temporary assistance, which is an extension of the same model with in Mahabhashyam et al. (2…
Fluid approach to two-sided Markov-modulated Brownian motion
Guy Latouche, Giang T. Nguyen
We extend to Markov-modulated Brownian motion (MMBM) the renewal approach which has been successfully applied to the analysis of Markov-modulated fluid models. It has recently been…
The morphing of fluid queues into Markov-modulated Brownian motion
Guy Latouche, Giang T. Nguyen
Ramaswami showed recently that standard Brownian motion arises as the limit of a family of Markov-modulated linear fluid processes. We pursue this analysis with a fluid approximati…
Poisson's equation for discrete-time quasi-birth-and-death processes
Sarah Dendievel, Guy Latouche, Yuanyuan Liu
We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. On…
Extinction probabilities of branching processes with countably infinitely many types
Sophie Hautphenne, Guy Latouche, Giang Nguyen
We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabili…
On the nature of Phase-Type Poisson distributions
Sophie Hautphenne, Guy Latouche, Giang Nguyen
Matrix-form Poisson probability distributions were recently introduced as one matrix generalization of Panjer distributions. We show in this paper that under the constraint that th…