6 papers · 1 filter
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,…
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…
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…
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…
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…