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Markovian Transition Counting Processes: An Alternative to Markov Modulated Poisson Processes
Azam Asanjarani, Sophie Hautphenne, Yoni Nazarathy
Stochastic models for performance analysis, optimization and control of queues hinge on a multitude of alternatives for input point processes. In case of bursty traffic, one very p…
Extinction probabilities in branching processes with countably many types: a general framework
Daniela Bertacchi, Peter Braunsteins, Sophie Hautphenne +1
We consider Galton-Watson branching processes with countable typeset . We study the vectors recording the conditional probabili…
The probabilities of extinction in a branching random walk on a strip
Peter Braunsteins, Sophie Hautphenne
We consider a class of multitype Galton-Watson branching processes with a countably infinite type set whose mean progeny matrices have a block lower Hessenberg form…
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…
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…