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math.PR2013
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…
math.PR2013★ 11 cited
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…