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math.PR2025
Weak convergence of quasi-birth-and-death processes with rational arrival process components to fluid queues
Nigel Bean, Angus Lewis
In this paper we construct a new approximation to a fluid queue as a quasi-birth-and-death process with rational arrival process components (QBD-RAP) and prove its convergence. Flu…
math.PR2019
A discontinuous Galerkin method for approximating the stationary distribution of stochastic fluid-fluid processes
Nigel Bean, Giang T. Nguyen, Malgorzata M. O'Reilly +1
Introduced by Bean and O'Reilly (2014), a stochastic fluid-fluid process is a Markov processes , where the first fluid is driven by the Markov c…