Slowing time: Markov-modulated Brownian motions with a sticky boundary |
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Authors: | Guy Latouche Giang T Nguyen |
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Institution: | 1. Département d’informatique, Université libre de Bruxelles, Bruxelles, Belgium;2. School of Mathematical Sciences, The University of Adelaide, Adelaide, SA, Australia |
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Abstract: | We define a new family of stochastic processes called Markov modulated Brownian motions with a sticky boundary at zero. Intuitively, each process is a regulated Markov-modulated Brownian motion whose boundary behavior is modified to slow down at level zero. To determine the stationary distribution of a sticky MMBM, we follow a Markov-regenerative approach similar to the one developed with great success in the context of quasi-birth-and-death processes and fluid queues. Our analysis also relies on recent work showing that Markov-modulated Brownian motions arise as limits of a parametrized family of fluid queues. |
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Keywords: | Fluid queues Markov-modulated Brownian motion regenerative processes sticky boundary |
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