Markov modulation of a two-sided reflected Brownian motion with application to fluid queues

Bernardo D'Auria*, Offer Kella

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In this paper, we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time Markov chain. The goal is to compute the stationary distribution of this Markov process, which in addition to the complication of having a stochastic boundary can also include jumps at state change epochs of the underlying Markov chain because of the boundary changes. We give the general theory and then specialize to the case where the underlying Markov chain has two states.

Original languageAmerican English
Pages (from-to)1566-1581
Number of pages16
JournalStochastic Processes and their Applications
Issue number4
StatePublished - Apr 2012

Bibliographical note

Funding Information:
The authors thank the two anonymous referees for their valuable suggestions which helped in improving the paper. This research has been partially supported by the Spanish Ministry of Education and Science Grants MTM2007-63140 , MTM2010-16519 , SEJ2007-64500 and RYC-2009-04671 . The second author was supported in part by grant 434/09 from the Israel Science Foundation and the Vigevani Chair in Statistics .


  • Brownian motion
  • Fluid queues
  • Markov modulation
  • Two sided reflection


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