Queueing Systems

, Volume 44, Issue 2, pp 109–123 | Cite as

Properties of the Reflected Ornstein–Uhlenbeck Process

  • Amy R. Ward
  • Peter W. Glynn


Consider an Ornstein–Uhlenbeck process with reflection at the origin. Such a process arises as an approximating process both for queueing systems with reneging or state-dependent balking and for multi-server loss models. Consequently, it becomes important to understand its basic properties. In this paper, we show that both the steady-state and transient behavior of the reflected Ornstein–Uhlenbeck process is reasonably tractable. Specifically, we (1) provide an approximation for its transient moments, (2) compute a perturbation expansion for its transition density, (3) give an approximation for the distribution of level crossing times, and (4) establish the growth rate of the maximum process.

diffusion approximation Ornstein–Uhlenbeck process reflecting diffusion steady-state transient moment level crossing time maximum process 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Amy R. Ward
    • 1
  • Peter W. Glynn
    • 2
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Management Science & EngineeringStanford UniversityStanfordUSA

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