Queueing Systems

, Volume 44, Issue 2, pp 109–123

Properties of the Reflected Ornstein–Uhlenbeck Process

Authors

  • Amy R. Ward
    • School of Industrial and Systems EngineeringGeorgia Institute of Technology
  • Peter W. Glynn
    • Department of Management Science & EngineeringStanford University
Article

DOI: 10.1023/A:1024403704190

Cite this article as:
Ward, A.R. & Glynn, P.W. Queueing Systems (2003) 44: 109. doi:10.1023/A:1024403704190

Abstract

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 approximationOrnstein–Uhlenbeck processreflecting diffusionsteady-statetransient momentlevel crossing timemaximum process
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© Kluwer Academic Publishers 2003