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Properties of the reflected Ornstein-Uhlenbeck process. (English) Zbl 1026.60106

An Ornstein-Uhlenbeck process with reflection at the origin appearing as an approximating process both for queueing systems with reneging or state-dependent balking and for multiserver loss models is considered. It is shown that both the steady-space and transient behavior of the reflected Ornstein-Uhlenbeck process is reasonably tractable. More specifically, an approximation for its transient moments is provided, a perturbation expansion for its transition density is computed, an approximation for the distribution of level crossing times is given, and the growth rate of the maximum process is established.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
60J60 Diffusion processes
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