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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.

60K25Queueing theory
90B22Queues and service (optimization)
60J60Diffusion processes
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