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