On Busy Periods of the Unbounded Brownian Storage |
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Authors: | Paavo Salminen Ilkka Norros |
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Institution: | (1) Mathematical Department, Åbo Akademi, FIN-20500 Åbo, Finland;(2) VTT Information Technology, PO Box 1202, FIN-02044 VTT, Finland |
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Abstract: | A stationary storage process with Brownian input and constant service rate is studied. Explicit formulae for quantities related to busy periods (excursions) are derived. In particular, we compute the distributions of the occupation times the process spends above and below, respectively, the present level during the on-going busy period, and make the surprising observation that these occupation times are identically distributed. |
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