On Busy Periods of the Unbounded Brownian Storage

Authors:
Paavo Salminen;Ilkka Norros
Affiliations:
Åbo Akademi, Mathematical Department, FIN-20500 Åbo, Finland phsalmin@abo.fi;VTT Information Technology, PO Box 1202, FIN-02044 VTT, Finland norros@vtt.fi
Venue:
Queueing Systems: Theory and Applications
Year:
2001

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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.