ON/OFF STORAGE SYSTEMS WITH STATE-DEPENDENT INPUT, OUTPUT, AND
SWITCHING RATES
Onno
Boxma
a1
, Haya
Kaspi
a2
, Offer
Kella
a3
and David
Perry
a4
a1 EURANDOM and Department of Mathematics and Computer
Science, Eindhoven University of Technology, 5600 MB Eindhoven,
The Netherlands, and, CWI, 1090 GB Amsterdam, The Netherlands,
E-mail: boxma@win.tue.nl
a2 Faculty of Industrial Engineering and Management,
Technion—Israel Institute of Technology, Haifa 32000,
Israel, E-mail: iehaya@techunix.technion.ac.il
a3 Department of Statistics, The Hebrew University of
Jerusalem, Mount Scopus, Jerusalem 91905, Israel, E-mail:
Offer.Kella@huji.ac.il
a4 Department of Statistics, University of
Haifa, Haifa 31905, Israel, E-mail:
dperry@stat.haifa.ac.il
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AbstractWe consider a storage model that can be on or off. When on, the
content increases at some state-dependent rate and the system can
switch to the off state at a state-dependent rate as well. When off,
the content decreases at some state-dependent rate (unless it is at
zero) and the system can switch to the on position at a state-dependent
rate. This process is a special case of a piecewise deterministic
Markov process. We identify the stationary distribution and conditions
for its existence and uniqueness.
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