On/off Storage Systems with State-Dependent Input, Output, and Switching Rates

Authors:
Onno Boxma;Haya Kaspi;Offer Kella;David Perry
Affiliations:
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 ...;Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Haifa 32000, Israel, E-mail: iehaya@techunix.technion.ac.il;Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel, E-mail: Offer.Kella@huji.ac.il;Department of Statistics, University of Haifa, Haifa 31905, Israel, E-mail: dperry@stat.haifa.ac.il
Venue:
Probability in the Engineering and Informational Sciences
Year:
2005

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Abstract

We 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.