Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-26T23:04:35.613Z Has data issue: false hasContentIssue false
  • English
  • Français

ON/OFF STORAGE SYSTEMS WITH STATE-DEPENDENT INPUT, OUTPUT, AND SWITCHING RATES

Published online by Cambridge University Press:  01 January 2005

Onno Boxma ,
Haya Kaspi ,
Offer Kella  and
David Perry
Onno Boxma
Affiliation:
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
Haya Kaspi
Affiliation:
Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Haifa 32000, Israel, E-mail: iehaya@techunix.technion.ac.il
Offer Kella
Affiliation:
Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel, E-mail: Offer.Kella@huji.ac.il
David Perry
Affiliation:
Department of Statistics, University of Haifa, Haifa 31905, Israel, E-mail: dperry@stat.haifa.ac.il
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 1 , January 2005 , pp. 1 - 14
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adan, I.J.B.F., Van Doorn, E.A., Resing, J.A.C., & Scheinhardt, W.R.W. (1998). Analysis of a single-server queue interacting with a fluid reservoir. Queueing Systems 29: 313–336.Google Scholar
Anick, D., Mitra, D., & Sondhi, M.M. (1982). Stochastic theory of a data-handling system with multiple sources. Bell System Technical Journal 61: 1871–1894.Google Scholar
Azéma, J., Kaplan-Duflo, M., & Revuz, D. (1967). Measure invariante sur les classes récurrentes des processus de Markov. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 8: 157–181.Google Scholar
Bekker, R., Borst, S.C., Boxma, O.J., & Kella, O. (2003). Queues with workload-dependent arrival and service rates. Queueing Systems 46: 537–556.Google Scholar
Davis, M.H.A. (1984). Piecewise-deterministic Markov processes: A general class of non diffusion stochastic models. Journal of the Royal Statistical Society Series B 46: 353–388.Google Scholar
Gaver, D.P. & Miller, R.G. (1962). Limiting distributions for some storage problems. In K.J. Arrow, S. Karlin, & H. Scarf (eds.), Studies in applied probability and management science. Stanford, CA: Stanford University Press, pp. 110–126.
Harrison, J.M. & Resnick, S.I. (1976). The stationary distribution and first exit probabilities of a storage process with general release rule. Mathematics of Operations Research 1: 347–358.Google Scholar
Kaspi, H., Kella, O., & Perry, D. (1996). Dam processes with state dependent batch sizes and intermittent production processes with state dependent rates. Queueing Systems 24: 37–57.Google Scholar
Kella, O. & Whitt, W. (1992). A storage model with a two-state random environment. Operations Research 40: S257–S262.Google Scholar
Mandjes, M., Mitra, D., & Scheinhardt, W.R.W. (2002). A simple model of network access: Feedback adaptation of rates and admission control. In Proceedings of INFOCOM 2002, pp. 3–12.
Mandjes, M., Mitra, D., & Scheinhardt, W.R.W. (2003). Models of network access using feedback fluid queues. Queueing Systems 44: 365–398.Google Scholar
Meyn, S.P. & Tweedie, R.L. (1993). Markov chains and stochastic stability. New York: Springer-Verlag.CrossRef
Meyn, S.P. & Tweedie, R.L. (1993). Stability of Markovian processes III: Foster Lyapunov criteria for continuous time processes. Advances in Applied Probability 25: 518–548.Google Scholar
Scheinhardt, W.R.W., Van Foreest, N., & Mandjes, M. (2003). Continuous feedback fluid queues. Report Department of Applied Mathematics, University of Twente.