Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-29T12:20:02.496Z Has data issue: false hasContentIssue false
  • English
  • Français

AN INTERMITTENT FLUID SYSTEM WITH EXPONENTIAL ON-TIMES AND SEMI-MARKOV INPUT RATES

Published online by Cambridge University Press:  10 April 2001

Onno Boxma ,
Offer Kella  and
David Perry
Onno Boxma
Affiliation:
EURANDOM and Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, and, CWI, 1090 GB Amsterdam, The Netherlands, E-mail: boxma@win.tue.nl
Offer Kella
Affiliation:
Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel, E-mail: mskella@mscc.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 fluid system in which during off-times the buffer content increases as a piecewise linear process according to some general semi-Markov process, and during on-times, it decreases with a state-dependent rate (or remains at zero). The lengths of off-times are exponentially distributed. We show that such a system has a stationary distribution which satisfies a decomposition property where one component in the decomposition is associated with some dam process and the other with a clearing process. For the cases of constant and linear decrease rates, the steady-state Laplace–Stieltjes transform and moments of the buffer content are computed explicitly.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 15 , Issue 2 , April 2001 , pp. 189 - 198
Copyright
© 2001 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.)