Fluid models with jumps

Elena Tzenova, Ivo J B F Adan, Vidyadhar G. Kulkarni

Research output: Contribution to journalArticle

Abstract

□ In this paper we study a general stochastic fluid model with a single infinite capacity buffer, where the buffer content can change continuously as well as by instantaneous upward jumps. The continuous as well as the instantaneous change is modulated by an external environment process modelled as a finite state continuous time Markov chain. The Laplace-Stieltjes transform of the steady-state joint distribution of the buffer content and the state of the environment is determined explicitly in terms of the solutions of a generalized eigenvalue problem. The methodology is illustrated by several well-known queueing problems.

Original languageEnglish (US)
Pages (from-to)37-55
Number of pages19
JournalStochastic Models
Volume21
Issue number1
DOIs
StatePublished - Nov 28 2005

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Laplace transforms
Fluid Model
Markov processes
Buffer
Jump
Instantaneous
Fluids
Laplace-Stieltjes Transform
Generalized Eigenvalue Problem
Steady-state Distribution
Continuous-time Markov Chain
Queueing
Joint Distribution
Stochastic Model
Methodology

ASJC Scopus subject areas

  • Modeling and Simulation

Cite this

Tzenova, E., Adan, I. J. B. F., & Kulkarni, V. G. (2005). Fluid models with jumps. Stochastic Models, 21(1), 37-55. https://doi.org/10.1081/STM-200046459

Fluid models with jumps. / Tzenova, Elena; Adan, Ivo J B F; Kulkarni, Vidyadhar G.

In: Stochastic Models, Vol. 21, No. 1, 28.11.2005, p. 37-55.

Research output: Contribution to journalArticle

Tzenova, E, Adan, IJBF & Kulkarni, VG 2005, 'Fluid models with jumps', Stochastic Models, vol. 21, no. 1, pp. 37-55. https://doi.org/10.1081/STM-200046459
Tzenova E, Adan IJBF, Kulkarni VG. Fluid models with jumps. Stochastic Models. 2005 Nov 28;21(1):37-55. https://doi.org/10.1081/STM-200046459
Tzenova, Elena ; Adan, Ivo J B F ; Kulkarni, Vidyadhar G. / Fluid models with jumps. In: Stochastic Models. 2005 ; Vol. 21, No. 1. pp. 37-55.
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