Exact results for a fluid model with state-dependent flow rates

Offer Kella; Wolfgang Stadje

doi:10.1017/S0269964802164011

Exact results for a fluid model with state-dependent flow rates

Offer Kella^*
, Wolfgang Stadje

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We consider a modulated fluid system with a finite state-space Markov chain J_t as modulating process and general state-dependent net input rates. We derive differential equations for the transient and the stationary distribution of (W_t, J_t), where W_t is the content process, and the corresponding Laplace transforms with respect to time. Moreover, we study the level hitting times of W_t. Our results lead to explicit formulas in the case of two modulating states.

Original language	English
Pages (from-to)	389-402
Number of pages	14
Journal	Probability in the Engineering and Informational Sciences
Volume	16
Issue number	4
DOIs	https://doi.org/10.1017/S0269964802164011
State	Published - 2002

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title = "Exact results for a fluid model with state-dependent flow rates",

abstract = "We consider a modulated fluid system with a finite state-space Markov chain Jt as modulating process and general state-dependent net input rates. We derive differential equations for the transient and the stationary distribution of (Wt, Jt), where Wt is the content process, and the corresponding Laplace transforms with respect to time. Moreover, we study the level hitting times of Wt. Our results lead to explicit formulas in the case of two modulating states.",

author = "Offer Kella and Wolfgang Stadje",

year = "2002",

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T1 - Exact results for a fluid model with state-dependent flow rates

AU - Kella, Offer

AU - Stadje, Wolfgang

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N2 - We consider a modulated fluid system with a finite state-space Markov chain Jt as modulating process and general state-dependent net input rates. We derive differential equations for the transient and the stationary distribution of (Wt, Jt), where Wt is the content process, and the corresponding Laplace transforms with respect to time. Moreover, we study the level hitting times of Wt. Our results lead to explicit formulas in the case of two modulating states.

AB - We consider a modulated fluid system with a finite state-space Markov chain Jt as modulating process and general state-dependent net input rates. We derive differential equations for the transient and the stationary distribution of (Wt, Jt), where Wt is the content process, and the corresponding Laplace transforms with respect to time. Moreover, we study the level hitting times of Wt. Our results lead to explicit formulas in the case of two modulating states.

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SN - 0269-9648

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EP - 402

JO - Probability in the Engineering and Informational Sciences

JF - Probability in the Engineering and Informational Sciences

IS - 4

ER -

Exact results for a fluid model with state-dependent flow rates

Abstract

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