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May 1998 The superposition of alternating on-off flows and a fluid model
Zbigniew Palmowski, Tomasz Rolski
Ann. Appl. Probab. 8(2): 524-540 (May 1998). DOI: 10.1214/aoap/1028903537

Abstract

An on-off process is a 0-1 process $\xi_t$ in which consecutive 0-periods ${T_{0, n}}$ alternate with 1-periods ${T_{1, n}}(n = 1, 2,\dots)$. The on and off time sequences are independent, each consisting of i.i.d. r.v.s. By the superposed flow, we mean the process $Z_t = \Sigma_{\ell=1}^N r^{\ell}\xi_t^{\ell}$, where $r^{\ell} > 0$ and ${\xi_t^1}, \dots,{\xi_t^N}$ are independent on-off flows. The process $\xi_t^{\ell}$ is not Markovian; however, with the age component $\eta_t^{\ell}$, the process $w_t^{\ell} = (\xi_t^{\ell}, \eta_t^{\ell})$ is a piecewise deterministic Markov process. In this paper we study the buffer content process for which the tail of its steady-state distribution $\Psi (b)$ fulfills inequality $C_- e^{\gammab} \leq \Psi (b) \leq C_+ e^{-\gammab}, where $\gamma > 0$ is the solution of some basic nonlinear system of equations.

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Zbigniew Palmowski. Tomasz Rolski. "The superposition of alternating on-off flows and a fluid model." Ann. Appl. Probab. 8 (2) 524 - 540, May 1998. https://doi.org/10.1214/aoap/1028903537

Information

Published: May 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0942.60089
MathSciNet: MR1624957
Digital Object Identifier: 10.1214/aoap/1028903537

Subjects:
Primary: 60K25
Secondary: 68M20 , 90B22

Keywords: $on-off$ flow , exponential bound , generator , Queueing fluid model , superposition of $on-off$ flows

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 2 • May 1998
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