Heavy traffic steady state approximations in stochastic networks with Lévy inputs

Jean-Paul Haddad; Ravi R. Mazumdar

4th International ICST Conference on Performance Evaluation Methodologies and Tools

Research Article

Heavy traffic steady state approximations in stochastic networks with Lévy inputs

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@INPROCEEDINGS{10.4108/ICST.VALUETOOLS2009.7463,
    author={Jean-Paul Haddad and Ravi R. Mazumdar},
    title={Heavy traffic steady state approximations in stochastic networks with L\^{e}vy inputs},
    proceedings={4th International ICST Conference on Performance Evaluation Methodologies and Tools},
    publisher={ICST},
    proceedings_a={VALUETOOLS},
    year={2010},
    month={5},
    keywords={Diffusion approximations Weak convergence Stationary distribution Reflected brownian motion},
    doi={10.4108/ICST.VALUETOOLS2009.7463}
}

Jean-Paul Haddad
Ravi R. Mazumdar
Year: 2010
Heavy traffic steady state approximations in stochastic networks with Lévy inputs
VALUETOOLS
ICST
DOI: 10.4108/ICST.VALUETOOLS2009.7463

Jean-Paul Haddad¹^,*, Ravi R. Mazumdar¹^,*

1: Department of Electrical and Computer Engineering, University of Waterloo, 200 University West, Waterloo, Ontario, Canada N2L 3G1

*Contact email: jhaddad@uwaterloo.ca, mazum@ece.uwaterloo.ca

Abstract

It has recently been shown [3, 5] that in the heavy traf- fc limit, the stationary distributions of the scaled queue length process of Generalized Jackson Networks converges to the stationary distribution of its corresponding Re ected Brownian Motion limit. In this paper we show that such an interchange of limits" is valid for the workload process of Stochastic Fluid Networks with Levy inputs. Our technique is of independent interest because we do not require the use of any Lyapunov techniques, a method that was used in the previous two papers.

Keywords: Diffusion approximations Weak convergence Stationary distribution Reflected brownian motion

Published: 2010-05-16
Publisher: ICST
Modified: 2010-05-16

: http://dx.doi.org/10.4108/ICST.VALUETOOLS2009.7463