Heavy traffic steady state approximations in stochastic networks with Lévy inputs

Authors:
Jean-Paul Haddad;Ravi R. Mazumdar
Affiliations:
University of Waterloo, Waterloo, Ontario, Canada;University of Waterloo, Waterloo, Ontario, Canada
Venue:
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Year:
2009

Citing 3
Cited 0

The Finite Element Method for Computing the Stationary Distribution of an SRBM in a Hypercube with Applications to Finite Buffer Queueing Networks

Queueing Systems: Theory and Applications
On a Class of Lévy Stochastic Networks

Queueing Systems: Theory and Applications
Stationary Distribution Convergence for Generalized Jackson Networks in Heavy Traffic

Mathematics of Operations Research

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Abstract

It has recently been shown [3, 5] that in the heavy traffic limit, the stationary distributions of the scaled queue length process of Generalized Jackson Networks converges to the stationary distribution of its corresponding Reflected 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 Lévy 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.