Queue-and-Idleness-Ratio Controls in Many-Server Service Systems
Mathematics of Operations Research
Heavy traffic steady state approximations in stochastic networks with Lévy inputs
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Queueing Systems: Theory and Applications
Diffusion limit of a two-class network: stationary distributions and interchange of limits
ACM SIGMETRICS Performance Evaluation Review
Heavy traffic approximation for the stationary distribution of stochastic fluid networks
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Stability of Constrained Markov-Modulated Diffusions
Mathematics of Operations Research
Interchange of limits in heavy traffic analysis under a moment condition
ACM SIGMETRICS Performance Evaluation Review
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In a recent paper, Gamarnik and Zeevi [Gamarnik, D., A. Zeevi. 2006. Validity of heavy traffic steady-state approximations in open queueing networks. Ann. Appl. Probab.16(1) 56--90], it was shown that under suitable conditions stationary distributions of the (scaled) queue-lengths process for a generalized Jackson network converge to the stationary distribution of the associated reflected Brownian motion in the heavy traffic limit. The proof relied on certain exponential integrability assumptions on the primitives of the network. In this note we show that the above result holds under much weaker integrability conditions. We provide an alternative proof of this result assuming (in addition to natural heavy traffic and stability assumptions) only standard independence and square integrability conditions on the network primitives that are commonly used in heavy traffic analysis. Furthermore, under additional integrability conditions we establish convergence of moments of stationary distributions.