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Heavy-traffic limits for stationary network flows

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Abstract

This paper studies stationary customer flows in an open queueing network. The flows are the processes counting customers flowing from one queue to another or out of the network. We establish the existence of unique stationary flows in generalized Jackson networks and convergence to the stationary flows as time increases. We establish heavy-traffic limits for the stationary flows, allowing an arbitrary subset of the queues to be critically loaded. The heavy-traffic limit with a single bottleneck queue is especially tractable because it yields limit processes involving one-dimensional reflected Brownian motion. That limit plays an important role in our new nonparametric decomposition approximation of the steady-state performance using indices of dispersion and robust optimization.

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Acknowledgements

We thank Karl Sigman, Hanqin Zhang and Editor Sergey Foss for helpful discussion about Harris recurrence. This work was done while the Wei You was a graduate student at Columbia University, where both authors received support from NSF Grant CMMI 1634133.

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Authors and Affiliations

  1. Department of IEOR, Columbia University, New York, NY, USA

    Ward Whitt

  2. Department of IEDA, HKUST, Clear Water Bay, Hong Kong

    Wei You

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  1. Ward Whitt
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  2. Wei You
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Correspondence to Ward Whitt.

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Whitt, W., You, W. Heavy-traffic limits for stationary network flows. Queueing Syst 95, 53–68 (2020). https://doi.org/10.1007/s11134-019-09645-8

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  • DOI: https://doi.org/10.1007/s11134-019-09645-8

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