Heavy-traffic limits for stationary network flows

Ward Whitt () and Wei You ()
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Ward Whitt: Columbia University
Wei You: HKUST

Queueing Systems: Theory and Applications, 2020, vol. 95, issue 1, No 3, 53-68

Abstract: 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.

Keywords: Generalized Jackson networks; Heavy traffic; Stationary point processes; Stability; Index of dispersion; Asymptotic methods; Primary 60F17; Secondary 60K25; 90B22 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-019-09645-8

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