Attractiveness of Brownian queues in tandem

Eric A. Cator (), Sergio I. López () and Leandro P. R. Pimentel ()
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Eric A. Cator: Radboud University
Sergio I. López: UNAM
Leandro P. R. Pimentel: UFRJ

Queueing Systems: Theory and Applications, 2019, vol. 92, issue 1, No 2, 25-45

Abstract: Abstract Consider a sequence of n bi-infinite and stationary Brownian queues in tandem. Assume that the arrival process entering the first queue is a zero mean ergodic process. We prove that the departure process from the n-th queue converges in distribution to a Brownian motion as n goes to infinity. In particular this implies that the Brownian motion is an attractive invariant measure for the Brownian queueing operator. Our proof exploits the relationship between Brownian queues in tandem and the last-passage Brownian percolation model, developing a coupling technique in the second setting. The result is also interpreted in the related context of Brownian particles acting under one-sided reflection.

Keywords: Brownian queue; Tandem queues; Last-passage percolation; Exclusion process; 60K25; 60K35 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-019-09609-y

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