Attractiveness of Brownian queues in tandem

Attractiveness of Brownian queues in tandem

Consider a sequence of n bi-infinite and stationary Brownian queues in tandem. Assume that the arrival process entering in 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...

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Veröffentlicht in:arXiv.org 2019-03
Hauptverfasser: Cator, Eric A, Lopez, Sergio I, Pimentel, Leandro P R
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Brownian motion
Ergodic processes
Markov analysis
Percolation
Queues
Queuing theory
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description Consider a sequence of n bi-infinite and stationary Brownian queues in tandem. Assume that the arrival process entering in 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 the 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.
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subjects Brownian motion
Ergodic processes
Markov analysis
Percolation
Queues
Queuing theory
title Attractiveness of Brownian queues in tandem
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