On the rate of convergence to equilibrium for reflected Brownian motion

Peter W. Glynn () and Rob J. Wang ()
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Peter W. Glynn: Stanford University
Rob J. Wang: Stanford University

Queueing Systems: Theory and Applications, 2018, vol. 89, issue 1, No 7, 165-197

Abstract: Abstract This paper discusses the rate of convergence to equilibrium for one-dimensional reflected Brownian motion with negative drift and lower reflecting boundary at 0. In contrast to prior work on this problem, we focus on studying the rate of convergence for the entire distribution through the total variation norm, rather than just moments of the distribution. In addition, we obtain computable bounds on the total variation distance to equilibrium that can be used to assess the quality of the steady state for queues as an approximation to finite horizon expectations.

Keywords: Reflected Brownian motion; Queueing theory; Total variation distance; Rate of convergence to equilibrium; Large deviations; Steady-state simulation; Diffusion processes; 60F05; 60F10; 60G05; 60J60; 60K25 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s11134-018-9574-1

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