Measuring the Initial Transient: Reflected Brownian Motion

2014/07/08 by Rob J. Wang, Peter W. Glynn, Wang, Rob J. +1
Business, Management and Accounting · Computer Science · Engineering · #Advanced Queuing Theory Analysis #FOS: Computer and information sciences #Methodology (stat.ME) #Network Traffic and Congestion Control #Power Line Communications and Noise

paper · pdf · doi:10.48550/arxiv.1407.2267

openalex publication_date 2014/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the convergence to equilibrium of one-dimensional reflected Brownian motion (RBM) and compute a number of related initial transient formulae. These formulae are of interest as approximations to the initial transient for queueing systems in heavy traffic, and help us to identify settings in which initialization bias is significant. We conclude with a discussion of mean square error for RBM. Our analysis supports the view that initial transient effects for RBM and related models are typically of modest size relative to the intrinsic stochastic variability, unless one chooses an especially poor initialization.

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