Rates of Convergence to Stationarity for Multidimensional RBM

2016/01/16 by José Blanchet, Jose Blanchet, Xinyun Chen +2 · 1 citation
Business, Management and Accounting · Decision Sciences · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Supply Chain and Inventory Management #math.PR

paper · pdf · doi:10.48550/arxiv.1601.04111

openalex publication_date 2016/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28 · arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

We provide the first rate of convergence analysis for RBM as the dimension grows under natural uniformity conditions. In particular, if the underlying routing matrix is uniformly contractive, uniform stability of the drift vector holds, and the variances of the underlying Brownian Motion (BM) are bounded, then we show that the RBM converges exponentially fast to stationarity with a relaxation time of order O(d⁴log(d)²) as d→∞.

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