Peköz EA, Blanchet J. HEAVY TRAFFIC LIMITS VIA BROWNIAN EMBEDDINGS. Probability in the Engineering and Informational Sciences. 2006;20(4):595-598. doi:10.1017/S0269964806060360

View Publication

Abstract

For the GI/GI/1 queue we show that the scaled queue size converges to reflected Brownian motion in a critical queue and converges to reflected Brownian motion with drift for a sequence of subcritical queuing models that approach a critical model. Instead of invoking the topological argument of the usual continuous-mapping approach, we give a probabilistic argument using Skorokhod embeddings in Brownian motion.

Authors
Erol A Peköz, Jose Blanchet
Publication date
2006/10
Journal
Probability in the Engineering and Informational Sciences
Volume
20
Issue
4
Pages
595-598
Publisher
Cambridge University Press