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Graduate Seminar

Yangxi Ou
Carnegie Mellon University
Title: Time to Reflect: Queueing, Skorohod Map, and Brownian Motion

Abstract: It is interesting that reflected Brownian motion (RBM) arises naturally in queueing theory, a subject seemingly unrelated to stochastic calculus. In this talk, we start with a toy model of a single queue, and demonstrate that its limiting distribution of scaled waiting time is a RBM. We then turn to the pure analytic tool of Skorohod Map and show that it appears as a byproduct of our queueing model. Meanwhile, the concept of local time is introduced. Following the same spirit, we play with a more complex queueing model and show that how RBM in multidimensional polyhedron appears as the limit waiting time of such queue. A result of 2D RBM due to Varadhan and Williams is then given.

Date: Tuesday, January 12, 2016
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Yangxi Ou
Note: Video on Youtube: https://youtu.be/zOtJ6Rdr_ck