Multidimensional sticky Brownian motions: Heavy traffic limit and rough tail asymptotics

Inspired by the concept of sticky Brownian motion on the half-line, we investigate a time-changed semimartingale reflecting Brownian motion in the orthant, which we refer to as multidimensional sticky Brownian motion. We first show that it can be obtained as a natural diffusion approximation for a certain tandem queue with exceptional arrival rates. Furthermore, we examine the tail dependence structure of the joint stationary distribution. Under some mild conditions, we derive rough tail asymptotics for the joint stationary distribution. Finally, in some special cases, we present the exact tail asymptotics of the joint stationary distribution.