Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs

In this paper, we consider a three-dimensional Brownian-driven tandem queue with intermediate inputs, which corresponds to semimartingale reflecting Brownian motion whose reflection matrix is triangular. For three-node queue, no closed form formula known, not only for its stationary distribution but also the corresponding transform. We are interested in exact tail asymptotics distributions. By generalizing kernel method, and using extreme value theory copula, obtain marginal of buffer content third joint distribution.