On the Generalized Drift Skorokhod Problem in One Dimension

This is the authors' abstract. We don't add key points for this paper.

We show how to write the solution to the generalized drift Skorokhod problem in one-dimension in terms of the supremum of the solution of a tractable unrestricted integral equation (that is, an integral equation with no boundaries). As an application of our result, we equate the transient distribution of a reflected Ornstein–Uhlenbeck (OU) process to the first hitting time distribution of an OU process (that isnotreflected). Then, we use this relationship to approximate the transient distribution of the GI/GI/1 + GI queue in conventional heavy traffic and the M/M/N/Nqueue in a many-server heavy traffic regime.