Boundary conditions for diffusion approximations to queueing problems

One of the main difficulties of the diffusion approximation to queues is that it underestimates the probability of an empty queue. This is due to the use of instantaneous reflection at the boundary. In this paper the use of diffusion processes with delayed reflections is suggested. A survey of the available mathematical literature on this topic is given. A method is suggested to give a rational choice of the stickyness of the boundary, based on how long the queue is empty in an interval up to the first buffer overflow. Some applications (ergodic theorems and recursive estimation) and some problems for further research are outlined.