On the dynamics of a finite buffer queue conditioned on the amount of loss

This paper is concerned with computing large‐deviation asymptotics for the loss process in a stylized queueing model that is fed by a Brownian input process. In addition, the dynamics of the queue, conditional on such a large deviation in the loss, is calculated. Finally, the paper computes the quasi‐stationary distribution of the system and the corresponding dynamics, conditional on no loss occurring.