On the Dynamics of a Finite Buffer Queue Conditioned on the Amount of Loss

X. Zhang and P. W. Glynn

Queueing Systems: Theory and Applications, Vol. 67 (2), 91-110 (2011)

This paper is concerned with computing large deviations 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.