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.
Large deviations Reflected Brownian motion Local time Quasi-stationary
Mathematics Subject Classification (2000)
60F10 60J55 60J65 60K25 60F05 34L99 90B15
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