Queueing Systems

, Volume 67, Issue 2, pp 91–110 | Cite as

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

  • Xiaowei Zhang
  • Peter W. Glynn


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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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Management Science and EngineeringStanford UniversityStanfordUSA

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