A fluid queue with a finite buffer and subexponential input

We consider a fluid model similar to that of Kella and Whitt [32], but with a buffer having finite capacity K. The connections between the infinite bu ffer fluid model and the G/G/1 queue established by Kella and Whitt are ext ended to the finite buffer case: it is shown that the stationary distributi on of the buffer content is related to the stationary distribution of the f inite dam. We also derive a number of new results for the latter model. In particular, an asymptotic expansion for the loss fraction is given for the case of subexponential service times. The stationary buffer content distrib ution of the fluid model is also related to that of the corresponding model with infinite buffer size, by showing that the two corresponding probabili ty measures are proportional on [0, K) if the silence periods are exponenti ally distributed. These results are applied to obtain large buffer asymptot ics for the loss fraction and the mean buffer content when the fluid queue is fed by N On-Off sources with subexponential on-periods. The asymptotic r esults show a significant influence of heavy-tailed input characteristics o n the performance of the fluid queue.