We consider a fl??uid model similar to that of Kella and Whitt , but with a buff??er having ??finite capacity K. The connections between the infi??nite buff??er fl??uid model and the G/G/1 queue established in  are extended to the ??finite buff??er case. It is shown that the stationary distribution of the buff??er content is related to the stationary distribution of the ??finite 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 buff??er content distribution of the fl??uid model is also related to that of the corresponding model with infi??nite buff??er size??, by showing that the two corresponding probability measures are proportional on [0,K) if the silence periods are exponentially distributed. These results are applied to obtain large buff??er asymptotics for the loss fraction and the mean bu??ffer content when the fl??uid queue is fed by N on-off sources with subexponential on-
periods. The asymptotic results show a signi??ficant infl??uence of heavy
-tailed input characteristics on the performance of the fl??uid queue.
Keywords: Phrases?? on
o?? processes?? ??nite bu??ers?? ??uid queues?? loss fractions?? proportionality of probability
measures?? regenerative processes?? regular variation?? subexponentiality?? Tauberian theorems
|ISSN van geprinte versie||0926-4493|