Abstract
We study the time it takes until a fluid queue with a finite, but large, holding capacity reaches the overflow point. The queue is fed by an on/off process with a heavy tailed on distribution which is known to have long memory. It turns out that the expected time until overflow, as a function of capacity L, increases only polynomially fast; so overflows happen much more often than in the "classical" light tailed case, where the expected over-flow time increases as an exponential function of L. Moreover, we show that in the heavy tailed case overflows are basically caused by single huge jobs. An implication is that the usual
Citation
David Heath. Sidney Resnick. Gennady Samorodnitsky. "Patterns of buffer overflow in a class of queues with long memory in the input stream." Ann. Appl. Probab. 7 (4) 1021 - 1057, November 1997. https://doi.org/10.1214/aoap/1043862423
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