The Annals of Applied Probability

Patterns of buffer overflow in a class of queues with long memory in the input stream

David Heath, Sidney Resnick, and Gennady Samorodnitsky

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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 $GI/G/1$ queue with finite but large holding capacity and heavy tailed service times will overflow about equally often no matter how much we increase the service rate. We also study the time until overflow for queues fed by a superposition of k iid on/off processes with a heavy tailed on distribution, and we show the benefit of pooling the system resources as far as time until overflow is concerned.

Article information

Ann. Appl. Probab., Volume 7, Number 4 (1997), 1021-1057.

First available in Project Euclid: 29 January 2003

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Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22] 90B15: Network models, stochastic

Long range dependence heavy tails on/off models $G/G/1$ queue fluid models long memory heavy tailed distribution regular variation time to hit a level buffer overflow maximum work load weak convergence


Heath, David; Resnick, Sidney; Samorodnitsky, Gennady. Patterns of buffer overflow in a class of queues with long memory in the input stream. Ann. Appl. Probab. 7 (1997), no. 4, 1021--1057. doi:10.1214/aoap/1043862423.

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