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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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 $GI/G/1$ 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

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

Dates
First available in Project Euclid: 29 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1043862423

Digital Object Identifier
doi:10.1214/aoap/1043862423

Mathematical Reviews number (MathSciNet)
MR1484796

Zentralblatt MATH identifier
0905.60070

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

Keywords
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

Citation

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. https://projecteuclid.org/euclid.aoap/1043862423


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