Asymptotics of palm-stationary buffer content distributions in fluid flow queues

Tomasz Rolski · Sabine Schlegel · Volker Schmidt

27 citations0/0 files storedAdvances in Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

We study a fluid flow queueing system with m independent sources alternating between periods of silence and activity; m ≥ 2. The distribution function of the activity periods of one source, is supposed to be intermediate regular varying. We show that the distribution of the net increment of the buffer during an aggregate activity period (i.e. when at least one source is active) is asymptotically tail-equivalent to the distribution of the net input during a single activity period with intermediate regular varying distribution function. In this way, we arrive at an asymptotic representation of the Palm-stationary tail-function of the buffer content at the beginning of aggregate activity periods. Our approach is probabilistic and extends recent results of Boxma (1996; 1997) who considered the special case of regular variation.

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References

1982Estimates for the probability of ruin with special emphasis on the possibility of large claims 1979Subexponentiality and infinite divisibility 1975On the tails of waiting-time distributions 1986Convolution tails, product tails and domains of attraction 1998Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models 1976On Regenerative Processes in Queueing Theory 1980Subexponential distribution functions 1993Tail probabilities with statistical multiplexing and effective bandwidths in multi-class queues

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