Convergence rates for M/G/1 queues and ruin problems with heavy tails
- 1 December 1996
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 33 (4) , 1181-1190
- https://doi.org/10.2307/3214995
Abstract
The time-dependent virtual waiting time in a M/G/1 queue converges to a proper limit when the traffic intensity is less than one. In this paper we give precise rates on the speed of this convergence when the service time distribution has a heavy regularly varying tail.The result also applies to the classical ruin problem. We obtain the exact rate of convergence for the ruin probability after time t for the case where claims arrive according to a Poisson process and claim sizes are heavy tailed.Our result supplements similar theorems on exponential convergence rates for relaxation times in queueing theory and ruin probabilities in risk theory.Keywords
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