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Performance analysis with truncated heavy-tailed distributions

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Author

Summary, in English

This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form U boolean AND K for some r.v. U with distribution B which is heavy-tailed, say Pareto or Weibull, and a typically large K, say much larger than EU. We study the compound Poisson ruin probability psi(u) or, equivalently, the tail P(W > u) of the M/G/1 steady-state waiting time W. In the first part of the paper, we present numerical values of psi(u) for different values of K by using the classical Siegmund algorithm as well as a more recent algorithm designed for heavy-tailed claims/service times, and compare the results to different approximations of psi(u) in order to figure out the threshold between the light-tailed regime and the heavy-tailed regime. In the second part, we investigate the asymptotics as K -> infinity of the asymptotic exponential decay rate gamma = gamma((K)) in a more general truncated Levy process setting, and give a discussion of some of the implications for the approximations.

Publishing year

2005

Language

English

Pages

439-457

Publication/Series

Methodology and Computing in Applied Probability

Volume

7

Issue

4

Document type

Journal article

Publisher

Springer

Topic

  • Probability Theory and Statistics

Keywords

  • regular variation
  • ruin probability
  • insurance risk
  • M/G/1 queue
  • Levy
  • process

Status

Published

ISBN/ISSN/Other

  • ISSN: 1573-7713