Performance analysis with truncated heavy-tailed distributions
Författare
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.
Avdelning/ar
Publiceringsår
2005
Språk
Engelska
Sidor
439-457
Publikation/Tidskrift/Serie
Methodology and Computing in Applied Probability
Volym
7
Issue
4
Dokumenttyp
Artikel i tidskrift
Förlag
Springer
Ämne
- Probability Theory and Statistics
Nyckelord
- regular variation
- ruin probability
- insurance risk
- M/G/1 queue
- Levy
- process
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 1573-7713