Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment

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We develop accurate approximations for the delay distribution of the MArP/G/1 queue that capture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive corrected phase-type approximations as a sum of the delay in a MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples. Keywords: Corrected phase-type approximations; Delay distribution; Heavy-tailed service times; MArP/G/1 queue; Perturbation; Tail asymptotics
Originele taal-2Engels
Pagina's (van-tot)598-638
Aantal pagina's41
TijdschriftStochastic Models
Volume30
Nummer van het tijdschrift4
DOI's
StatusGepubliceerd - 2014

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