The class of distributions associated with the generalized Pollaczek-Khinchine formula

Offer Kella*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The goal is to identify the class of distributions to which the distribution of the maximum of a Lévy process with no negative jumps and negative mean (equivalently, the stationary distribution of the reflected process) belongs. An explicit new distributional identity is obtained for the case where the Lévy process is an independent sum of a Brownian motion and a general subordinator (nondecreasing Lévy process) in terms of a geometrically distributed sum of independent random variables. This generalizes both the distributional form of the standard Pollaczek-Khinchine formula for the stationary workload distribution in the M/G/1 queue and the exponential stationary distribution of a reflected Brownian motion.

Original languageAmerican English
Pages (from-to)883-887
Number of pages5
JournalJournal of Applied Probability
Volume49
Issue number3
DOIs
StatePublished - Sep 2012

Keywords

  • Generalized Pollaczek-Khinchine formula
  • Lévy process with no negative jumps
  • Reflected Lévy process
  • Spectrally positive Lévy process
  • Supremum of a Lévy process

Fingerprint

Dive into the research topics of 'The class of distributions associated with the generalized Pollaczek-Khinchine formula'. Together they form a unique fingerprint.

Cite this