Synchronized Lévy queues

Offer Kella (Corresponding author), Onno Boxma (Corresponding author)

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Abstract

We consider a multivariate Lévy process where the first coordinate is a Lévy process with no negative jumps which is not a subordinator and the others are non-decreasing. We determine the Laplace-Stieltjes transform of the steady-state buffer content vector of an associated system of parallel queues. The special structure of this transform allows us to rewrite it as a product of joint Laplace-Stieltjes transforms. We are thus able to interpret the buffer content vector as a sum of independent random vectors.

Original languageEnglish
Pages (from-to)1222-1233
Number of pages12
JournalJournal of Applied Probability
Volume57
Issue number4
DOIs
Publication statusPublished - Dec 2020

Funding

The authors thank Liron Ravner and Bert Zwart for interesting discussions. Offer Kella is supported in part by grant 1647/17 from the Israel Science Foundation and the Vigevani Chair in Statistics. Onno Boxma is partly funded by an NWO TOP grant, grant 613.001.352, and by the NWO Gravitation project NETWORKS, grant 024.002.003.

Keywords

  • decomposition
  • Lévy driven queues
  • synchronized Lévy queues

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