Synchronized Lévy queues

Offer Kella; Onno Boxma

doi:10.1017/jpr.2020.75

Synchronized Lévy queues

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

Stochastic Operations Research

Research output: Contribution to journal › Article › Academic › peer-review

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 language	English
Pages (from-to)	1222-1233
Number of pages	12
Journal	Journal of Applied Probability
Volume	57
Issue number	4
DOIs	https://doi.org/10.1017/jpr.2020.75
Publication status	Published - Dec 2020

Keywords

decomposition
Lévy driven queues
synchronized Lévy queues

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10.1017/jpr.2020.75

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abstract = "We consider a multivariate L{\'e}vy process where the first coordinate is a L{\'e}vy 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. ",

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AB - 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.

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