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Synchronized Lévy queues

Part of: Operations research and management science Special processes Stochastic processes

Published online by Cambridge University Press:  23 November 2020

Offer Kella  and
Onno Boxma
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
Onno Boxma*
Affiliation:
Eindhoven University of Technology
*
*Postal address: Department of Statistics and Data Science, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 9190501, Israel. Email: offer.kella@gmail.com
**Postal address: EURANDOM and Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email: o.j.boxma@tue.nl
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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.

Keywords

Lévy driven queuessynchronized Lévy queuesdecomposition

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes 60K25: Queueing theory
Secondary: 90B05: Inventory, storage, reservoirs
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1222 - 1233
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Copyright
© Applied Probability Trust 2020

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