Another look into decomposition results

Authors:
Jevgenijs Ivanovs;Offer Kella
Affiliations:
Department of Actuarial Sciences, University of Lausanne, Lausanne, Switzerland 1015;Department of Statistics, The Hebrew University of Jerusalem, Jerusalem, Israel 91905
Venue:
Queueing Systems: Theory and Applications
Year:
2013

Citing 2
Cited 0

Queueing systems with vacations—a survey

Queueing Systems: Theory and Applications
A heavy-traffic limit for the cycle counting process in G/G/1, optional interruptions and elastic screen Brownian motion

Mathematics of Operations Research

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Abstract

In this note, we identify a simple setup from which one may easily infer various decomposition results for queues with interruptions as well as càdlàg processes with certain secondary jump inputs. Special cases are processes with stationary or stationary and independent increments. In the Lévy process case, the decomposition holds not only in the limit but also at independent exponential times, due to the Wiener---Hopf decomposition. A similar statement holds regarding the GI/GI/1 setting with multiple vacations.