Another look into decomposition results

Jevgenijs Ivanovs; Offer Kella

doi:10.1007/s11134-013-9347-9

Another look into decomposition results

Jevgenijs Ivanovs, Offer Kella

Department of Statistics

The Hebrew University of Jerusalem

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

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.

Original language	English
Pages (from-to)	19-28
Number of pages	10
Journal	Queueing Systems
Volume	75
Issue number	1
DOIs	https://doi.org/10.1007/s11134-013-9347-9
State	Published - Sep 2013

Keywords

G/G/1 queue
Lévy process
Random walk
Reflection
Secondary jump input
Server vacations
Wiener-Hopf factorization

All Science Journal Classification (ASJC) codes

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

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10.1007/s11134-013-9347-9

Cite this

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title = "Another look into decomposition results",

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 c{\`a}dl{\`a}g processes with certain secondary jump inputs. Special cases are processes with stationary or stationary and independent increments. In the L{\'e}vy 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.",

keywords = "G/G/1 queue, L{\'e}vy process, Random walk, Reflection, Secondary jump input, Server vacations, Wiener-Hopf factorization",

author = "Jevgenijs Ivanovs and Offer Kella",

note = "Funding Information: Acknowledgments Jevgenijs Ivanovs study was supported by the Swiss National Science Foundation Project 200021-124635/1, and Offer Kella study was supported in part by Grant No. 434/09 from the Israel Science Foundation and the Vigevani Chair in Statistics.",

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AU - Kella, Offer

N1 - Funding Information: Acknowledgments Jevgenijs Ivanovs study was supported by the Swiss National Science Foundation Project 200021-124635/1, and Offer Kella study was supported in part by Grant No. 434/09 from the Israel Science Foundation and the Vigevani Chair in Statistics.

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N2 - 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.

AB - 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.

KW - G/G/1 queue

KW - Lévy process

KW - Random walk

KW - Reflection

KW - Secondary jump input

KW - Server vacations

KW - Wiener-Hopf factorization

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DO - 10.1007/s11134-013-9347-9

M3 - مقالة

SN - 0257-0130

VL - 75

SP - 19

EP - 28

JO - Queueing Systems

JF - Queueing Systems

IS - 1

ER -

Another look into decomposition results

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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