Performability analysis of an unreliable M/M/1-type queue

Ruslan Krenzler; Hans Daduna

Performability analysis of an unreliable M/M/1-type queue

Ruslan Krenzler
, Hans Daduna

University of Hamburg

Research output: Contributions to collected editions/works › Article in conference proceedings › Research › peer-review

Abstract

We consider a single server exponential queue with infinite waiting room and state dependent service rates. The server is unreliable and wears down when active and additionally may break down randomly. Repair times are random as well. The system is controlled with the possibility of preventive maintenance after a fixed number of services. This number is subject of optimization under a prescribed general cost structure. In case of breakdown (i.e. under repair) or during preventive maintenance no service is possible and no new customers are admitted.

We determine explicitly the stationary distribution of the queueing-availability process and how that the system is separable, i.e. the steady state is of product form.

Original language	English
Title of host publication	Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen : 8. GI/ITG-Workshop MMBnet 2015, 10./11. September 2015
Editors	Bernd E. Wolfinger, Klaus-D. Heidtmann
Number of pages	6
Place of Publication	Hamburg
Publisher	Universität Hamburg
Publication date	2015
Pages	90-95
Publication status	Published - 2015
Externally published	Yes
Event	Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen : 8. GI/ITG-Workshop MMBnet 2015: Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen - Hamburg, Germany Duration: 10.09.2015 → 11.09.2015 Conference number: 8 http://www.informatik.uni-hamburg.de/TKRN/MMBnet/

Bibliographical note

urn:nbn:de:gbv:18-228-7-2163

Research areas and keywords

Mathematics
Informatics

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Krenzler, R., & Daduna, H. (2015). Performability analysis of an unreliable M/M/1-type queue. In B. E. Wolfinger, & K.-D. Heidtmann (Eds.), Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen : 8. GI/ITG-Workshop MMBnet 2015, 10./11. September 2015 (pp. 90-95). (Berichte des Fachbereichs Informatik der Universität Hamburg; Vol. 302). Universität Hamburg. http://edoc.sub.uni-hamburg.de/informatik/volltexte/2015/216/

Krenzler, Ruslan ; Daduna, Hans. / Performability analysis of an unreliable M/M/1-type queue. Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen : 8. GI/ITG-Workshop MMBnet 2015, 10./11. September 2015. editor / Bernd E. Wolfinger ; Klaus-D. Heidtmann. Hamburg : Universität Hamburg, 2015. pp. 90-95 (Berichte des Fachbereichs Informatik der Universität Hamburg).

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Krenzler, R & Daduna, H 2015, Performability analysis of an unreliable M/M/1-type queue. in BE Wolfinger & K-D Heidtmann (eds), Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen : 8. GI/ITG-Workshop MMBnet 2015, 10./11. September 2015. Berichte des Fachbereichs Informatik der Universität Hamburg, vol. 302, Universität Hamburg, Hamburg, pp. 90-95, Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen : 8. GI/ITG-Workshop MMBnet 2015, Hamburg, Germany, 10.09.15. <http://edoc.sub.uni-hamburg.de/informatik/volltexte/2015/216/>

Performability analysis of an unreliable M/M/1-type queue. / Krenzler, Ruslan; Daduna, Hans.
Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen : 8. GI/ITG-Workshop MMBnet 2015, 10./11. September 2015. ed. / Bernd E. Wolfinger; Klaus-D. Heidtmann. Hamburg: Universität Hamburg, 2015. p. 90-95 (Berichte des Fachbereichs Informatik der Universität Hamburg; Vol. 302).

Research output: Contributions to collected editions/works › Article in conference proceedings › Research › peer-review

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AU - Krenzler, Ruslan

AU - Daduna, Hans

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PY - 2015

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N2 - We consider a single server exponential queue with infinite waiting room and state dependent service rates. The server is unreliable and wears down when active and additionally may break down randomly. Repair times are random as well. The system is controlled with the possibility of preventive maintenance after a fixed number of services. This number is subject of optimization under a prescribed general cost structure. In case of breakdown (i.e. under repair) or during preventive maintenance no service is possible and no new customers are admitted. We determine explicitly the stationary distribution of the queueing-availability process and how that the system is separable, i.e. the steady state is of product form.

AB - We consider a single server exponential queue with infinite waiting room and state dependent service rates. The server is unreliable and wears down when active and additionally may break down randomly. Repair times are random as well. The system is controlled with the possibility of preventive maintenance after a fixed number of services. This number is subject of optimization under a prescribed general cost structure. In case of breakdown (i.e. under repair) or during preventive maintenance no service is possible and no new customers are admitted. We determine explicitly the stationary distribution of the queueing-availability process and how that the system is separable, i.e. the steady state is of product form.

KW - Mathematics

KW - queueing systems

KW - random breakdown and repair

KW - product form steady state

KW - availability

KW - reactive and preventive maintenance

KW - loss systems

KW - Informatics

KW - availability

M3 - Article in conference proceedings

T3 - Berichte des Fachbereichs Informatik der Universität Hamburg

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BT - Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen : 8. GI/ITG-Workshop MMBnet 2015, 10./11. September 2015

A2 - Wolfinger, Bernd E.

A2 - Heidtmann, Klaus-D.

PB - Universität Hamburg

CY - Hamburg

T2 - Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen : 8. GI/ITG-Workshop MMBnet 2015

Y2 - 10 September 2015 through 11 September 2015

ER -

Krenzler R, Daduna H. Performability analysis of an unreliable M/M/1-type queue. In Wolfinger BE, Heidtmann KD, editors, Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen : 8. GI/ITG-Workshop MMBnet 2015, 10./11. September 2015. Hamburg: Universität Hamburg. 2015. p. 90-95. (Berichte des Fachbereichs Informatik der Universität Hamburg).

Performability analysis of an unreliable M/M/1-type queue

Abstract

Bibliographical note

Research areas and keywords

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