Analysis of the Discrete-time Multi-queue System with a Cycle-based Scheduler

• Autorzy: Burakowski Wojciech , Sosnowski Maciej
• Języki publikacji: EN

Abstrakty

EN

This paper presents an analysis of a discrete-time multi-queue system handling a number of packet streams. The analysis focuses on calculating system state distribution and packet sojourn time distribution. The method relied upon for determining system state distribution is based on creating a number of equations that are solved numerically. Next, based on the distribution calculated in such a manner, we derive relations for packet sojourn time distribution. The models studied may be useful for instance in a system supporting a number of virtual links (each of a constant bitrate) that share a common physical link. Isolation of performance of those virtual links needs to be assured. Finally, we present some exemplary numerical results showing the usefulness of the proposed analysis for supporting the system dimensioning process.

Słowa kluczowe

EN

discrete-time queueing system with vacations; system state distribution; packet sojourn time distribution; virtualized system

• Wydawca: Instytut Łączności - Państwowy Instytut Badawczy
• Czasopismo: Journal of Telecommunications and Information Technology
• Rocznik: 2021
• Tom: nr 2
• Strony: 68--76
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Burakowski Wojciech

• National Institute of Telecommunications, Szachowa 1, 04-894 Warsaw, Poland

• https://orcid.org/0000-0002-8486-8004

autor

Sosnowski Maciej

• National Institute of Telecommunications, Szachowa 1, 04-894 Warsaw, Poland

• https://orcid.org/0000-0003-0563-1111

Bibliografia

• [1] W. Burakowski, „Virtualized network infrastructure supporting co existence of Parallel Internets", in Proc. 13th ACIS Int. Conf. On Software Engin., Artif. Intell., Network. and Parall./Distrib. Compu. SNPD 2012, Kyoto, Japan, 2012 (DOI: 10.1109/SNPD.2012.67).
• [2] B. Vinck and H. Brunnel, „Relationships between delay and buffer contents in ATM queues", Electron. Lett., vol. 31, no. 12, 1995 (DOI: 10.1049/el:19950662).
• [3] N. P. Dellaert, “Production to Order. Models and Rules for Production Planning”. Berlin Heidelberg: Springer, 1988 (ISBN: 9783540513094).
• [4] M. J. A. Eenige, “Queueing Systems with Periodic Service”. TU Eind-hoven, Netherlands, 1996 (ISBN: 9038603487).
• [5] H. Takagi, “Queueing Analysis: Vacation and Priority Systems”, pt. 1. Amsterdam: North-Holland, 1991 (ISBN: 9780444817709).
• [6] N. Tian and Z. G. Zhang, “Vacation Queueing Models - Theory and Applications”. New York: Springer, 2006 (ISBN: 9780387337210).
• [7] B. T. Doshi, „Queueing systems with vacation: A survey", Queueing Systems, vol. 1, pp. 29-66, 1986 (DOI: 10.1007/BF01149327).
• [8] J. C. Ke, C. H. Wu, and Z. G. Zhang, „Recent developments in vacations queueing models: A short survey", Int. J. of Oper. Res., vol. 7, no. 4, pp. 3-8, 2010 [Online]. Available: http://www.orstw.org.tw/ijor/vol7no4/2-Vol.%207,%20No.4%20pp.3-8.pdf
• [9] D. R. McNeil, „A solution to the fixed-cycle traffic light problem for compound Poisson arrivals", J. of Appl. Probab., vol. 5, no. 3, 1968, pp. 624-635 (DOI: 10.2307/3211926).
• [10] A. Chydzinski and B. Adamczyk: „Analysis of scheduler for virtualization of links with performance isolation", Appl. Mathem. & Inform. Sci., vol. 8, no. 6, pp. 2653-2666, 2014 (DOI:10.12785/amis/080601).
• [11] M. Sosnowski and W. Burakowski. „Analysis of the system with vacations under Poissonian input stream and constant service times", J. of Telecommun. and Inform. Technol., no. 3, 2013 [Online]. Available: https://www.il-pib.pl/czasopisma/JTIT/2013/3/3.pdf
• [12] W. Burakowski and M. Sosnowski, „On cycle based schedulers with time alternating priorities", in Proc. of 27th Int. Telecommun. Netw. and Appl. Conf. ITNAC 2017, Melbourne, Australia, 2017, pp. 1-6 (DOI: 10.1109/ATNAC.2017.8215377).

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).