MODELLING AND SIMULATION OF UNRELIABLE M/M/n/n QUEUEING SYSTEM
Keywords:
M/M/n/n, Queueing system, Breakdown, Petri netAbstract
This paper is devoted to modelling and simulation of a Markov multi-server queueing system subject to breakdowns and with an ample repair capacity, the system do not form the queue of waiting customers. The paper introduces a mathematical model of the studied system and a simulation model created by using software CPN Tools. At the end of the paper the outcomes which were reached by both approaches will be shown and statistically evaluated.
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References
[1] MITRANI, I. L., AVI-ITZHAK, B. A many-server queue with service
interruptions. Operations Research, 1968, Vol. 16, No. 3, pp. 628 – 638. ISSN
0030–364X.
[2] NEUTS, M. F., LUCANTONI, D. M. A Markovian queue with N servers subject
to breakdowns and repairs. Management Science, 1979, Vol. 25, No. 9, pp. 849 –
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[3] WARTENHORST, P. N parallel queueing systems with server breakdown and
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[5] MADAN, K. C., ABU-DEYYEH, W., GHARAIBEH, M. On two parallel servers
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[6] YUE, D., YUE, W., YU, J., TIAN, R. A heterogeneous two-server queueing
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[7] WANG, K., CHANG, Y. Cost analysis of a finite M/M/R queueing system with
balking, reneging, and server breakdowns. Mathematical Methods of Operations
Research, 2002, Vol. 56, No. 2, pp. 169 – 180. ISSN 1432–5217.
interruptions. Operations Research, 1968, Vol. 16, No. 3, pp. 628 – 638. ISSN
0030–364X.
[2] NEUTS, M. F., LUCANTONI, D. M. A Markovian queue with N servers subject
to breakdowns and repairs. Management Science, 1979, Vol. 25, No. 9, pp. 849 –
861. ISSN 1526–5501.
[3] WARTENHORST, P. N parallel queueing systems with server breakdown and
repair. European Journal of Operational Research, 1995, Vol. 82, No. 2, pp. 302
– 322. ISSN 0377–2217.
[4] MITRANI, I., KING, J. B. Multiserver systems subject to breakdowns: an
empirical study. IEEE Transactions on Computers, 1983, Vol. 32, No. 1, pp. 96 –
98. ISSN 0018-9340.
[5] MADAN, K. C., ABU-DEYYEH, W., GHARAIBEH, M. On two parallel servers
with random breakdowns. Soochow Journal of Mathematics, 2003, Vol. 29, No. 4,
pp. 413 – 423. ISSN 0250–3255.
[6] YUE, D., YUE, W., YU, J., TIAN, R. A heterogeneous two-server queueing
system with balking and server breakdowns. In The Eighth International
Symposium on Operations Research and Its Applications. Zhangjiajie, China,
2009, pp. 230 – 244. ISBN 978–7–5100–0548–0/O763.
[7] WANG, K., CHANG, Y. Cost analysis of a finite M/M/R queueing system with
balking, reneging, and server breakdowns. Mathematical Methods of Operations
Research, 2002, Vol. 56, No. 2, pp. 169 – 180. ISSN 1432–5217.
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Published
2010-12-30
How to Cite
Dorda, M. (2010). MODELLING AND SIMULATION OF UNRELIABLE M/M/n/n QUEUEING SYSTEM. Perner’s Contacts, 5(4), 37–45. Retrieved from https://pernerscontacts.upce.cz/index.php/perner/article/view/1040
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Copyright (c) 2020 Michal Dorda
This work is licensed under a Creative Commons Attribution 4.0 International License.
