Abstract
In this paper, we show through the example of the M/G/1 queue with working vacations, how queueing theory can help to the performance evaluation of some modern systems. We obtain the joint probability distribution of the server state and the number of orbiting customers in the system.This distribution is obtained in terms of Laplace and z- transforms. We show how mean performance measures can be obtained.
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References
Artalejo, J.R.: A Classified Bibliography on Retrial Queues: Progress in 2000-2009. Math. & Comput. Modelling 51(9), 1071–1081 (2009)
Do, T.V.: M/M/1 Retrial Queue with Working Vacation. Acta Informatica 47, 67–75 (2009)
Jain, M., Agrawal, P.K.: M/E k /1 Queueing System with Working Vacacation. Quality Tech. & Quantit. Managmt. 4(4), 455–470 (2006)
Ke, J., Wu, C., Zhang, Z.G.: Recent Developments in Vacation Queueing Models-A Survey. Int. J. Oper. Res. 7(4), 3–8 (2010)
Li, J.H., Tian, N.S., Zhang, Z.G., Lu, H.P.: Analysis of the M/G/1 Queue with Exponential Working Vacations- A Matrix Analytic Approach. Queueing Syst. 61, 139–166 (2009)
Liu, W., Xu, X., Tian, N.: Some results on the M/M/1 Queue with Working Vacacations. Operat. Res. Letters 35(5), 595–600 (2007)
Servi, L.D., Finn, S.G.: M/M/1 Queues with Working Vacations (M/M/1/WV). Performance Evaluation 50, 41–52 (2002)
Wu, D., Takagi, H.: M/G/1 Queue with Multiple Working Vacacations. Performance Evaluation 63(7), 654–681 (2009)
Xu, X., Liu, M.X., Zhao, X.H.: The balk Input M X /M/1 Queue with Working Vacacations. J. Syst. Sci. & Syst. Engineering 18(3), 358–368 (2009)
Yang, D.Y., Wang, K.H., Wu, C.H.: Optimization and Sensitivity Analysis of Controlling Arrivals in the Queueing System with Single Working Vacation. J. of Comput. & Appl. Math. 234, 545–556 (2010)
Zhang, M., Hou, H.: Performance Analysis of MAP/G/1 Queue with Working Vacacations and Vacation Interruption. Appl. Math. Modelling 35(4), 1551–1560 (2011)
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© 2014 Springer International Publishing Switzerland
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Aissani, A., Taleb, S., Kernane, T., Saidi, G., Hamadouche, D. (2014). An M/G/1 Retrial Queue with Working Vacation. In: SwiÄ…tek, J., Grzech, A., SwiÄ…tek, P., Tomczak, J. (eds) Advances in Systems Science. Advances in Intelligent Systems and Computing, vol 240. Springer, Cham. https://doi.org/10.1007/978-3-319-01857-7_43
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DOI: https://doi.org/10.1007/978-3-319-01857-7_43
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01856-0
Online ISBN: 978-3-319-01857-7
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