Abstract
An two-phases-service M/M/1/N queuing system with the server breakdown and multiple vacations was considered. Firstly, equations of steady-state probability were derived by applying the Markov process theory. Then, we obtained matrix form solution of steady-state probability by using blocked matrix method. Finally, some performance measures of the system such as the expected number of customers in the system and the expected number of customers in the queue were also presented.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Gray, W.J., Wang, P.P., Scot, M.: A Vacation Queueing Model with Service Breakdowns. Applied Mathematics Modelling 24, 391–400 (2000)
Madan, K.C.: An M/G/1 Queue with Second Optional Service. Queue. Syst. (34), 37–46 (2000)
Medhi, J.: A Single Server Poisson input Queue with a Second Optional Channel. Queue. Syst. (42), 239–242 (2002)
Yue, D., Zhang, Y., Yue, W.: Optimal Performance Analysis of an M/M/1/N Queue System with Balking, Reneging and Server Vacation. International Journal of Pure and Applied Mathematics 28, 101–115 (2006)
Tian, R., Yue, D., Hu, L.: M/ H2 / 1 Queuing System with Balking, N-Policy and Multiple Vacations. Operation Research and Management Science 4, 56–60 (2007)
Yue, D., Sun, Y.: The Waiting Time of the M/M/1/N Queuing System with Balking Reneging and Multiple Vacations. Chinese Journal of Engineering Mathematics 5, 943–946 (2008)
Yue, D., Sun, Y.: The Waiting Time of MPMPCPN Queuing System with Balking, Reneging and Multiple Synchronous Vacations of Partial Servers. Systems Engineering Theory & Practice 2, 89–97 (2008)
Wu, J., Yin, X., Liu, Z.: The M/G/1 retrial G-queues with N-policy, Feedback, Preemptive Resume and Unreliable Server. ACTA Mathematicae Applicatae Sinica 32, 323–335 (2009)
Tang, Y.: Some Seliability Indices in Siscrete Geomx/G/1 Repairable Queueing System with Delayed Multiple Vacations. System Engineering—Theory & Practice 29, 135–143 (2009)
Feng, Y.: A Repairable M/G/1 Queue System with Negative Arrivals Under Multiple Vacation Policy. College Mathema TICS 25, 86–90 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hui, Z., Wei, G. (2011). The Two-Phases-Service M/M/1/N Queuing System with the Server Breakdown and Multiple Vacations. In: Liu, B., Chai, C. (eds) Information Computing and Applications. ICICA 2011. Lecture Notes in Computer Science, vol 7030. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25255-6_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-25255-6_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25254-9
Online ISBN: 978-3-642-25255-6
eBook Packages: Computer ScienceComputer Science (R0)