Advertisement

The Pseudo-fault Geo/Geo/1 Queue with Setup Time and Multiple Working Vacation

  • Zhanyou Ma
  • Pengcheng Wang
  • Wuyi Yue
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 383)

Abstract

In this paper, we consider a discrete time Geo/Geo/1 repairable queueing system with pseudo-fault, setup time, N-policy and multiple working vacations. We assume that the service interruption is caused by pseudo-fault and breakdown, and occurs only when the server is busy. Using quasi birth-and-death chain, we establish a two-dimensional Markov chain. We obtain the distribution of the steady-state queue length by using matrix-geometric solution method. Moreover, We provide several performance indices of the system in steady-state. Finally, we present numerical results to illustrate the effect of several parameters on the systems.

Keywords

Pseudo-fault Setup time Multiple working vacation Matrix-geometric solution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Meisling, T.: Discrete-time Queuing Theory. Operations Research 6(1), 96–105 (1958)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Ndreca, S., Scoppola, B.: Discrete Time GI/Geom/1 Queueing System with Priority. European Journal of Operational Research 189(3), 1403–1408 (2008)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Servi, L., Finn, S.: M/M/1 Queues with Working Vacations (M/M/1/WV). Performance Evaluation 50(1), 41–52 (2002)CrossRefGoogle Scholar
  4. 4.
    Baba, Y.: Analysis of a GI/M/1 Queue with Multiple Working Vacations. Operations Research Letters 33(2), 201–209 (2005)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Yadin, M., Naor, P.: Queueing Systems with a Removable Service Station. Operations Research 14, 393–405 (1963)CrossRefGoogle Scholar
  6. 6.
    Goswami, V., Mund, G.: Analysis of Discrete-time Batch Service Renewal Input Queue with Multiple Working Vacations. Computers & Industrial Engineering 61(3), 629–636 (2011)CrossRefGoogle Scholar
  7. 7.
    Avi-Itzhak, B., Naor, P.: Some Queuing Problems with the Service Station Subject to Breakdown. Operations Research 11(3), 303–320 (1963)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Kulkarni, V., Choi, B.: Retrial Queues with Server Subject to Breakdowns and Repairs. Queueing Systems 7(2), 191–208 (1990)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Kalidass, K., Gnanaraj, J., Gopinath, S., Kasturi, R.: Transient Analysis of an M/M/1 Queue with a Repairable Server and Multiple Vacations. International Journal of Mathematics in Operational Research 6(2), 193–216 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Wan, G., Ren, Z., Wang, S.: Reliability Evaluation Algorithm of Power System using System False Fault Indices Pruning. Automation of Electric Power Systems 28(23), 56–60 (2004)Google Scholar
  11. 11.
    Neuts, M.F.: Matrix-geometric Solution in Stochastic Model: An Algorithmic Application. The Johns Hopkins University Press, Baltimore (1981)Google Scholar
  12. 12.
    Latouche, G., Ramaswami, V.: Introduction to Matrix Analytic Methods in Stochastic Modeling. ASA-SIAM Series on Statistic and Applied Probability, Philadelphia (1999)CrossRefMATHGoogle Scholar
  13. 13.
    He, Q.M.: Fundamentals of Matrix-analytic Methods. Springer, New York (2014)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.College of ScienceYanshan UniversityQinhuangdaoChina
  2. 2.Department of Intelligence and InformaticsKonan UniversityKobeJapan

Personalised recommendations