Skip to main content
SpringerLink
Log in

Analysis of Markovian queueing system with second optional service operating under the triadic policy

  • Theoretical Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

In this paper, we investigate an M/M/2 queueing system with a second optional service that operates under a triadic (0, Q, N, M) policy. The stability condition and stationary probability distribution of the system size are computed by adopting the matrix-geometric method. Numerous system performance measures are also derived. The quadratic fit search method is applied to the cost optimization problem in order to optimize service rates during the first essential service and the second optional service. Finally, numerical results are presented for the illustration of the effect of model parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Balachandran, K.R.: Control policies for a single server system. Manage Sci. 19(9), 1013–1018 (1973)

    Article  Google Scholar 

  2. Chakravarthy, S.R.: Queueing models with optional cooperative services. Eur. J. Oper. Res. 18(1), 1–12 (2015)

    Google Scholar 

  3. Gupur, G.: On the eigenvalues of the \(M/M/1\) queueing model with second optional service. J Pseudo-Diff Oper Appl. 5, 359–410 (2014)

    Article  Google Scholar 

  4. Heyman, D.P.: The \(T\) policy for the \(M/G/1\) queue. Manage Sci. 23(7), 775–778 (1977)

    Article  Google Scholar 

  5. Kathirvel, J.: A single server perishable inventory system with \(N\) additional options for service. J. Math Model. 2(2), 187–216 (2015)

    Google Scholar 

  6. Ke, J.C.: Optimal \(NT\) policies for \(M/G/1\) system with a startup and unreliable server. Comput. Ind. Eng. 50(3), 248–262 (2006)

    Article  Google Scholar 

  7. Ke, J.C., Chang, C.J., Chang, F.M.: Controlling arrivals for a Markovian queueing system with a second optional service. Int. J. Ind. Eng. 17(1), 48–57 (2010)

    Google Scholar 

  8. Ke, J.C., Wu, C.H., Pearn, W.L.: Analysis of an infinite multi-server queue with an optional service. Computers & Industrial Engineering 65(2), 216–225 (2013)

    Article  Google Scholar 

  9. Lin, C.H., Ke, J.C.: Genetic algorithm for optimal thresholds of an infinite capacity multi-server system with triadic policy. Expert Syst. Appl. 37(6), 4276–4282 (2010)

    Article  Google Scholar 

  10. Lin, C.H., Ke, J.C.: Optimization analysis for an infinite capacity queueing system with multiple queue dependent servers: genetic algorithm. Int. J. Comput. Math. 88(7), 1430–1442 (2011)

    Article  Google Scholar 

  11. Liou, C.D., Wang, K.H., Liou, M.W.: Genetic algorithm to the machine repair problem with two removable servers operating under the triadic (0, Q, N, M) policy. Appl. Math. Model. 37(18–19), 8419–8430 (2013)

    Article  Google Scholar 

  12. Madan, K.C.: An \(M/G/1\) queue with second optional service. Queueing Syst. 34, 37–46 (2000)

    Article  Google Scholar 

  13. Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. John Hopkins University Press, Baltimore (1981)

    Google Scholar 

  14. Rardin, R.L.: Optimization in Operations Research. Prentice Hall, New Jersey (1997)

    Google Scholar 

  15. Rhee, H.K., Sivazlian, B.D.: Distribution of the busy period in a controllable \(M/M/2\) queue operating under the triadic \((0, K, N, M)\) policy. J. Appl. Probab. 27(2), 425–432 (1990)

    Article  Google Scholar 

  16. Sekar, G., Ayyappan, G., Subramanian, A.M.G.: Single server retrial queues with second optional service under Erlang services. Int. J. Math. Arch. 1(3), 174–182 (2011)

    Google Scholar 

  17. Vijaya Laxmi, P., Jyothsna, K.: Analysis of a working vacations queue with impatient customers operating under a triadic policy. Int. J. Manag. Sci. Eng. Manag. 9(3), 191–200 (2014)

    Google Scholar 

  18. Wang, K.H., Wang, Y.L.: Optimal control of an \(M/M/2\) queueing system with finite capacity operating under the triadic \((0, Q, N, M)\) policy. Math. Meth. Oper. Res. 55, 447–460 (2002)

    Article  Google Scholar 

  19. Yadin, M., Naor, P.: Queueing systems with a removable service station. J. Oper. Res. Soc. 14, 393–405 (1963)

    Article  Google Scholar 

  20. Yang, D.Y., Chen, Y.H.: Computation and optimization of a working breakdown queue with second optional service. J. Ind. Prod. Eng. 35(3), 181–188 (2018)

    Google Scholar 

  21. Yang, D.Y., Wang, K.H., Kuo, Y.T.: Economic application in a finite capacity multi-channel queue with second optional channel. Appl. Math. Comput. 217(18), 7412–7419 (2011)

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the editors and the anonymous referees for their valuable comments and suggestions which have helped in improving the quality and presentation of the paper. The authors would also like to thank the Department of Science and Technology, Government of India, for providing the Lab facility in the department under the DST-FIST Project grant No.SR/FST/MS-I/2017/3(c).

Funding

The authors declare that there is no funding source for this research.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Andhra University, Visakhapatnam, 530 003, India

    P. Vijaya Laxmi & E. Girija Bhavani

  2. Department of Basic Sciences and Humanities, Vignan’s Institute of Engineering for Women, Visakhapatnam, 530 049, India

    K. Jyothsna

Authors
  1. P. Vijaya Laxmi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Girija Bhavani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Jyothsna
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors have equally contributed to the research work of this manuscript.

Corresponding author

Correspondence to P. Vijaya Laxmi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Laxmi, P.V., Bhavani, E.G. & Jyothsna, K. Analysis of Markovian queueing system with second optional service operating under the triadic policy. OPSEARCH 60, 256–275 (2023). https://doi.org/10.1007/s12597-022-00588-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-022-00588-y

Keywords

Mathematics Subject Classification

Search

Navigation