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Admission control policy of a two heterogeneous server finite capacity retrial queueing system with maintenance activity

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Abstract

This paper investigates the concept of admission control policy of a two heterogeneous server finite capacity retrial queueing system with maintenance activity. An arriving customer can receive service immediately if any one of the servers is found to be available. If the servers are busy, the customer may await its turn in the orbit. After a random amount of time, the orbital customers may check for the availability of servers and retry requesting service on a first come first serve basis. The concept of admission control policy is adopted to ensure a smooth utilization of the orbit space. In this policy, when the system size reaches the maximum capacity, the arriving customers are restricted from joining the orbit until the system size reduces to a threshold level. When a server becomes idle with no customer waiting to be served, it is subject to maintenance. The Chapman–Kolmogorov equations of the governing model are derived to study their queueing characteristics. Recursive technique is used to analyse the system size distributions in steady state. This enables us to acquire the various performance measures of the model under study. The effects induced by the system parameters on the performance metrics are numerically and graphically analysed.

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References

  1. Ammar, S.I.: Transient solution of an m/m/1 vacation queue with a waiting server and impatient customers. J. Egypt. Math. Soc. 25(3), 337–342 (2017)

    Article  Google Scholar 

  2. Arivudainambi, D., Godhandaraman, P.: Retrial queueing system with balking, optional service and vacation. Ann. Op. Res. 229(1), 67–84 (2015)

    Article  Google Scholar 

  3. Arivudainambi, D., Godhandaraman, P., Rajadurai, P.: Performance analysis of a single server retrial queue with working vacation. Opsearch 51(3), 434–462 (2014)

    Article  Google Scholar 

  4. Artalejo, J.R.: Accessible bibliography on retrial queues: progress in 2000–2009. Math. Comput. Model. 51(9–10), 1071–1081 (2010)

    Article  Google Scholar 

  5. Bouchentouf, A.A., Messabihi, A.: Heterogeneous two-server queueing system with reverse balking and reneging. Opsearch 55(2), 251–267 (2018)

    Article  Google Scholar 

  6. D’Arienzo, M., Dudin, A.N., Dudin, S.A., Manzo, R.: Analysis of a retrial queue with group service of impatient customers. J. Ambient Intell. Humanized Comput. 11(6), 2591–2599 (2020)

    Article  Google Scholar 

  7. Dimitrakopoulos, Y., Economou, A., Leonardos, S.: Strategic customer behavior in a queueing system with alternating information structure. Euro. J. Op. Res. 291(3), 1024–1040 (2021)

    Article  Google Scholar 

  8. Do, T.V., Papp, D., Chakka, R., Wang, J., Sztrik, J.: A closed-form solution for a two-server heterogeneous retrial queue with threshold policy. Sādhanā 41(8), 817–823 (2016)

    Article  Google Scholar 

  9. Fiems, D.: Retrial queues with constant retrial times. Queueing Syst. 103, 347–365 (2022)

    Article  Google Scholar 

  10. Gao, S., Dong, H., Wang, X.: Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation. Op. Res. 21(1), 621–643 (2021)

    Google Scholar 

  11. Gupta, S.M.: Interrelationship between controlling arrival and service in queueing systems. Comput. Op. Res. 22(10), 1005–1014 (1995)

    Article  Google Scholar 

  12. Hanukov, G., Avinadav, T., Chernonog, T., Spiegel, U., Yechiali, U.: A queueing system with decomposed service and inventoried preliminary services. Appl. Math. Model. 47, 276–293 (2017)

    Article  Google Scholar 

  13. Ibrahim, R.: Managing queueing systems where capacity is random and customers are impatient. Prod. Op. Manag. 27(2), 234–250 (2018)

    Article  Google Scholar 

  14. Jain, M., Sanga, S.S.: Optimal control f-policy for m/m/r/k queue with an additional server and balking. Int. J. Appl. Comput. Math. 5(6), 1–16 (2019)

    Article  Google Scholar 

  15. Jain, M., Sanga, S.S.: State dependent queueing models under admission control f-policy: A survey. J.Ambient Intell. Humanized Comput. 11(9), 3873–3891 (2020)

    Article  Google Scholar 

  16. Karpagam, S., Ayyappan, G., Somasundaram, B.: A bulk queueing system with rework in manufacturing industry with starting failure and single vacation. Int. J. Appl. Comput. Math. 6(6), 1–22 (2020)

    Article  Google Scholar 

  17. Ke, J.C., Chang, F.M., Liu, T.H.: M/m/c balking retrial queue with vacation. Qual. Technol. Quant. Manag. 16(1), 54–66 (2019)

    Article  Google Scholar 

  18. Kim, J., Kim, B.: A survey of retrial queueing systems. Ann. Op. Res. 247(1), 3–36 (2016)

    Article  Google Scholar 

  19. Kumar, P.S.: Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set. Int. J. Syst. Assur. Eng. Manag. 11(1), 189–222 (2020)

    Article  Google Scholar 

  20. Liu, Z., Yu, S.: The m/m/c queueing system in a random environment. J. Math. Anal. Appl. 436(1), 556–567 (2016)

    Article  Google Scholar 

  21. Sanga, S.S., Jain, M.: Cost optimization and anfis computing for admission control of m/m/1/k queue with general retrial times and discouragement. Appl. Math. Comput. 363, 124624 (2019)

    Google Scholar 

  22. Sudhesh, R., Savitha, P., Dharmaraja, S.: Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience. Top 25(1), 179–205 (2017)

    Article  Google Scholar 

  23. Upadhyaya, S.: Queueing systems with vacation: an overview. Int. J. Math. Op. Res. 9(2), 167–213 (2016)

    Article  Google Scholar 

  24. Yang, D.Y., Yang, N.C.: Performance and cost analysis of a finite capacity queue with two heterogeneous servers under f-policy. Int. J. Serv. Op. Inf. 9(2), 101–115 (2018)

    Google Scholar 

  25. Zhang, Y., Wang, J., Wang, F.: Equilibrium pricing strategies in retrial queueing systems with complementary services. Appl. Math. Model. 40(11–12), 5775–5792 (2016)

    Article  Google Scholar 

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Acknowledgements

The authors would like to extend their gratitude towards the Editorial board and referees for their valuable insights and suggestions that has let to the enhancement of the quality of the original manuscript.

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  1. V. Poongothai and P. Godhandaraman have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu, Tamil Nadu, 603203, India

    V. Saravanan, V. Poongothai & P. Godhandaraman

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  1. V. Saravanan
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  2. V. Poongothai
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  3. P. Godhandaraman
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Contributions

SV, PV and GP have put in their joint efforts towards achieving the results established. Mathematical model, application, methodology, numerical analysis and writing of the paper is done by SV. PV and GP have extended their support by supervising and suggesting necessary revisions for enhancing quality of the work.

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Correspondence to P. Godhandaraman.

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Saravanan, V., Poongothai, V. & Godhandaraman, P. Admission control policy of a two heterogeneous server finite capacity retrial queueing system with maintenance activity. OPSEARCH 60, 1902–1925 (2023). https://doi.org/10.1007/s12597-023-00669-6

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