Skip to main content
SpringerLink
Log in

An Algorithmic Approach for Multiserver Retrial Queues with Two Customers Classes and Non-preemptive Priority

  • Conference paper
  • First Online:
Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10378))

  • 477 Accesses

Abstract

Retrial queueing models with multiple servers and two classes of customers arise in various practical computer and telecommunication systems. The consideration of retrials (or repeated attempts) introduces analytical difficulties and most of works consider either models with preemptive priority or non-preemptive priority in the single server case. This paper aims to propose a recursive algorithmic approach for the performance analysis of a multiserver retrial queue with non-preemptive priority and two customers classes: ordinary customers whose access to the service depends on the number of available servers and who join the orbit when blocked; and impatient priority customers who have access to all servers and are lost when no server is available. In addition, we develop the formula of the main stationary performance measures. Through numerical examples, we study the effect of the system parameters on the blocking probability for ordinary customers and the loss probability for priority customers.

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Kim, C., Klimenok, V.I., Dudin, A.N.: Analysis and optimization of Guard Channel Policy in cellular mobile networks with account of retrials. Comput. Oper. Res. 43, 181–190 (2014)

    Article  MathSciNet  Google Scholar 

  2. Gharbi, N., Nemmouchi, B., Mokdad, L., Ben-Othmane, J.: The impact of breakdowns disciplines and repeated attempts on performances of small cell networks. J. Comput. Sci. 5, 633–644 (2014)

    Article  Google Scholar 

  3. Gharbi, N., Charabi, L., Mokdad, L.: Performance evaluation of heterogeneous servers allocation disciplines in networks with retrials. In: The IEEE 17th International Conference on High Performance Computing and Communications (HPCC 2015), New York, USA, 24–26, August (2015)

    Google Scholar 

  4. Gharbi, N.: Using GSPNs for performance analysis of a new admission control strategy with retrials and guard channels. In: The 3rd International Conference on Mobile and Wireless Technology 2016 (ICMWT 2016), Korea (2016)

    Google Scholar 

  5. Charabi, L., Gharbi, N., Ben-Othman, J., Mokdad, L.: Call admission control in small cell networks with retrials and guard channels. In: Proceedings of The IEEE Global Communications Conference 2016 (GLOBECOM 2016), USA (2016)

    Google Scholar 

  6. Wüchner, P., Sztrik, J., Meer, H.: Modeling wireless sensor networks using finite-source retrial queues with unreliable orbit. In: Hummel, K.A., Hlavacs, H., Gansterer, W. (eds.) PERFORM 2010. LNCS, vol. 6821, pp. 73–86. Springer, Heidelberg (2011). doi:10.1007/978-3-642-25575-5_7

    Chapter  Google Scholar 

  7. Falin, G.I., Templeton, J.G.C.: Retrial Queues. Chapman and Hall, London (1997)

    Book  Google Scholar 

  8. Artalejo, J.R., Gmez-Corral, A.: Retrial Queueing Systems: A Computational Approach. Springer, Berlin (2008)

    Book  Google Scholar 

  9. Kim, J., Kim, B.: A survey of retrial queueing systems. Ann. Oper. Res. 1–34 (2015)

    Google Scholar 

  10. Do, T.V., Do, N.H., Zhang, J.: An enhanced algorithm to solve multiserver retrial queueing systems with impatient customers. Comput. Ind. Eng. 65(4), 719–728 (2013)

    Article  Google Scholar 

  11. Dudin, A.N., Dudina, O.S.: Analysis of multiserver retrial queueing system with varying capacity and parameters. Math. Probl. Eng. 2015 (2015)

    Google Scholar 

  12. Kim, B., Kim, J.: Exact tail asymptotics for the \(M/M/m\) retrial queue with nonpersistent customers. Oper. Res. Lett. 40, 537–540 (2012)

    Article  MathSciNet  Google Scholar 

  13. Kim, J., Kim, J., Kim, B.: Tail asymptotics of the queue size distribution in the M/M/m retrial queue. J. Comput. Appl. Math. 236, 3445–3460 (2012)

    Article  MathSciNet  Google Scholar 

  14. Kim, J., Kim, J.: Waiting time distribution in the M/M/m retrial queue. Bull. Korean Math. Soc. 50, 1659–1671 (2013)

    Article  MathSciNet  Google Scholar 

  15. Phung-Duc, T., Masuyama, H., Kasahara, S., Takahashi, Y.: A matrix continued fraction approach to multiserver retrial queues. Ann. Oper. Res. 202, 161–183 (2013)

    Article  MathSciNet  Google Scholar 

  16. Shin, Y.W., Moon, D.H.: M/M/c retrial queue with multiclass of customers. Method. Comput. Appl. Probab. 16, 931–949 (2014)

    Article  MathSciNet  Google Scholar 

  17. Avrachenkov, K., Morozov, E., Steyaert, B.: Sufficient stability conditions for multi-class constant retrial rate systems. Queueing Syst. 82(1), 149–171 (2016)

    Article  MathSciNet  Google Scholar 

  18. Artalejo, J.R., Phung-Duc, T.: Single server retrial queues with two way communication. Appl. Math. Model. 37, 1811–1822 (2013)

    Article  MathSciNet  Google Scholar 

  19. Avrachenkov, K., Nain, P., Yechiali, U.: A retrial system with two input streams and two orbit queues. Queueing Syst. 77(1), 1–31 (2014)

    Article  MathSciNet  Google Scholar 

  20. Choi, B.D., Chang, Y.: Single server retrial queues with priority calls. Math. Comput. Model. 30(3–4), 7–32 (1999)

    Article  MathSciNet  Google Scholar 

  21. Gao, S.: A preemptive priority retrial queue with two classes of customers and general retrial times. Oper. Res. 15(2), 233–251 (2015)

    MathSciNet  Google Scholar 

  22. Choi, B.D., Chang, Y.: MAP1, MAP2/M/c retrial queue with the retrial group of finite capacity and geometric loss. Math. Comput. Model. 30, 99–113 (1999)

    Article  Google Scholar 

  23. Kumar, M.S., Chakravarthy, S.R., Arumuganathan, R.: Preemptive resume priority retrial queue with two classes of MAP arrivals. Appl. Math. Sci. 7(52), 2569–2589 (2013)

    Google Scholar 

  24. Gharbi, N., Dutheillet, C., Ioualalen, M.: Colored stochastic petri nets for modelling and analysis of multiclass retrial systems. Math. Comput. Model. 49, 1436–1448 (2009)

    Article  Google Scholar 

  25. Kim, B., Kim, J.: Stability of a two-class two-server retrial queueing system. Perform. Eval. 88–89, 1–17 (2015)

    Google Scholar 

  26. Boutarfa, L., Djellab, N.: On the performance of the M1, M2/G1, G2/1 retrial queue with pre-emptive resume policy. Yugoslav J. Oper. Res. 25(1), 153–164 (2015)

    Article  MathSciNet  Google Scholar 

  27. Dimitriou, I.: A preemptive resume priority retrial queue with state dependent arrivals, unreliable server and negative customers. TOP 21(3), 542–571 (2013)

    Article  MathSciNet  Google Scholar 

  28. Ayyapan, G., Muthu Ganapathi Subramanian, A., Sekar, G.: M/M/1 retrial queueing system with loss and feedback under non-pre-emptive priority service by matrix geometric method. Appl. Math. Sci. 4(48), 2379–2389 (2010)

    MathSciNet  MATH  Google Scholar 

  29. Madan, K.C.: A non-preemptive priority queueing system with a single server serving two queues M/G/1 and M/D/1 with optional server vacations based on exhaustive service of the priority units. Appl. Math. 2, 791–799 (2011)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Sciences and Technology USTHB, Algiers, Algeria

    Nawel Gharbi

  2. National Computer Science Engineering School ESI, Algiers, Algeria

    Leila Charabi

Authors
  1. Nawel Gharbi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leila Charabi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nawel Gharbi .

Editor information

Editors and Affiliations

  1. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Nigel Thomas

  2. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Matthew Forshaw

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Gharbi, N., Charabi, L. (2017). An Algorithmic Approach for Multiserver Retrial Queues with Two Customers Classes and Non-preemptive Priority. In: Thomas, N., Forshaw, M. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2017. Lecture Notes in Computer Science(), vol 10378. Springer, Cham. https://doi.org/10.1007/978-3-319-61428-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-61428-1_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61427-4

  • Online ISBN: 978-3-319-61428-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation