Skip to main content

The Simulation of Finite-Source Retrial Queueing Systems with Two-Way Communication and Impatient Customers

  • Conference paper
  • First Online:
Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2021)

Abstract

The aim of the paper is to analyze a M/M/1//N finite-source, two-way communication retrial queueing system with an unreliable server and impatient customers. In this model, every request in the source is eligible to generate customers when the server does not function but they are forwarded immediately to the orbit. Customers may depart from the system during its waiting in the orbit after a random time and they get back to the source. All random variables involved in the model construction are supposed to be independent of each other. The novelty of the investigation is to carry out a sensitivity analysis comparing various distributions of failure time on the performance measures such as the mean number of customers in the orbit, the mean waiting time of an arbitrary customer, probability of abandonment, etc. With the help of self-developed simulation program, results are illustrated graphically.

The research was supported by the Thematic Excellence Programme (TKP2020-IKA-04) of the Ministry for Innovation and Technology in Hungary.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Artalejo, J., Corral, A.G.: Retrial Queueing Systems: A Computational Approach. Springer, Heidelberg (2008)

    Google Scholar 

  2. Chen, E.J., Kelton, W.D.: A procedure for generating batch-means confidence intervals for simulation: checking independence and normality. Simulation 83(10), 683–694 (2007)

    Article  Google Scholar 

  3. Dragieva, V., Phung-Duc, T.: Two-way communication M/M/1//N retrial queue. In: Thomas, N., Forshaw, M. (eds.) ASMTA 2017. LNCS, vol. 10378, pp. 81–94. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-61428-1_6

    Chapter  MATH  Google Scholar 

  4. Dragieva, V.I.: Number of retrials in a finite source retrial queue with unreliable server. Asia-Pac. J. Oper. Res. 31(2), 23 (2014). https://doi.org/10.1142/S0217595914400053

    Article  MathSciNet  MATH  Google Scholar 

  5. Falin, G., Artalejo, J.: A finite source retrial queue. Eur. J. Oper. Res. 108, 409–424 (1998)

    Article  Google Scholar 

  6. Fiems, D., Phung-Duc, T.: Light-traffic analysis of random access systems without collisions. Ann. Oper. Res. 277(2), 311–327 (2017). https://doi.org/10.1007/s10479-017-2636-7

    Article  MathSciNet  MATH  Google Scholar 

  7. Fishwick, P.A.: Simpack: getting started with simulation programming in C and C++. In: In 1992 Winter Simulation Conference, pp. 154–162 (1992)

    Google Scholar 

  8. Francini, A., Neri, F.: A comparison of methodologies for the stationary analysis of data gathered in the simulation of telecommunication networks. In: Proceedings of MASCOTS ’96 - 4th International Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, pp. 116–122 (Feb 1996)

    Google Scholar 

  9. Gharbi, N., Nemmouchi, B., Mokdad, L., Ben-Othman, J.: The impact of breakdowns disciplines and repeated attempts on performances of small cell networks. J. Comput. Sci. 5(4), 633–644 (2014)

    Article  Google Scholar 

  10. Kim, J., Kim, B.: A survey of retrial queueing systems. Ann. Oper. Res. 247(1), 3–36 (2015). https://doi.org/10.1007/s10479-015-2038-7

    Article  MathSciNet  MATH  Google Scholar 

  11. Krishnamoorthy, A., Pramod, P.K., Chakravarthy, S.R.: Queues with interruptions: a survey. TOP 22(1), 290–320 (2012). https://doi.org/10.1007/s11750-012-0256-6

    Article  MathSciNet  MATH  Google Scholar 

  12. Kuki, A., Sztrik, J., Tóth, Á., Bérczes, T.: A contribution to modeling two-way communication with retrial queueing systems. In: Dudin, A., Nazarov, A., Moiseev, A. (eds.) ITMM/WRQ -2018. CCIS, vol. 912, pp. 236–247. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-97595-5_19

    Chapter  MATH  Google Scholar 

  13. Kumar, B.K., Vijayalakshmi, G., Krishnamoorthy, A., Basha, S.S.: A single server feedback retrial queue with collisions. Comput. Oper. Res. 37(7), 1247–1255 (2010)

    Article  MathSciNet  Google Scholar 

  14. Law, A.M., Kelton, W.D.: Simulation Modeling and Analysis. McGraw-Hill Education (1991)

    Google Scholar 

  15. Nazarov, A., Sztrik, J., Kvach, A.: A survey of recent results in finite-source retrial queues with collisions. In: Dudin, A., Nazarov, A., Moiseev, A. (eds.) ITMM/WRQ -2018. CCIS, vol. 912, pp. 1–15. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-97595-5_1

    Chapter  Google Scholar 

  16. Nazarov, A., Sztrik, J., Kvach, A., Bérczes, T.: Asymptotic analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs. Ann. Oper. Res. 277(2), 213–229 (2018). https://doi.org/10.1007/s10479-018-2894-z

    Article  MathSciNet  MATH  Google Scholar 

  17. Sztrik, J., Tóth, Á., Pintér, Á., Bács, Z.: The simulation of finite-source retrial queueing systems with two-way communications to the orbit and blocking. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds.) DCCN 2020. CCIS, vol. 1337, pp. 171–182. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-66242-4_14

    Chapter  Google Scholar 

  18. Toth, A., Sztrik, J., Kuki, A., Berczes, T., Efrosinin, D.: Reliability analysis of finite-source retrial queues with outgoing calls using simulation. In: 2019 International Conference on Information and Digital Technologies (IDT), pp. 504–511, June 2019

    Google Scholar 

  19. Tóth, A.., Bérczes, T.., Sztrik, J.., Kuki, A.., Schreiner, W..: The simulation of finite-source retrial queueing systems with collisions and blocking. J. Math. Sci. 246(4), 548–559 (2020). https://doi.org/10.1007/s10958-020-04759-4

    Article  MathSciNet  Google Scholar 

  20. Zhang, F., Wang, J.: Performance analysis of the retrial queues with finite number of sources and service interruptions. J. Korean Stat. Soc. 42(1), 117–131 (2012). https://doi.org/10.1016/j.jkss.2012.06.002

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ádám Tóth .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sztrik, J., Tóth, Á., Pintér, Á., Bács, Z. (2021). The Simulation of Finite-Source Retrial Queueing Systems with Two-Way Communication and Impatient Customers. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2021. Lecture Notes in Computer Science(), vol 13144. Springer, Cham. https://doi.org/10.1007/978-3-030-92507-9_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-92507-9_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92506-2

  • Online ISBN: 978-3-030-92507-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics