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Cyclic Retrial Queue for Building Data Transmission Networks

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Performance Evaluation Methodologies and Tools (VALUETOOLS 2022)

Abstract

This paper considers a mathematical model of a cyclic multiple access communication network. The model can be used to build specialized “flying” FANET data transmission networks. We consider a single server retrial queue for modeling one node in such network. The input consists of multiple Poisson processes with different arrival rates. Service and retrial rates depend on the origin flow. Thus, each flow has its own orbit for redial. Under the condition when the retrial rate is low, we obtain an asymptotic probability distribution of the number of customers in the orbits.

This study was supported by the Tomsk State University Development Programme (Priority-2030).

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References

  1. Khan, M.F., Yau, K.-L.A., Noor, R.M., Imran, M.A.: Routing schemes in FANETs: a survey. Sensors 20, 38 (2020)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Artalejo, J.R.: A classified bibliography of research on retrial queues: progress in 1990–1999. TOP 7(2), 187–211 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Artalejo, J.R., Gómez-Corral, A.: Retrial queueing systems: a computational approach. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78725-9

  5. Artalejo, J.R., Falin, G.I.: Standard and retrial queueing systems: a comparative analysis. Revista Matematica Complutense 15, 101–129 (2002)

    MathSciNet  MATH  Google Scholar 

  6. Vishnevskii, V., Semenova, O.: Sistemy pollinga: teoriya i primenenie v shirokopolosnykh besprovodnykh setyakh [Polling systems: theory and applications in broadband wireless networks], 312 p. Tekhnosfera Publ., Moscow (2007)

    Google Scholar 

  7. Vishnevskii, V., Semenova, O.: Mathematical research methods polling systems. Autom. Telemechanics 2, 3–56 (2006)

    MATH  Google Scholar 

  8. Nazarov, A., Paul, S.: A cyclic queueing system with priority customers and T-strategy of service. Commun. Comput. Inf. Sci. 678, 182–193 (2016)

    MATH  Google Scholar 

  9. Nazarov, A., Paul, S.: A number of customers in the system with server vacations. Commun. Comput. Inf. Sci. 601, 334–343 (2015)

    MATH  Google Scholar 

  10. Nazarov, A.A., Paul, S.V., Klyuchnikova, P.N.: Research of a cyclic system with repeated calls. In: Distributed Computer and Telecommunication Networks: Control, Calculation, Communication (DCCN-2020), 14–18 September 2020, Moscow, Russia (2020)

    Google Scholar 

  11. Langaris, C.: A polling model with retrial customers. J. Oper. Res. Soc. Japan 40(4), 489–508 (1997)

    MathSciNet  MATH  Google Scholar 

  12. Langaris, C.: Gated polling models with customers in orbit. Math. Comput. Model. 30(3–4), 171–187 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Langaris, C.: Markovian polling system with mixed service disciplines and retrial customers. TOP 7, 305–322 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  14. Boxma, O., Resing, J.: Vacation and polling models with retrials. In: Horváth, A., Wolter, K. (eds.) EPEW 2014. LNCS, vol. 8721, pp. 45–58. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10885-8_4

    Chapter  Google Scholar 

  15. Abidini, M.A., Boxma, O., Resing, J.: Analysis and optimization of vacation and polling models with retrials. Perform. Eval. 98, 52–69 (2016)

    Article  Google Scholar 

  16. Moiseev, A., Nazarov, A., Paul, S.: Asymptotic diffusion analysis of multi-server retrial queue with hyper-exponential service. Mathematics 8(4), 531 (2020)

    Article  Google Scholar 

  17. Nazarov, A., Phung-Duc, T., Paul, S., Lizyura, O.: Diffusion limit for single-server retrial queues with renewal input and outgoing calls. Mathematics 10(6), 948 (2022)

    Article  Google Scholar 

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Correspondence to Ksenia Shulgina .

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Nazarov, A., Phung-Duc, T., Shulgina, K., Lizyura, O., Paul, S., Shashev, D. (2023). Cyclic Retrial Queue for Building Data Transmission Networks. In: Hyytiä, E., Kavitha, V. (eds) Performance Evaluation Methodologies and Tools. VALUETOOLS 2022. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 482. Springer, Cham. https://doi.org/10.1007/978-3-031-31234-2_10

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  • DOI: https://doi.org/10.1007/978-3-031-31234-2_10

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  • Print ISBN: 978-3-031-31233-5

  • Online ISBN: 978-3-031-31234-2

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