Skip to main content

On a numerical method for calculating stationary characteristics of the switching node with retrial transmissions

Abstract

The model is considered of the switching node of packages with a limited buffer storage and retrials of transmissions, which is represented in the form of a multiflow queueing system. Results are presented for the investigation of an iteration method and an algorithm of its realization for calculating the stationary characteristics of the model node. The necessary and sufficient conditions for the realizability of the input primary flow in the system are obtained, in which the total input flows are Poisson ones, and the convergence of the algorithm for estimating the characteristics is proved.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Artalejo, J.R., Accessible Bibliography on Retrial Queues, Math. Comput. Model., 1999, no. 30, pp. 223–233.

  2. 2.

    Bocharov, P.P., Pechinkin, A.V., and Phong, N.H., Stationary Probabilities of the States of the MAP/G/1/r Retrial System with Priority Servicing of Primary Customers, Autom. Remote Control, 2000, no. 8, pp. 1300–1309.

  3. 3.

    Atencia, I.M., Bocharov, P.P., D’Apice, C., and Phong, N.H., A Single-Server Retrial Queue System with the Multidimensional Poisson Flow, Autom. Remote Control, 2000, no. 11, pp. 1871–1884.

  4. 4.

    Klimenok, V.I. and Kim, C.S., BMAP/PH/1 Retrial System Operating in Random Environment, Proc. 5 St.-Petersburg Workshop Simulat., St.-Petersburg: NII Chemistry St.-Petersburg Univ., 2005, pp. 367–372.

    Google Scholar 

  5. 5.

    Krishnamoorthy, A. and Babu, S., MAP/(PH,PH)/c Retrial Queue with Self-Generation of Priorities and Nonpreemptive Service, Proc. 14 Int. Conf. Analyt. Stochast. Model. Techn. Appl., 4–6 June 2007, Prague, Sbr.-Dudweiler: Digitaldruck Pirrot GmbH, 2007, pp. 70–74.

    Google Scholar 

  6. 6.

    D’Apice, C., De Simone, T., Manzo, R., and Rizelian, G., M/G/1/r Retrial Queueing System with Priority Service of Primary Customers and a Customer—Searching Server, in Distributed Computer and Communication Networks. Stochastic Modeling and Optimization, Moscow: Technosphera, 2003, pp. 106–117.

    Google Scholar 

  7. 7.

    Mushko, V.V., System MAP/M/c with Address Strategy of Retrial Calls and Identical Devices, Comput. Model. New Technol., 2005, vol. 9, no. 2, pp. 33–40.

    MathSciNet  Google Scholar 

  8. 8.

    Shin, Y.W. and Moon, D.H., An Algorithmic Solution for the Stationary Distribution of M/M/c/K Retrial Queue, 6 Int. Symp. Oper. Res. Its Appl. (ISORA’06), Xinjiang, China, 2006, pp. 8–12.

  9. 9.

    Shin, Y.W. and Moon, D.H., Retrial Queues with Limited Number of Retrials: Numerical Investigations, 7 Int. Symp. Oper. Res. and Its Appl. (ISORA’08), Lijiang, China, 2008, pp. 237–247.

  10. 10.

    Kuznetspv, O.I., Link of the Multiservice Communication Network with Retrial Calls, Elektrosvyaz’, 2006, no. 9, pp. 43–46.

  11. 11.

    Stepanov, S.N., Chislennye metody rascheta system s povtornymi vyzovami (Numerical Methods of Calculation of Systems with Retrial Calls), Moscow: Nauka, 1983.

    Google Scholar 

  12. 12.

    Stepanov, S.N., Optimization of Numerical Calculation of Characteristics of Multiflow Models with Retrials, Probl. Peredachi Inf., 1989, vol. 25, no. 2, pp. 67–78.

    Google Scholar 

  13. 13.

    Basharin, G.P., Bocharov, P.P., and Kogan, Ya.A., Analiz ocheredei v vychislitel’nykh setyakh (Analysis of Queues in Computational Networks), Moscow: Nauka, 1989.

    Google Scholar 

  14. 14.

    Vishnevskii, V.M., Teoreticheskie osnovy proektirovaniya komp’yuternykh setei (Theoretical Bases of Design of Computer Networks), Moscow: Tekhnosphera, 2003.

    Google Scholar 

  15. 15.

    Agalarov, Ya.M., The Approximate Method for Calculating Characteristics of the Node of the Telecommunication Network with Retrial Transmissions, Informat. Primen., 2009, vol. 3, no. 2, pp. 2–10.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ya. M. Agalarov.

Additional information

Original Russian Text © Ya.M. Agalarov, 2011, published in Avtomatika i Telemekhanika, 2011, No. 1, pp. 95–106.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Agalarov, Y.M. On a numerical method for calculating stationary characteristics of the switching node with retrial transmissions. Autom Remote Control 72, 88–98 (2011). https://doi.org/10.1134/S0005117911010073

Download citation

Keywords

  • Remote Control
  • Stationary Characteristic
  • Queue System
  • Retrial Queue
  • Labor Intensity