Queuing Model of Wireless Access System

  • Sławomir HanczewskiEmail author
  • Maciej Stasiak
  • Piotr Zwierzykowski
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 521)


The paper presents a new multi-dimensional Erlang’s Ideal Grading (EIG) model with queues and priority that can service a number of call classes with differentiated access to resources. The model was used to determine delays and packet loss probabilities in the wireless access system. The analytical results obtained in the study were then compared with the results of a simulation, which confirmed the essential and required accuracy of the proposed model. The model developed in the study can be used to analyse, design and optimize present-day wireless access system.


EIG Queuing systems Priority 


  1. 1.
    Yin, Z., Yu, F., BU, S., Han, Z.: Joint cloud and wireless networks operations in mobile cloud computing environments with telecom operator cloud. IEEE Trans. Wireless Commun. 99, 1–1 (2015)Google Scholar
  2. 2.
    Martignon, F., Paris, S., Filippini, I., Chen, L., Capone, A.: Efficient and truthful bandwidth allocation in wireless mesh community networks. IEEE/ACM Trans. Netw. 23(1), 161–174 (2015)CrossRefGoogle Scholar
  3. 3.
    Wikisource: Telecommunications act of 1996. (2009) (Online)
  4. 4.
    Stasiak, M., Hanczewski, S.: Approximation for multi-service systems with reservation by systems with limited-availability. In: Computer Performance Engineering, LNCS, vol. 5261, pp. 257–267. Springer (2008)Google Scholar
  5. 5.
    Stasiak, M., Głąbowski, M., Hanczewski, S.: The application of the Erlang’s Ideal Grading for modelling of UMTS cells. In: 8th International Symposium on Communication Systems, Networks Digital Signal Processing (CSNDSP), July 2012, pp. 1–6Google Scholar
  6. 6.
    Hanczewski, S., Stasiak, M., Zwierzykowski, P.: Modelling of the access part of a multi-service mobile network with service priorities. EURASIP J. Wireless Commun. Netw. 2015(1), 1–14 (2015)CrossRefGoogle Scholar
  7. 7.
    Brockmeyer, E.: A survey of A.K. Erlang’s mathematical works. Danish Acad. Tech. Sci. 2, 101–126 (1948)Google Scholar
  8. 8.
    Lotze, A.: History and development of grading theory. In: Proceedings of 5th International Teletraffic Congress, pp. 148–161 (1967)Google Scholar
  9. 9.
    Brockmeyer, E., Halstrom, H., Jensen, A.: The life and works of A.K. Erlang. Acta Polytechnika Scandinavia 6, 287 (1960)Google Scholar
  10. 10.
    Thierer, M.: Delay System with Limited Accessibility. In Prebook of the 5th International Teletraffic Congress, 1967, pp. 203–213Google Scholar
  11. 11.
    Thierer, M.: Delay system with limited availability and constant holding time. In: Prebook of the 6th International Teletraffic Congress, Munich, pp. 322/1–322/6 (1970)Google Scholar
  12. 12.
    Gambe, E.: A study on the efficiency of graded multiple delay systems through artificial traffic trials. In: Proceedings of 3rd International Teletraffic Congress, Paris, doc. 16 (1961)Google Scholar
  13. 13.
    Kühn, P. (1970) Combined delay and loss systems with several input queues, full and limited accessibility. In: Proceedings of 6th International Teletraffic Congress, Munich, pp. 323/1–7 (1970)Google Scholar
  14. 14.
    Kühn, P.: Waiting time distributions in multi-queue delay systems with gradings. In: Proceedings of 7th International Teletraffic Congress, Stockholm, pp. 53–61 (1973)Google Scholar
  15. 15.
    Kampe, G., Kühn, P.: Graded systems with infinite or finite source traffic and exponential or constant holding time. In: Proceedings of 8th International Teletraffic Congress, Melbourne, pp. 251/1–10 (1976)Google Scholar
  16. 16.
    Stasiak, M.: An approximate model of a switching network carrying mixture of different multichannel traffic streams. IEEE Trans. Commun. 41(6), 836–840 (1993)CrossRefzbMATHGoogle Scholar
  17. 17.
    Hanczewski, S., Stasiak, M.: Performance modelling of Video-on-Demand systems. In: 17th Asia-Pacific Conference on Communications (APCC), pp. 784–788 (2011)Google Scholar
  18. 18.
    Głąbowski, M., Hanczewski, S., Stasiak, M.: Erlang’s Ideal Grading in Diffserv modelling. In: AFRICON, 2011, pp. 1–6 (2011)Google Scholar
  19. 19.
    Głąbowski, M., Hanczewski, S., Stasiak, M.: Modelling of Cellular Networks with Traffic Overflow. Mathematical Problems in Engineering, Article ID 286490 (2015)Google Scholar
  20. 20.
    Hanczewski, S., Stasiak, M., Weissenberg, J., Zwierzykowski, P.: Queuing model of the access system in the packet network. In: Computer Networks, ser. Communications in Computer and Information Science. Springer, vol. accepted for publication (2016)Google Scholar
  21. 21.
    Katzschner, L., Scheller, R.: Probability of loss of data traffics with different bit rates hunting one common PCM-channel, pp. 525/1–8 (1976)Google Scholar
  22. 22.
    Stasiak, M., Wiewióra, J., Zwierzykowski, P., Parniewicz, D.: An approximate model of the WCDMA interface servicing a mixture of multi-rate traffic streams with priorities. In: Thomas, N., Juiz, C. (eds.) 5th European Performance Engineering Workshop, vol. 5261, pp. 168–180 (2008)Google Scholar
  23. 23.
    Głąbowski, M., Hanczewski, S., Stasiak, M., Weissenberg, J.: Modeling Erlang’s Ideal Grading with Multirate BPP traffic. Mathematical Problems in Engineering, Article ID 456910 (2012)Google Scholar
  24. 24.
    Roberts, J. (ed.): Performance evaluation and design of multiservice networks. Final Report COST 224. Commission of the European Communities, Brussels (1992)Google Scholar
  25. 25.
    Little, J.: A proof for the queueing formula: L = w. Oper. Res. 9(3), 383–387 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Chydziński, A., Adamczyk, B.: Analysis of a scheduler for virtualization of links with performance isolation. Appl. Math. Inf. Sci. 8(6), 2653–2666 (2014)CrossRefGoogle Scholar
  27. 27.
    Chydziński, A.: Delay analysis for an AQM queue with dropping function. In: Proceedings of the 11th WSEAS International Conference on Data Networks, Communications and Computers. World Scientific and Engineering Academy and Society, September 2012, pp. 53–57Google Scholar
  28. 28.
    Domański, A., Domańska, J., Czachórski, T.: Comparison of aqm control systems with the use of fluid flow approximation. In: Computer Networks, ser. Communications in Computer and Information Science, vol. 291, pp. 82–90. Springer (2012)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Sławomir Hanczewski
    • 1
    Email author
  • Maciej Stasiak
    • 1
  • Piotr Zwierzykowski
    • 1
  1. 1.Faculty of Electronics and TelecommunicationsPoznan University of TechnologyPoznańPoland

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