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A Model of Erlang’s Ideal Grading with Multi-service Traffic Sources

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 522))

Abstract

The paper, Maciej presents a new model of Erlang’s Ideal Grading with multi-service traffic sources. Traffic sources of this kind correspond better with actual devices utilized by network users. As the proposed model is an approximate one, the results obtained with its help have been compared to the results of a computer simulation. The comparison has confirmed the correctness of the model’s theoretical assumptions. The new model may successfully be used for modeling modern communication systems.

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Notes

  1. 1.

    The allocation unit (AU) defines a certain, and basic for a given system, bit rate expressed in bps [26]. Back in Erlang times [13] the equivalent to AU was a link with the capacity that would make a transmission of one call (voice service) possible.

References

  1. Kaufman, J.: Blocking in a shared resource environment. IEEE Trans. Commun. 29(10), 1474–1481 (1981)

    Article  Google Scholar 

  2. Roberts, J.: A service system with heterogeneous user requirements - application to multi-service telecommunications systems. In: Performance of Data Communications Systems and their Applications, pp. 423–431 (1981)

    Google Scholar 

  3. Głąbowski, M., Stasiak, M.: Point-to-point blocking probability in switching networks with reservation. Annales Des Télécommunications 57(7–8), 798–831 (2002)

    Google Scholar 

  4. Stasiak, M., Wiewióra, J., Zwierzykowski, P., Parniewicz, D.: Analytical model of traffic compression in the UMTS network. In: Bradley, J.T. (ed.) EPEW 2009. LNCS, vol. 5652, pp. 79–93. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Głąbowski, M., Sobieraj, M.: Modelling of network nodes with threshold mechanisms and multi-service sources. In: 16th International Telecommunications Network Strategy and Planning Symposium, pp. 1–7 (2014)

    Google Scholar 

  6. Stasiak, M., Sobieraj, M., Weissenberg, J., Zwierzykowski, P.: Analytical model of the single threshold mechanism with hysteresis for multi-service networks. IEICE Trans. Commun. E95–B(1), 120–132 (2012)

    Google Scholar 

  7. Sobieraj, M., Stasiak, M., Zwierzykowski, P.: Model of the threshold mechanism with double hysteresis for multi-service networks. In: Kwiecień, A., Gaj, P., Stera, P. (eds.) CN 2012. CCIS, vol. 291, pp. 299–313. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  8. Głąbowski, M., Sobieraj, M., Stasiak, M.: Modelling limited-availability groups with BPP traffic and bandwidth reservation. In: 5th Advanced International Conference on Telecommunications, pp. 89–94 (2009)

    Google Scholar 

  9. Głąbowski, M., Sobieraj, M., Stasiak, M.: A full-availability group model with multi-service sources and threshold mechanisms. In: 8th International Symposium on Communication Systems. Networks Digital Signal Processing, pp. 1–5 (2012)

    Google Scholar 

  10. Hanczewski, S., Stasiak, M., Weissenberg, J.: A queueing model of a multi-service system with state-dependent distribution of resources for each class of calls. IEICE Trans. Commun. E97–B(8), 1592–1605 (2014)

    Article  Google Scholar 

  11. Kaliszan, A., Głąbowski, M., Stasiak, M.: Generalised convolution algorithm for modelling state-dependent systems. Circuits, Devices Syst. IET 8(5), 378–386 (2014)

    Article  Google Scholar 

  12. Moscholios, I., Vardakas, J., Logothetis, M., Boucouvalas, A.: Congestion probabilities in a batched poisson multirate loss model supporting elastic and adaptive traffic. Annales Des Télécommunications 68(5–6), 327–344 (2013)

    Article  Google Scholar 

  13. Brockmeyer, E., Halstrøm, H.L., Jensen, A.: The life and works of A.K. Erlang. In: Transactions of the Danish Academy of Technical Sciences, no. 2. Copenhagen Telephone Comany (1948)

    Google Scholar 

  14. Lotze, A.: History and development of grading theory. In: 5th International Teletraffic Congress, pp. 148–161 (1967)

    Google Scholar 

  15. Palm, C.: Nagra foljdsatser urde Erlang’ska formlerna. Tekniska meddelanden frün Kungliga Telegrafstyrdsen (1–3) (1943)

    Google Scholar 

  16. Ershova, E., Ershov, V.: Digital Systems for Information Distribution. Radio and Communications, Moscow (1983). [in Russian]

    Google Scholar 

  17. Stasiak, M.: Blocage interne point a point dans les reseaux de connexion. Annales Des Télécommunications 43(9–10), 561–575 (1988)

    Google Scholar 

  18. Hanczewski, S., Stasiak, M.: Point-to-group blocking in 3-stage switching networks with multicast traffic streams. In: Dini, P., Lorenz, P., Souza, J.N. (eds.) SAPIR 2004. LNCS, vol. 3126, pp. 219–230. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  19. Stasiak, M.: An approximate model of a switching network carrying mixture of different multichannel traffic streams. IEEE Trans. Commun. 41(6), 836–840 (1993)

    Article  MATH  Google Scholar 

  20. Głąbowski, M., Hanczewski, S., Stasiak, M., Weissenberg, J.: Modeling Erlang’s ideal grading with multirate BPP traffic. Math. Probl. Eng. 2012, 35 (2012). Article ID 456910

    Google Scholar 

  21. Stasiak, M., Hanczewski, S.: Approximation for multi-service systems with reservation by systems with limited-availability. In: Thomas, N., Juiz, C. (eds.) EPEW 2008. LNCS, vol. 5261, pp. 257–267. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  22. 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, pp. 1–6 (2012)

    Google Scholar 

  23. Hanczewski, S., Stasiak, M.: Performance modelling of video-on-demand systems. In: 17th Asia-Pacific Conference on Communications, pp. 784–788 (2011)

    Google Scholar 

  24. Głąbowski, M., Hanczewski, S., Stasiak, M.: Erlang’s ideal grading in DiffServ modelling. IEEE Africon 2011, 1–6 (2011)

    Google Scholar 

  25. Głąbowski, M., Hanczewski, S., Stasiak, M.: Modelling of cellular networks with traffic overflow. Math. Probl. Eng. 2015, 15 (2015). Artical ID 286490

    Google Scholar 

  26. Roberts, J., Mocci, V., Virtamo, I. (eds.): Broadband Network Teletraffic, Final Report of Action COST 242. Commission of the European Communities. Springer, Berlin (1996)

    Google Scholar 

  27. Głąbowski, M., Sobieraj, M., Stasiak, M.: Blocking probability calculation in UMTS networks with bandwidth reservation, handoff mechanism and finite source population. In: International Symposium on Communications and Information Technologies, pp. 433–438 (2007)

    Google Scholar 

  28. Głąbowski, M., Sobieraj, M., Stasiak, M.: Analytical modelling of multi-service systems with multi-service BBP traffic sources. In: 2nd European Teletraffic Seminar, pp. 1–6 (2013)

    Google Scholar 

  29. Głąbowski, M., Kaliszan, A., Stasiak, M.: Modeling product-form state-dependent systems with BPP traffic. Perform. Eval. 67(3), 174–197 (2010)

    Article  Google Scholar 

  30. Głąbowski, M.: Modelling of state-dependent multirate systems carrying BPP traffic. Annales des Télécommunications 63(7–8), 393–407 (2008)

    Article  Google Scholar 

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Acknowledgements

The presented work has been funded by the Polish Ministry of Science and Higher Education within the status activity task “Struktura, analiza i projektowanie nowoczesnych systemów komutacyjnych i sieci telekomunikacyjnych” in 2015.

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Correspondence to Sławomir Hanczewski .

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Hanczewski, S., Sobieraj, M., Weissenberg, J. (2015). A Model of Erlang’s Ideal Grading with Multi-service Traffic Sources. In: Gaj, P., Kwiecień, A., Stera, P. (eds) Computer Networks. CN 2015. Communications in Computer and Information Science, vol 522. Springer, Cham. https://doi.org/10.1007/978-3-319-19419-6_30

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  • DOI: https://doi.org/10.1007/978-3-319-19419-6_30

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