Properties of the Multiservice Erlang's Ideal Gradings

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DOI:

https://doi.org/10.26636/jtit.2016.1.702

Keywords:

Erlang’s Ideal Grading, multiservice systems, traffic engineering

Abstract

The design and optimization process of modern telecommunications networks is supported by a range of appropriate analytical models. A number of these models are based on the Erlang’s Ideal Grading (EIG) model, which is a particular case of non-full-availability groups. A possibility of the application of the EIG model results from the fact that telecommunications systems show properties and features distinctive to non-full-availability systems. No detailed studies that would decisively help determine appropriate conditions for the application of the EIG model for modeling of other non-full-availability groups, that would be models corresponding to real telecommunications systems, have been performed. Therefore, this article attempts to find an answer to the following question: what are the prerequisite conditions for the application of the EIG model and when the model can be reliably used?

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References

[1] “Ericsson Mobility Report”, Tech. Rep., Ericsson, 2014.
View in Google Scholar

[2] “Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update 2014–2019 – White Paper”, Tech. Rep., Cisco, 2015.
View in Google Scholar

[3] J. Roberts, “Teletraffic models for the Telecom 1 integrated services network”, in Proc. 10th Int. Teletraff. Congr. ITC 83, Montreal, Canada, 1983, p. 1.1.2.
View in Google Scholar

[4] P. Tran-Gia and F. Hübner, “An analysis of trunk reservation and grade of service balancing mechanisms in multiservice broadband networks”, in Modelling and Evaluation of ATM Networks, H. G. Perros, G. Pujolle, and Y. Takahashi, Eds., IFIP Trans., vol. C-15, pp. 83–97. Amsterdam: North-Holland, 1993.
View in Google Scholar

[5] M. Stasiak and S. Hanczewski, “Approximation for multi-service systems with reservation by systems with limited-availability”, in 5th European Performance Engineering Workshop, N. Thomas and C. Juiz, Eds., LNCS, vol. 5261, pp. 257–267. Palma de Mallorca, Spain: Springer, 2008.
View in Google Scholar

[6] M. Głąbowski, A. Kaliszan, and M. Stasiak, “Modeling product-form state-dependent systems with BPP traffic”, J. Perform. Eval., vol. 67, no. 3, pp. 174–197, 2010.
View in Google Scholar

[7] I. D. Moscholios, J. S. Vardakas, M. D. Logothetis, and A. C. Boucouvalas, “Congestion probabilities in a batched Poisson multi-rate loss model supporting elastic and adaptive traffic”, Annales des Télécommun., vol. 68, no. 5–6, pp. 327–344, 2013.
View in Google Scholar

[8] J. Kaufman, “Blocking with retrials in a completely shared resource environment”, J. Perform. Eval., vol. 15, no. 2, pp. 99–113, 1992.
View in Google Scholar

[9] S. Rácz, B. P. Gerö, and G. Fodor, “Flow level performance analysis of a multi-service system supporting elastic and adaptive services”, Perform. Eval., vol. 49, no. 1–4, pp. 451–469, 2002.
View in Google Scholar

[10] M. Sobieraj, M. Stasiak, J. Weissenberg, and P. Zwierzykowski, “Analytical model of the single threshold mechanism with hysteresis for multi-service networks”, IEICE Trans. Commun., vol. E95-B, no. 1, pp. 120–132, 2012.
View in Google Scholar

[11] I. Moscholios, M. Logothetis, and G. Kokkinakis, “Connection-dependent threshold model: a generalization of the Erlang multiple rate loss model”, Perform. Eval., vol. 48, no. 1–4, pp. 177–200, 2002.
View in Google Scholar

[12] M. Stasiak, M. Głąbowski, A. Wiśniewski, and P. Zwierzykowski, Modeling and Dimensioning of Mobile Networks. Wiley, 2011.
View in Google Scholar

[13] M. Stasiak, P. Zwierzykowski, J. Wiewióra, and D. Parniewicz, “An approximate model of the WCDMA interface servicing a mixture of multi-rate traffic streams with priorities”, in Computer Performance Engineering, D. Parniewicz, M. Stasiak, J. Wiewióra, and P. Zwierzykowski, Eds. LNCS, vol. 5261, pp. 168–180. Springer, 2008 (doi: 10.1007/978-3-540-87412).
View in Google Scholar

[14] L. Katzschner and R. Scheller, “Probability of loss of data traffics with different bit rates hunting one common PCM-channel”, in Proc. 8th Int. Teletraff. Congr., Melbourne, Australia, 1976, pp. 525/1–8.
View in Google Scholar

[15] K. Subramaniam and A. A. Nilsson, “An analytical model for adaptive call admission control scheme in a heterogeneous UMTS-WCDMA system”, in Proc. IEEE Int. Conf. Commun. ICC 2005, Seoul, South Korea, 2005, vol. 5, pp. 3334–3338.
View in Google Scholar

[16] A. Fredericks, “Congestion in blocking systems – a simple approximation technique”, Bell System Tech. J., vol. 59, no. 6, pp. 805–827, 1980.
View in Google Scholar

[17] M. Głąbowski, K. Kubasik, and M. Stasiak, “Modeling of systems with overflow multi-rate traffic”, Telecommun. Syst., vol. 37, no. 1–3, pp. 85–96, 2008.
View in Google Scholar

[18] M. Głąbowski, S. Hanczewski, and M. Stasiak, “Erlang’s ideal grading in diffserv modelling”, in Proc. IEEE Africon 2011, Livingstone, Zambia, 2011, pp. 1–6.
View in Google Scholar

[19] M. Głąbowski, A. Kaliszan, and M. Stasiak, “Two-dimensional convolution algorithm for modelling multiservice networks with overflow traffic”, Mathem. Problems in Engin., vol. 2013, p. 18, 2013 (article ID 852082).
View in Google Scholar

[20] J. Kaufman, “Blocking in a shared resource environment”, IEEE Trans. Commun., vol. 29, no. 10, pp. 1474–1481, 1981.
View in Google Scholar

[21] J. Roberts, “A service system with heterogeneous user requirements – application to multi-service telecommunications systems”, in Performance of Data Communications Systems and their Applications, G. Pujolle, Ed. Amsterdam: North-Holland, 1981, pp. 423–431.
View in Google Scholar

[22] M. Stasiak, “Blocking probability in a limited-availability group carrying mixture of different multichannel traffic streams”, Annales des Télécommun., vol. 48, no. 1–2, pp. 71–76, 1993.
View in Google Scholar

[23] E. Brockmeyer, H. L. Halstrøm, and A. Jensen, “The life and works of A. K. Erlang”, Acta Polytechnica Scandinavica, vol. 6, no. 287, 1960.
View in Google Scholar

[24] V. Eršov, “Rasčët komutacionnych sistem metodom rasdel’nyh poter’”, in Sistemy massovogo obsluživaniâ i kommutacii, Moscow: Nauka, 1974, pp. 54–66 (in Russian).
View in Google Scholar

[25] V. Eršov, “Srednââ dostupnost’ i rekurrentnyj rasčët poter’ v kommutacionnych sistemah”, in Sistemy upravleniâ setâmi, Moscow: Nauka, 1980, pp. 121–126 (in Russian).
View in Google Scholar

[26] M. Stasiak, “An approximate model of a switching network carrying mixture of different multichannel traffic streams”, IEEE Trans. Commun., vol. 41, no. 6, pp. 836–840, 1993.
View in Google Scholar

[27] M. Stasiak and S. Hanczewski, “A model of WCDMA radio interface with reservation”, in Proc. Int. Symp. Inform. Theory and Its Appl. ISITA 2008, Auckland, New Zealand, 2008.
View in Google Scholar

[28] S. Hanczewski and M. Stasiak, “Performance modelling of video-on-demand systems”, in Proc. 17th Asia-Pacific Conf. Commun. APCC 2011, Kuala Lumpur, Malaysia, 2011, pp. 784–788.
View in Google Scholar

[29] M. Głąbowski, S. Hanczewski, and M. Stasiak, “Modelling of cellular networks with traffic overflow”, Mathem. Problems in Engin., vol. 2015, p. 158, 2015 (article ID 286490).
View in Google Scholar

[30] Broadband Network Teletraffic, Final Report of Action COST 242, J. Roberts, V. Mocci, and J. Virtamo, Eds. Berlin: Springer, 1996.
View in Google Scholar

[31] M. Stasiak, M. Głąbowski, and S. Hanczewski, “The application of the Erlang’s Ideal Grading for modelling of UMTS cells”, in 8th Int. Symp. Commun. Syst., Netw. Digit. Sig. Process. CSNDSP 2012, Poznan, Poland, 2012, pp. 1–6.
View in Google Scholar

[32] A. Jajszczyk, Wstęp do Telekomutacji. Wydawnictwa Naukowo-Techniczne, 1998 (in Polish).
View in Google Scholar

[33] M. Głąbowski, S. Hanczewski, M. Stasiak, and J. Weissenberg, “Modeling Erlang’s Ideal Grading with multi-rate BPP traffic”, Mathem. Problems in Engin., vol. 2012, p. 35, 2012 (article ID 456910).
View in Google Scholar

[34] J. Tyszer, Object-Oriented Computer Simulation of Discrete-Event Systems. Kluwer, 1999.
View in Google Scholar

[35] S. Hanczewski and M. Stasiak, “Point-to-group blocking in 3-stage switching networks with multicast traffic streams”, in Proceedings of First International Workshop (SAPIR 2004), P. Dini, P. Lorenz, and J. N. de Souza, Eds. LNCS, vol. 3126, pp. 219–230. Springer, 2004.
View in Google Scholar

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Submitted

2023-06-22

Published

2016-03-30

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How to Cite

[1]
S. Hanczewski and D. Kmiecik, “Properties of the Multiservice Erlang’s Ideal Gradings”, JTIT, vol. 63, no. 1, pp. 37–43, Mar. 2016, doi: 10.26636/jtit.2016.1.702.

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