Abstract
Classical Erlang and Engset formulae determining the availability of channels, loss probability, and characteristics of overflow traffic are still used in telecommunications. Moreover, they are also interesting for traffic management in mobile networks and in Internet. They are based on the assumption of Poisson flows and exponentially distributed time of connections. By means of diffusion approximation queuing models, we extend these results to the case of general distributions and transient state analysis.
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References
T.O. Engset, Die Wahrscheinlichkeitsrechnung zur Bestimmung der Whlerzahl in automatischen Fernsprechmtern. Elektrotechnische Zeitschrift, Heft 31, (1918)
A.K. Erlang, The theory of probabilities and telephone conversations. Nyt Tidsskrift Matematik, no. B 20, 33–39 (1909)
A.K. Erlang, Solutions of some problems in the theory of probabilities of significance in automatic telephone exchnges. Electroteknikeren 13, 5–13 (1917)
L. Kleinrock, Queueing Systems, vol. II (Wiley, New York, 1976)
R.I. Wilkinson, Teories of toll traffic engineering in the USA. Bell Syst. Tech. J. 40, 421–514 (1956)
C. McArdle, D. Tafani, L. P. Barry, Overflow Traffic Moments in Channel Groups with Bernoulli-Poisson-Pascal (BPP) Load. in: Proceedings of the IEEE International Conference on Communications (IEEE ICC 2013), pp. 2403-2408, Budapest, Hungary, (2013)
M. Stasiak, M. Gabowski, A. Wisniewski, P. Zwierzykowski, Modelling and dimensioning of mobile networks, from GSM to LTE, Wiley (2011)
T. Bonald, J. Roberts, Internet and the Erlang formula. ACM SIGCOMM Comput. Commun. Rev. 42(1), 25–30 (2012)
E. Chromy, J. Suran, M. Kovacik, M. Kavacky, Usage of Erlang formula in IP networks. Commun. Netw. 3, 161–167 (2011)
J.W. Roberts, Traffic theory and the internet. IEEE Commun. Mag. 39(1), 94–99 (2001)
J. Kaufman, Blocking in a shared resource environment. IEEE Trans. Commun. COM–29(10), 1474–1481 (1981)
J. W. Roberts, A service system with heterogenous user requirements—application to multi-service telecommunications systems, in: Proceedings of the Performance of Data Communicatons Systems and their Applications, ed. by G. Pujolle. Amsterdam, North Holland, pp. 423–431, (1981)
M. Glabowski, A. Kaliszan, M. Stasiak, Modeling product form state dependent systems with BPP traffic. J. Perform. Eval. 67(3), 174–190 (2010)
E. Gelenbe, On approximate computer systems models. J. ACM 22(2), 261–269 (1975)
E. Gelenbe, G. Pujolle, The behaviour of a single queue in a general queueing network. Acta Informatica 7, 123–136 (1976). Fasc. 2
R.P. Cox, H.D. Miller, The Theory of Stochastic Processes (Chapman and Hall, London, 1965)
H. Stehfest, Algorithm 368: numeric inversion of laplace transform. Comm. ACM 13(1), 47–49 (1970)
T. Czachorski, J.-M. Fourneau, T. Nycz, F. Pekergin, Diffusion approximation model of multiserver stations with losses. Electron. Notes Theor. Comput. Sci. 232, 125143 (2009)
Acknowledgments
This work was supported by Polish project NCN nr 4796/B/T02/2011/40 ‘Models for transmissions dynamics, congestion control and quality of service in Internet’ and the European Union from the European Social Fund (grant agreement number: UDA-POKL.04.01.01-00-106/09).
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Czachórski, T., Nycz, T., Nycz, M., Pekergin, F. (2014). Traffic Engineering: Erlang and Engset Models Revisited with Diffusion Approximation. In: Czachórski, T., Gelenbe, E., Lent, R. (eds) Information Sciences and Systems 2014. Springer, Cham. https://doi.org/10.1007/978-3-319-09465-6_26
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DOI: https://doi.org/10.1007/978-3-319-09465-6_26
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