Point-to-Point and Point-to-Group blocking probability in multi-service switching networks with BPP traffic

• Autorzy: Głąbowski M.
• Języki publikacji: EN

Abstrakty

EN

This paper presents three approximate calculation methods of occupancy distribution and blocking probability in switching networks which are offered multi-service traffic streams generated by Binomial (Engset) & Poisson (Erlang) & Pascal traffic sources. The proposed methods belong to the class of methods known as the effective availability methods. The basis of the proposed calculation algorithms is the occupancy distribution in interstage links as well as in the outgoing links (forming outgoing directions). These distributions are calculated with the help of the full-availability group model and the limited-availability group model. The results of analytical calculations of the blocking probabilities are compared with the simulation results of three-stage switching networks, and, therefore, the validity of the assumptions used in the model is proved.

Słowa kluczowe

EN

BPP traffic; switching networks; blocking probability

PL

przełączanie sieci; blokowanie prawdopodobieństwa

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: Electronics and Telecommunications Quarterly
• Rocznik: 2007
• Tom: Vol. 53, No 4
• Strony: 339--360
• Opis fizyczny: Bibliogr. 33 poz., rys., wykr.

Twórcy

autor

Głąbowski M.

• Chair of Communications and Computer Networks, Poznań University of Technology, ul. Polanka 3, 60-965 Poznań, Poland,

Bibliografia

• 1. H. Akimuru, K. Kawashima: Teletraffic: Theory and Application. Springer, Berlin-Heidelberg New York, 1999.
• 2. J. W. Roberts, V. Mocci, I. Virtamo, editors: Broadband Network Tele-traffic, Finał Report of Action COST 242. Commission of the European Communities, Springer, Berlin, 1996.
• 3. K. W. Ross: Multisewice Loss Models for Broadband Telecommunication Network. Springer, London, 1995.
• 4. W. Bziuk: Approximate state probabilities in large shared multi-rate loss systems with an application to trunk reservation. 2nd Polish-German Teletraffic Symposium, pp. 145-152, Gdańsk, Poland, 2002.
• 5. D. Moscholios, M. D. Logothetis, G. K. Kokkinakis: Connection-dependent threshold model: a generalization of the Erlang multiple rate loss model. J. Perf. Eval, Vol. 48, No. 1-4, pp. 177-200, 2002.
• 6. V. B. Iversen, editor: Teletraffic Engineering Handbook. ITU-D, Study Group 2, Question 16/2, Geneva, December 2003.
• 7. J. W. Roberts, editor: Performance Evaluation and Design of Multiservice Networks, Final Report COST 224. Commission of the European Communities, Brussels, 1992.
• 8. J. Conradt, A. Buchheister: Considerations on loss probability of multi-slot connections. 11th Int. Teletraffic Congress, paper. 4.4B-2.1, Kyoto, 1985.
• 9. M. E. Beshai, D. R. Manifield: Multichannel services performance of switching networks. 12th Int. Teletraffic Congress, pp. 857-864, Torino, 1988.
• 10. M. Stasiak: Combinatorial considerations for switching systems carrying multi-channel traffic streams. Annales des Telecommunications, vol. 51, No. 11-12, pp. 611-625, 1996.
• 11. M. Stasiak, M. Głąbowski: PPBMR method of blocking probability calcu-lation in switching networks with reservation. GLOBECOM 1999, Vol.la, pp. 32-36, Rio de Janeiro, 1999.
• 12. M. Stasiak, M. Głąbowski: Point-to-point blocking probability in switching networks with reservation. 16th Int. Teletraffic Congress, vol. 3A, pp. 519-528, Edinburgh, 1999.
• 13. M. Głąbowski, M. Stasiak: Point-to-point blocking probability in switching networks with reservation. Annales des Telecommunications, vol. 57, No. 7-8, pp. 798-831, 2002.
• 14. M. Stasiak, M. Głąbowski: Multi-service switching networks with point-to-group selection and several attempts of setting up a connection. 1st Int. Working Conference on Performance Modelling and Evaluation of Heterogeneous Networks, pp. 1/1-1/12, Ilkley, 2003.
• 15. V. B. Iversen: The exact evaluation of multi-service loss systems with access control. In Seventh Nordic Teletraffic Seminar, pp. 56-61, Lund, 1987.
• 16. J. S. Kaufman: Blocking in a shared resource environment. IEEE Transactions on Communications, Vol. 29, No. 10, pp. 1474-1481, 1981.
• 17. J. W. Roberts: A service system, with heterogeneous user requirements - application to multi-service telecommunications systems. Performance of Data Communications Systems and their Applications, pp. 423-431, Amsterdam, 1981.
• 18. A. Lotze, A. Roder, G. Thierer: PPL - a reliable method for the calculation of point-to-point loss in link systems. 8th Int. Teletraffic Congress, pp. 547/1-44, Melbourne, 1976.
• 19. E. B. Ershova, V. A. Ershov: Digital Systems for Information Distribution. Radio and Communications, Moscow, 1983. in Russian.
• 20. M. Stasiak: Blocage interne point a point dans les reseaux de connexion. Annales des Telecommunications, vol. 43, No. 9-10, pp. 561-575, 1988.
• 21. Y. Kogan, M. Shenfild: Asymptotic solution of generalized multiclass Engset model. 14th Int. Teletraffic Congress, volume 1b, pp. 1239-1249, Antibes Juan-les-Pins, 1994.
• 22. G. L. Choudhury, K. K. Leung, W. Whitt: An inversion algorithm to compute blocking probabilities in loss networks with state-dependent rates. IEEE/ACM Trans. Networking, Vol. 3, No. 5, pp. 585-601, 1995.
• 23. S. A. Berezner, A. E. Krzesinski: An efficient stable recursion to compute multiservice blocking probabilities. J. Perf. Eval., Vol. 43, No. 2-3, pp. 151-164, 2001.
• 24. G. M. Stamatelos, J. F. Hayes: Admission-control technics with application to broadband networks. Computer Communication, Vol. 17, No. 9, pp. 663-673, 1994.
• 25. D. P. Heyman, T. V. Lakshman, A. L. Neidhart: A new method for analyzing feedback based protocols with applications to engineering Web traffic over the Internet. Computer Communications, Vol. 26, No. 8, pp. 785-803, 2003.
• 26. M. Ermel, et al.: Performance of GSM networks with general packet radio services. J. Perf. Eval., Vol. 48, No. 1-4, pp. 285-310, 2002.
• 27. M. Głąbowski: Blocking probability in multi-service switching networks with finite source population. The 14th IEEE Int. Conference On Telecommunications, Penang, 2007.
• 28. M. Głąbowski: Point-to-Point Blocking Probability Calculation in Multi-service Switching Networks with BPP Traffic. The 14th Polish Teletraffic Symposium, Zakopane, September 2007, pp. 65-76.
• 29. M. Stasiak, M. Głąbowski: A simple approximation of the link model with reservation by a one-dimensional Markov chain. J. Perf. Eval., Vol. 41, No. 2-3, pp. 195-208, 2000.
• 30. A. Lotze, A. Roder, G. Thierer: Point-to-point selection versus point-to-group selection in link systems. 8th Int. Teletraffic Congress, pp. 541/1-5, Melbourne, 1976.
• 31. C. Lee: Analysis of switching networks. BSTJ, Vol. 34, No. 6, 1955.
• 32. A. Lotze: Loss formula, artificial traffic check and quality standards for characterizing one stage gradings. 3th Int. Teletraffic Congress, paper 28, Paris, 1961.
• 33. A. D. Charkiewicz: An approximate method for calculating the number of junctions in a crossbar system exchange. Elektrosvyaz, No. 2, pp. 55-63, 1959.