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On the Application of the Asymmetric Convolution Algorithm in Modeling of Full-Availability Group with Bandwidth Reservation

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Managing Traffic Performance in Converged Networks (ITC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 4516))

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Abstract

The paper proposes a new method to calculate the occupancy distribution and the blocking probability in the full-availability group with multi-rate traffic and bandwidth reservation. In the presented method, the occupancy distribution in a group is calculated with the application of the proposed asymmetric convolution operation that takes into consideration the influence of the reservation mechanism upon the probability of passing between the states. The results of the analytical calculations of the blocking probability in the system with bandwidth reservation obtained on the basis of the proposed analytical method are compared to the data obtained on the basis of other known analytical methods and to the results of the simulation.

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References

  1. Staehle, D., Mäder, A.: An analytic approximation of the uplink capacity in a UMTS network with heterogeneous traffic. In: 18th International Teletraffic Congress (ITC18), Berlin, pp. 81–91 (2003)

    Google Scholar 

  2. Głąbowski, M., Stasiak, M., Zwierzykowski, P.: Uplink blocking probability calculation for cellular systems with WCDMA radio interface, finite source population and differently loaded neighbouring cells. In: Proceedings of Asia-Pacific Conference on Communications, Perth, Australia, pp. 138–142 (2005)

    Google Scholar 

  3. Akimuru, H., Kawashima, K.: Teletraffic: Theory and Application. Springer, Heidelberg (1999)

    Google Scholar 

  4. 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 

  5. Ross, K.: Multiservice Loss Models for Broadband Telecommunication Network. Springer, London (1995)

    Google Scholar 

  6. Bziuk, W.: Approximate state probabilities in large shared multirate loss systems with an application to trunk reservation. In: Proceedings of 2nd Polish-German Teletraffic Symposium (9th Polish Teletraffic Symposium), Gdañsk, Poland, pp. 145–152 (2002)

    Google Scholar 

  7. Moscholios, I., Logothetis, M., Kokkinakis, G.: Connection-dependent threshold model: a generalization of the Erlang multiple rate loss model. Journal of Performance Evaluation 48, 177–200 (2002)

    Article  MATH  Google Scholar 

  8. Iversen, V. (ed.): Teletraffic Engineering Handbook. ITU-D, Study Group 2, Question 16/2, Geneva (2003)

    Google Scholar 

  9. Kelly, F.P.: Loss networks. The Annals of Applied Probability 1(3), 319–378 (1991)

    MATH  Google Scholar 

  10. Roberts, J. (ed.): Performance Evaluation and Design of Multiservice Networks, Final Report COST 224. Commission of the European Communities, Brussels, Holland (1992)

    Google Scholar 

  11. Kogan, Y., Shenfild, M.: Asymptotic solution of generalized multiclass Engset model. In: Labetoulle, J., Roberts, J. (eds.) Proceedings of 14th International Teletraffic Congress, Antibes Juan-les-Pins, France, vol. 1b, pp. 1239–1249. Elsevier, Amsterdam (1994)

    Google Scholar 

  12. Choudhury, G., Leung, K., Whitt, W.: An inversion algorithm to compute blocking probabilities in loss networks with state-dependent rates. IEEE/ACM Trans. on Networking 3, 585–601 (1995)

    Article  Google Scholar 

  13. Berezner, S., Krzesinski, A.: An efficient stable recursion to compute multiservice blocking probabilities. Journal of Performance Evaluation 43(2–3), 151–164 (2001)

    Article  MATH  Google Scholar 

  14. Nilson, A., Perry, M.: Multi-rate blocking probabilities: numerically stable computation. In: Ramaswami, V., Wirth, P. (eds.) Proceedings of 15th International Teletraffic Congress, Washington D.C., pp. 1359–1368. USA, Elsevier (1997)

    Google Scholar 

  15. Stamatelos, G., Hayes, J.: Admission-control technics with application to broadband networks. Computer Communication 17(9), 663–673 (1994)

    Article  Google Scholar 

  16. Aein, J.M.: A multi-user-class, blocked-calls-cleared, demand access model. IEEE Transactions on Communications COM-26(3), 378–385 (1978)

    Article  Google Scholar 

  17. Gimpelson, L.: Analysis of mixtures of wide and narrow-band traffic. IEEE Trans. Comm. Technology 13(3), 258–266 (1953)

    Article  Google Scholar 

  18. Beshai, M., Manfield, D.: Multichannel services performance of switching networks. In: Proceedings of 12th International Teletraffic Congress, Torino, Italy, pp. 857–864. Elsevier, Amsterdam (1988)

    Google Scholar 

  19. Stasiak, M.: Blocking probability in a limited-availability group carrying mixture of different multichannel traffic streams. Annales des Télécommunications 48(1-2), 71–76 (1993)

    Google Scholar 

  20. Stasiak, M.: An approximate model of a switching network carrying mixture of different multichannel traffic streams. IEEE Transactions on Communications 41(6), 836–840 (1993)

    Article  MATH  Google Scholar 

  21. Delbrouck, L.: On the steady-state distribution in a service facility carrying mixtures of traffic with different peakedness factors and capacity requirements. IEEE Transactions on Communications 31(11), 1209–1211 (1983)

    Article  Google Scholar 

  22. Fortet, R., Grandjean, C.: Congestion in a loss system when some calls want several devices simultaneously. Electrical Communication 39(4), 513–526 (1964)

    Google Scholar 

  23. Kaufman, J.: Blocking in a shared resource environment. IEEE Transactions on Communications 29(10), 1474–1481 (1981)

    Article  Google Scholar 

  24. Roberts, J.: A service system with heterogeneous user requirements — application to multi-service telecommunications systems. In: Pujolle, G. (ed.) Proceedings of Performance of Data Communications Systems and their Applications, pp. 423–431. North-Holland, Amsterdam (1981)

    Google Scholar 

  25. Iversen, V.B.: The exact evaluation of multi-service loss systems with access control. In: Seventh Nordic Teletraffic Seminar (NTS-7), Lund, Sweden, August 1987, pp. 56–61 (1987)

    Google Scholar 

  26. Roberts, J.W.: Teletraffic models for the Telcom 1 integrated services network. In: Proceedings of 10th International Teletraffic Congress, Montreal, Canada, paper 1.1.2 (1983)

    Google Scholar 

  27. Lindberger, K.: Simple approximations of overflow system quantities for additional demands in the optimisation. In: Proceedings of 10th International Teletraffic Congress, Montreal, Canada, paper 5.3.3 (1983)

    Google Scholar 

  28. Whitt, W.: Blocking when service is required from several facilities simultaneously. Bell System Technical Journal 64(8), 1807–1856 (1985)

    MATH  Google Scholar 

  29. Kawashima, K.: Trunk reservation models in telecommunication systems. Volume Teletraffic Analysis and Computer Performance Evaluation of Studies in Telecommunication. North Holland, Amsterdam (1986)

    Google Scholar 

  30. Lindberger, K.: Blocking for multislot heterogeneous traffic streams offered to a trunk group with reservation. In: Proceedings of the 5th ITC Seminar, Lake Como (1987)

    Google Scholar 

  31. Takagi, K., Sakita, Y.: Analysis of loss probability equalised by trunk reservation for mixtures of several bandwidth traffic. In: Proceedings of 12th International Teletraffic Congress, Torino, Italy, 5.1.A.1, Elsevier, Amsterdam (1988)

    Google Scholar 

  32. Gersht, A., Lee, K.J.: Virtual-circuit load control in fast packet-switched broadband networks. In: Proceedings of IEEE Global Telecommunications Conference (GLOBECOM 1989), Dallas, TX, USA, pp. 214–220 (1989)

    Google Scholar 

  33. Korner, U., Lubacz, J., Pióro, M.: Traffic engineering problems in multiservice circuit switched networks. In: Proceedings of International Teletraffic Congress Specialist Seminar - ITC–12, Adelaide (1989)

    Google Scholar 

  34. Roberts, J.: Traffic control in the B-ISDN. Computer Networks and ISDN Systems 25(10), 1055–1064 (1993)

    Article  Google Scholar 

  35. Tran-Gia, P., Hubner, F.: An analysis of trunk reservation and grade of service balancing mechanisms in multiservice broadband networks. In: IFIP Workshop TC6, La Martinique, vol. Modelling and Performance Evaluation of ATM Technology, paper 2.1 (1993)

    Google Scholar 

  36. Wajda, K.: Estimation of call blocking probabilities in telecommunication networks. Technical Report 93007, Kyoto University, University of Mining and Metallurgy, Kyoto, Kraków (1993)

    Google Scholar 

  37. Ritter, M., Tran-Gia, P.: Multi-rate models for dimesioning and performance evaluation of ATM networks. Technical report, Institue of Computer Science, University of Würzburg (1994)

    Google Scholar 

  38. Głąbowski, M., Kaliszan, A., Stasiak, M.: Blocking probability calculation in a fag with bandwidth reservation. In: Proceedings of the Advanced International Conference on Telecommunications, Guadeloupe (2006)

    Google Scholar 

  39. Głąbowski, M., Kaliszan, A., Stasiak, M.: A new convolution algorithm of blocking probability calculation in full-availability group with bandwidth reservation. In: Proceedings of the Fifth International Symposium on Communication Systems, Networks and Digital Signal Processing, Patras (2006)

    Google Scholar 

  40. Głąbowski, M., Kaliszan, A., Stasiak, M.: Asymmetric convolution algorithm for full-availability group with bandwidth reservation. In: Proceedings of the Asia-Pacific Conference on Communications, Busan, Korea (2006)

    Google Scholar 

  41. Iversen, V.: Teletraffic Engineering Handbook. ITU-D SG 2/16 and ITC Draft (2001)

    Google Scholar 

  42. Stasiak, M., Głąbowski, M., Zwierzykowski, P.: Equalisation of blocking probability in switching systems with limited availability. In: Kouvatsos, D. (ed.) Performance Analysis of ATM Networks, pp. 358–376. Kluwer Academic Publishers, Boston (2000)

    Google Scholar 

  43. Stasiak, M., Głąbowski, M.: A simple approximation of the link model with reservation by a one-dimensional Markov chain. Journal of Performance Evaluation 41(2–3), 195–208 (2000)

    Article  MATH  Google Scholar 

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Lorne Mason Tadeusz Drwiega James Yan

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Głąbowski, M., Kaliszan, A., Stasiak, M. (2007). On the Application of the Asymmetric Convolution Algorithm in Modeling of Full-Availability Group with Bandwidth Reservation. In: Mason, L., Drwiega, T., Yan, J. (eds) Managing Traffic Performance in Converged Networks. ITC 2007. Lecture Notes in Computer Science, vol 4516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72990-7_76

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  • DOI: https://doi.org/10.1007/978-3-540-72990-7_76

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72989-1

  • Online ISBN: 978-3-540-72990-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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