access icon free Generalised convolution algorithm for modelling state-dependent systems

This study proposes a new method for calculations of the blocking probability in multiservice state-dependent systems. In the method proposed in this study the occupancy distribution is determined on the basis of an appropriately modified convolution operation. This operation is of a universal applicability and provides an opportunity to model approximately any state-dependent systems. The results of the calculations were compared with the results of the simulation experiments of some selected multiservice systems and with the results provided by other analytical methods that are available in the literature of the subject. The study has confirmed high accuracy of the proposed method. The effectiveness of the computational process carried out according to the proposed method can be significantly increased as a result of parallelisation of computation.

Inspec keywords: convolution; telecommunication services; computational complexity; probability

Other keywords: universal applicability; analytical methods; computational process; occupancy distribution; multiservice state-dependent systems; modified convolution operation; generalised convolution algorithm; parallelisation; blocking probability

Subjects: Telecommunication applications; Signal processing and detection; Other topics in statistics

References

    1. 1)
      • 20. Głąbowski, M., Stasiak, M.: ‘Multi-rate model of the group of separated transmission links of various capacities’. Proc. 11th Int. Conf. Telecommunications, Fortaleza, Brazil, 1–6 August 2004, pp. 11011106.
    2. 2)
      • 5. Kumar, S., Kumar, A.: ‘Multistage interconnection networks: a transition to optical’, Int. J. Res. Eng. Technol., 2012, 1, (3), pp. 424429.
    3. 3)
      • 34. Roberts, J.: ‘Teletraffic models for the Telcom 1 integrated services network’. Proc. Tenth Int. Teletraffic Congress, Montreal, Canada, 1983, p. 1.1.2.
    4. 4)
      • 32. Roberts, J., Mocci, V., Virtamo, I. (Eds.): ‘Broadband network teletraffic’. Final Report of Action COST, 242, Commission of the European Communities, Springer, Berlin, 1996.
    5. 5)
    6. 6)
      • 35. Głąbowski, M., Hanczewski, S., Stasiak, M., Weissenberg, J.: ‘Modeling Erlang's ideal grading with multi-rate BPP traffic’, Math. Prob. Eng., 2012, 2012, p. 35, article ID 456910.
    7. 7)
      • 23. Głąbowski, M., Kaliszan, A., Stasiak, M.: ‘On the application of the asymmetric convolution algorithm in modeling of full-availability group with bandwidth reservation’. Proc. 20th Int. Teletraffic Congress, Ottawa, Canada, June 2007, pp. 878889.
    8. 8)
      • 17. Ramaswami, V., Rao, K.: ‘Flexible time slot assignment — a performance study for the integrated services digital network’. Proc. 11th Int. Teletraffic Congress, Kyoto, Japan, 1985.
    9. 9)
      • 7. Ross, K.: ‘Multiservice loss models for broadband telecommunication network’ (Springer, London, 1995).
    10. 10)
      • 30. Głąbowski, M., Stasiak, M.: ‘Point-to-point blocking probability in switching networks with reservation’, Ann. Télécommun., 2002, 57, (7–8), pp. 798831.
    11. 11)
      • 16. Conradt, J., Buchheister, A.: ‘Considerations on loss probability of multi-slot connections’. Proc. 11th Int. Teletraffic Congress, Kyoto, Japan, 1985, pp. 4.4B2.1.
    12. 12)
    13. 13)
    14. 14)
      • 15. Katzschner, L., Scheller, R.: ‘Probability of loss of data traffics with different bit rates hunting one common PCM-channel’. Proc. Eighth Int. Teletraffic Congress, Melbourne, Australia, 1976, pp. 525/18.
    15. 15)
      • 22. Głąbowski, M., Kaliszan, A., Stasiak, M.: ‘A new convolution algorithm of blocking probability calculation in full-availability group with bandwidth reservation’. Proc. Fifth Int. Symp. Communication Systems, Networks and Digital Signal Processing, Patras, Greece, 2006, pp. 5054.
    16. 16)
      • 12. Iversen, V.: ‘The exact evaluation of multi-service loss systems with access control’. ‘Seventh Nordic Teletraffic Seminar (NTS-7)’, Lund, Sweden, 1987, pp. 5661.
    17. 17)
      • 36. Głąbowski, M., Sobieraj, M., Stasiak, M.: ‘Analytical and simulation modeling of limited-availability systems with multi-service sources and bandwidth reservation’, Int. J. Adv. Telecommun., 2013, 6, (1–2), pp. 111.
    18. 18)
    19. 19)
      • 31. Roberts, J. (Ed.): ‘Performance evaluation and design of multiservice networks’. Final Report COST, 224, Commission of the European Communities, Brussels, 1992.
    20. 20)
    21. 21)
    22. 22)
      • 9. Roberts, J.: ‘A service system with heterogeneous user requirements — application to multi-service telecommunications systems’. Proc. Performance of Data Communications Systems and their Applications, Amsterdam, Netherlands, 1981, pp. 423431.
    23. 23)
      • 4. Vardakas, J.S., Moscholios, I.D., Logothetis, M.D., Stylianakis, V.G.: ‘Blocking performance of multi-rate OCDMA PONs with QoS guarantee’, Int. J. Adv. Telecommun., 2012, 5, (3 and 4), pp. 120130.
    24. 24)
      • 18. Karlsson, J.: ‘Loss performance in trunk groups with different capacity demands’. ‘Proc. 13th Int. Teletraffic Congress’, Copenhagen, Denmark, 1991, volume Discussion Circles, pp. 201212.
    25. 25)
      • 13. Iversen, V. (Ed.): ‘Teletraffic engineering handbook’ (ITU-D, Study Group 2, Question 16/2, Geneva, 2005).
    26. 26)
      • 37. Głąbowski, M., Kaliszan, A.: ‘Simulator of full-availability group with bandwidth reservation and multi-rate Bernoulli–Poisson–Pascal traffic streams’. Proc. Eurocon 2007, Warszawa, Poland, 2007, pp. 22712277, doi:10.1109/EURCON.2007.4400605.
    27. 27)
      • 14. Stasiak, M., Głąbowski, M., Wiśniewski, A., Zwierzykowski, P.: ‘Modeling and dimensioning of mobile networks’ (Wiley, U.K., 2011).
    28. 28)
      • 11. Głąbowski, M., Stasiak, M., Weissenberg, J.: ‘Properties of recurrent equations for the full-availability group with BPP traffic’, Math. Probl. Eng., 2012, 2012, p. 17, article ID 547909.
    29. 29)
    30. 30)
    31. 31)
    32. 32)
      • 19. Stasiak, M.: ‘Blocking probability in a limited-availability group carrying mixture of different multichannel traffic streams’, Ann. Télécommun., 1993, 48, (1–2), pp. 7176.
    33. 33)
    34. 34)
      • 6. ‘Cisco ONS 15454 100gbps coherent DWDM trunk card’. Available at http://www.cisco.com/c/en/us/products/collateral/optical-networking/ons-15454-series-multiservice-provisioning-platforms/data_sheet_c78-713298.html, accessed April 2014.
    35. 35)
    36. 36)
      • 25. Głąbowski, M., Kaliszan, A., Stasiak, M.: ‘Two-dimensional convolution algorithm for modelling multiservice networks with overflow traffic’, Math. Prob. Eng., 2013, 2013, p. 18, article ID 852082.
    37. 37)
      • 29. Vassilakis, V.G., Kallos, G.A., Moscholios, I.D., Logothetis, M.D.: ‘On call admission control in W-CDMA networks supporting handoff traffic’, Ubiquit. Comput. Commun. J., 2009, 4, (5), pp. 167179.
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