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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 286490, 15 pages
http://dx.doi.org/10.1155/2015/286490
Research Article

Modelling of Cellular Networks with Traffic Overflow

The Chair of Communication and Computer Networks, Poznań University of Technology, Polanka 3, 60-965 Poznań, Poland

Received 29 September 2014; Accepted 29 January 2015

Academic Editor: Jian Li

Copyright © 2015 Mariusz Głąbowski et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. 3GPP, “UMTS phase 1, release 99,” 3rd Generation Partnership Project (3GPP) TS 22.100, 2001, http://www.3gpp.org/DynaReport/22100.htm. View at Google Scholar
  2. H. Holma and A. Toskala, WCDMA for UMTS: HSPA Evolution and LTE, John Wiley & Sons, New York, NY, USA, 2007.
  3. 3GPP, “High speed packet access (HSPA) evolution: frequency division duplex (FDD) (release 7),” Tech. Rep. 25.999, 3rd Generation Partnership Project, 2008, http://www.3gpp.org/DynaReport/25999.htm. View at Google Scholar
  4. “Evolved universal terrestrial radio access (E-UTRA) and evolved universal terrestrial radio access (E-UTRAN); overall description; Stage 2 (Release 12),” Tech. Rep. 36.300, 3rd Generation Partnership Project (3GPP), 2014, http://www.3gpp.org/DynaReport/36300.htm.
  5. S. Zhao, Z. Xiong, and X. Wang, “Optimal resource allocation for wireless video over CDMA networks,” IEEE Transactions on Mobile Computing, vol. 4, no. 1, pp. 56–67, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. 3GPP, “Handover procedures (Release 11),” 3rd Generation Partnership Project (3GPP), TS 23.009, 2012, http://www.3gpp.org/DynaReport/23009.htm.
  7. J. Wang, Q.-A. Zeng, and D. P. Agrawal, “Performance analysis of a preemptive and priority reservation handoff scheme for integrated service-based wireless mobile networks,” IEEE Transactions on Mobile Computing, vol. 2, no. 1, pp. 65–75, 2003. View at Publisher · View at Google Scholar · View at Scopus
  8. 3GPP, “Handover requirements between UTRAN and GERAN or other radio systems (release 11),” 3rd Generation Partnership Project (3GPP) TS 22.129, 3GPP, 2012, http://www.3gpp.org/DynaReport/22129.htm. View at Google Scholar
  9. S. L. Salecker and C. S. Hood, “Traffic analysis of a diverse network that overflows dual mode phones,” in Proceedings of the IEEE Wireless Communications and Networking Confernce (WCNC '00), vol. 2, pp. 824–828, 2000. View at Scopus
  10. 3GPP, “Radio resource management strategies (Release 7),” 3rd Generation Partnership Project (3GPP), TR 25.922, 2007, http://www.3gpp.org/DynaReport/25922.htm.
  11. 3GPP, “General Packet Radio Service (GPRS) enhancements for evolved universal terrestrial radio access network (E-UTRAN) access (release 13),” Tech. Rep. TS 23.401, 3rd Generation Partnership Project (3GPP), 2014, http://www.3gpp.org/DynaReport/23401.htm. View at Google Scholar
  12. M. Stasiak, M. Głabowski, A. Wisńiewski, and P. Zwierzykowski, Modeling and Dimensioning of Mobile Networks, John Wiley & Sons, 2011.
  13. R. I. Wilkinson, “Theories of toll traffic engineering in the USA,” Bell System Technical Journal, vol. 40, pp. 421–514, 1956. View at Google Scholar · View at MathSciNet
  14. G. Bretschneider, “Die berechnung von leitungsgruppen für überfliessenden verkehr in fernsprechwählanlagen,” Nachrichtentechnische Zeitung, no. 11, pp. 533–540, 1956. View at Google Scholar
  15. A. A. Fredericks, “Congestion in blocking systems—a simple approximation technique,” The Bell System Technical Journal, vol. 59, no. 6, pp. 805–828, 1980. View at Publisher · View at Google Scholar · View at Scopus
  16. S.-P. Chung and J.-C. Lee, “Performance analysis and overflowed traffic characterization in multiservice hierarchical wireless networks,” IEEE Transactions on Wireless Communications, vol. 4, no. 3, pp. 904–918, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Gła̧bowski, K. Kubasik, and M. Stasiak, “Modeling of systems with overflow multi-rate traffic,” Telecommunication Systems, vol. 37, no. 1–3, pp. 85–96, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. Q. Huang, K.-T. Ko, and V. B. Iversen, “Approximation of loss calculation for hierarchical networks with multiservice overflows,” IEEE Transactions on Communications, vol. 56, no. 3, pp. 466–473, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. E. Brockmeyer, “A survey of A. K. Erlang's mathematical works,” Danish Academy of Technical Sciences, no. 2, pp. 101–126, 1948. View at Google Scholar
  20. M. Stasiak, “Approximate model of a switching network carrying mixture of different multichannel traffic streams,” IEEE Transactions on Communications, vol. 41, no. 6, pp. 836–840, 1993. View at Publisher · View at Google Scholar · View at Scopus
  21. M. Stasiak and S. Hanczewski, “Approximation for multi-service systems with reservation by systems with limited-availability,” in Computer Performance Engineering, N. Thomas and C. Juiz, Eds., vol. 5261 of Lecture Notes in Computer Science, pp. 257–267, Springer, Berlin, Germany, 2008. View at Publisher · View at Google Scholar
  22. M. Glabowski, S. Hanczewski, M. Stasiak, and J. Weissenberg, “Modeling Erlang's Ideal Grading with multirate BPP traffic,” Mathematical Problems in Engineering, vol. 2012, Article ID 456910, 35 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  23. H. Akimaru and K. Kawashima, Teletraffic: Theory and Application, Springer, Berlin , Germany, 1999.
  24. K. Ross, Multiservice Loss Models for Broadband Telecommunication Network, Springer, London, UK, 1995.
  25. U. Herzog and A. Lotze, “Das RDA-Verfahren, ein Streuwertverfahren für unvollkommene Bündel,” Nachrichtentechnische Zeitung, vol. 11, pp. 640–646, 1966. View at Google Scholar
  26. J. Roberts, V. Mocci, and I. Virtamo, Eds., Broadband Network Teletraffic: Final Report of Action COST 242, Commission of the European Communities, Berlin, Germany, 1996.
  27. V. G. Vassilakis, I. D. Moscholios, and M. D. Logothetis, “Call-level performance modelling of elastic and adaptive service-classes with finite population,” IEICE Transactions on Communications, vol. E91-B, no. 1, pp. 151–163, 2008. View at Google Scholar · View at Scopus
  28. J. F. Shortle, “An equivalent random method with hyper-exponential service,” Performance Evaluation, vol. 57, no. 3, pp. 409–422, 2004. View at Publisher · View at Google Scholar · View at Scopus
  29. R. Schehrer, “On the calculation of overflow systems with a finite number of sources and full availiable groups,” IEEE Transactions on Communications, vol. 26, no. 1, pp. 75–82, 1978. View at Publisher · View at Google Scholar · View at Scopus
  30. G. Bretschneider, “Extension of the equivalent random method to smooth traffics,” in Proceedings of the 7th International Teletraffic Congress, Stockholm, Sweden, 1973.
  31. M. Gła̧bowski, K. Kubasik, and M. Stasiak, “Modelling of systems with overflow multi-rate traffic and finite number of traffic sources,” in Proceedings of the 6th International Symposium Communication Systems, Networks and Digital Signal Processing (CSNDSP '08), pp. 196–199, July 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. L. Gimpelson, “Analysis of mixtures of wide- and narrow-band traffic,” IEEE Transactions on Communications, vol. 13, no. 3, pp. 258–266, 1965. View at Publisher · View at Google Scholar
  33. J. M. Aein, “A multi-user-class, blocked-calls-cleared, demand access model,” IEEE Transactions on Communications, vol. 26, no. 3, pp. 378–384, 1978. View at Publisher · View at Google Scholar · View at Scopus
  34. J. S. Kaufman, “Blocking in a shared resource environment,” IEEE Transactions on Communications, vol. 29, no. 10, pp. 1474–1481, 1981. View at Publisher · View at Google Scholar · View at Scopus
  35. J. Roberts, “A service system with heterogeneous user requirements—application to multi-service telecommunications system,” in Proceedings of Performance of Data Communications Systems and their Applications, G. Pujolle, Ed., pp. 423–431, North Holland, Amsterdam, The Netherlands, 1981. View at Google Scholar
  36. L. E. N. Delbrouck, “On the steady-state distribution in a service facility carrying mixtures of traffic with different peakedness factors and capacity requirements,” IEEE Transactions on Communications, vol. 31, no. 11, pp. 1209–1211, 1983. View at Publisher · View at Google Scholar · View at Scopus
  37. E. A. van Doorn and F. J. M. Panken, “Blocking probabilities in a loss system with arrivals in geometrically distributed batches and heterogenous service requirements,” IEEE/ACM Transactions on Networking, vol. 1, no. 6, pp. 664–667, 1993. View at Publisher · View at Google Scholar · View at Scopus
  38. J. S. Kaufman and K. M. Rege, “Blocking in a shared resource environment with batched Poisson arrival processes,” Performance Evaluation, vol. 24, no. 4, pp. 249–263, 1996. View at Publisher · View at Google Scholar · View at Scopus
  39. L.-R. Hu and S. S. Rappaport, “Personal communication systems using multiple hierarchical cellular overlays,” IEEE Journal on Selected Areas in Communications, vol. 13, no. 2, pp. 406–415, 1995. View at Publisher · View at Google Scholar · View at Scopus
  40. X. Lagrange and P. Godlewski, “Performance of a hierarchical cellular network with mobility-dependent hand-over strategies,” in Proceedings of the IEEE 46th Vehicular Technology Conference, vol. 3, pp. 1868–1872, May 1996. View at Scopus
  41. M. Głąbowski, “Modeling systems with multi-service overflow Erlang and Engset traffic streams,” International Journal on Advances in Telecommunications, vol. 1, no. 1, pp. 14–26, 2008. View at Google Scholar
  42. Q. Huang, K.-T. Ko, and V. B. Iversen, “An approximation method for multiservice loss performance in hierarchical networks,” in Managing Traffic Performance in Converged Networks: Proceedings of the 20th International Teletraffic Congress (ITC20 '07), Ottawa, Canada, June 17–21, L. Mason, T. Drwiega, and J. Yan, Eds., vol. 4516 of Lecture Notes in Computer Science, pp. 901–912, Springer, Berlin, Germany, 2007. View at Publisher · View at Google Scholar
  43. M. Gła̧bowski, K. Kubasik, and M. Stasiak, “Modeling of systems with overflowmulti-rate traffic,” in Proceedings of 3rd Advanced International Conference on Telecommunications (AICT '08), p. 6, IEEE, May 2007. View at Publisher · View at Google Scholar
  44. E. Brockmeyer, H. L. Halström, and A. Jensen, “The life and works of A.K. Erlang,” Acta Polytechnika Scandinavia, vol. 6, no. 287, 1960. View at Google Scholar · View at MathSciNet
  45. M. Stasiak and S. Hanczewski, “A model of WCDMA radio interface with reservation,” in Proceedings of the International Symposium on Information Theory and Its Applications (ISITA '08), pp. 1–6, December 2008. View at Publisher · View at Google Scholar · View at Scopus
  46. M. Gła̧bowski, S. Hanczewski, and M. Stasiak, “Erlang’s Ideal Grading in DiffServ modelling,” in Proceedings of the IEEE Africon, pp. 1–6, Livingstone, Zambia, September 2011. View at Publisher · View at Google Scholar · View at Scopus
  47. A. Lotze, “History and development of grading theory,” in Proceedings of the 5th International Teletraffic Congress, pp. 148–161, New York, NY, USA, 1967.
  48. M. Głąbowski, A. Kaliszan, and M. Stasiak, “Modeling product-form state-dependent systems with BPP traffic,” Performance Evaluation, vol. 67, no. 3, pp. 174–197, 2010. View at Publisher · View at Google Scholar · View at Scopus
  49. M. Gła̧bowski, “Modelling of state-dependent multirate systems carrying BPP traffic,” Annals of Telecommunications, vol. 63, no. 7-8, pp. 393–407, 2008. View at Publisher · View at Google Scholar · View at Scopus
  50. M. Głabowski, M. Stasiak, and J. Weissenberg, “Properties of recurrent equations for the full-availability group with BPP traffic,” Mathematical Problems in Engineering, vol. 2012, Article ID 547909, 17 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus