Skip to main content
Log in

Blocking probabilities of elastic and adaptive calls in the Erlang multirate loss model under the threshold policy

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

In this paper, we propose a new multirate teletraffic loss model of a single link with certain bandwidth capacity that accommodates Poisson arriving calls, which can tolerate bandwidth compression, under the threshold policy of admission control. When compression occurs, the service time may increase (elastic calls) or not (adaptive calls). The threshold policy can provide different QoS among service-classes by limiting the number of calls of a service-class up to a predefined threshold, which can be different for each service-class. The proposed model does not have a product form solution for the determination of the steady state probabilities. However, we approximate the model by a reversible Markov chain, and provide recursive formulas for the efficient calculation of the call-level performance metrics, such as call blocking probabilities and link utilization. In addition, we provide similar formulas when the threshold policy co-exists with the bandwidth reservation policy. The latter reserves part of the available link bandwidth to benefit calls of high bandwidth requirements. The accuracy of the proposed formulas is verified through simulation and found to be quite satisfactory. We also show the necessity and consistency of the proposed models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Notes

  1. Note that in the EMLM this call would be blocked.

References

  1. Altman, E., Ayesta, U., & Prabhu, B. J. (2011). Load balancing in processor sharing systems. Telecommunication Systems, 47(1–2), 35–48.

    Article  Google Scholar 

  2. Atmaca, S., Karahan, A., Ceken, C., & Erturk, I. (2014). A new MAC protocol for broadband wireless communications and its performance evaluation. Telecommunication Systems, 57(1), 13–23.

    Article  Google Scholar 

  3. Bonald, T., Proutiere, A., Roberts, J., & Virtamo, J. (2003). Computational aspects of balanced fairness. In Proceedings of the 18th International Teletraffic Congress (ITC-18) (pp. 801–810). Berlin: Springer.

  4. Bonald, T., & Virtamo, J. (2005). A recursive formula for multirate systems with elastic traffic. IEEE Communications Letters, 9(8), 753–755.

    Article  Google Scholar 

  5. Brandt, A., & Brandt, M. (2005). Individual overflow and freed carried traffics for a link with trunk reservation. Telecommunication Systems, 29(4), 283–308.

    Article  Google Scholar 

  6. Cruz-Perez, F., Vazquez-Avila, J., & Ortigoza-Guerrero, L. (2004). Recurrent formulas for the multiple fractional channel reservation strategy in multi-service mobile cellular networks. IEEE Communications Letters, 8(10), 629–631.

    Article  Google Scholar 

  7. Dimitrova, D. C., van den Berg, J. L., & Heijenk, G. (2011). Uplink packet scheduling in cellular networks with relaying comparative study. Telecommunication Systems, 48(3–4), 237–246.

    Article  Google Scholar 

  8. Farbod, A., & Liang, B. (2007). Efficient structured policies for admission control in heterogeneous wireless networks. ACM/Springer Mobile Networks and Applications (MONET), 12(5), 309–323.

    Article  Google Scholar 

  9. Fazekas, P., Imre, S., & Telek, M. (2002). Modelling and analysis of broadband cellular networks with multimedia connections. Telecommunication Systems, 19(3–4), 263–288.

    Article  Google Scholar 

  10. Fehske, A., Klessig, H., Voigt, J., & Fettweis, G. (2014). Flow-level models for capacity planning and management in interference-coupled wireless data networks. IEEE Communications Magazine, 52(2), 164–171.

    Article  Google Scholar 

  11. Fodor, G., & Telek, M. (2007). Bounding the blocking probabilities in multirate CDMA networks supporting elastic services. IEEE/ACM Transactions on Networking, 15(4), 944–956.

    Article  Google Scholar 

  12. Glabowski, M., & Stasiak, M. (2002). Point-to-point blocking probability in switching networks with reservation. Annals of Telecommunications, 57(7–8), 798–831.

    Google Scholar 

  13. Glabowski, M., Kubasik, K., & Stasiak, M. (2008). Modeling of systems with overflow multi-rate traffic. Telecommunication Systems, 37(1–3), 85–96.

    Article  Google Scholar 

  14. Glabowski, M., Kaliszan, A., & Stasiak, M. (2008). Asymmetric convolution algorithm for blocking probability calculation in full-availability group with bandwidth reservation. IET Circuits Devices and Systems, 2(1), 87–94.

    Article  Google Scholar 

  15. Glabowski, M., Stasiak, M., Wisniewski, A., & Zwierzykowski, P. (2009). Blocking probability calculation for cellular systems with WCDMA radio interface servicing PCT1 and PCT2 multirate traffic. IEICE Transactions on Communications, E92–B, 1156–1165.

  16. Hanczewski, S., Stasiak, M., & Weissenberg, J. (2014). A queueing model of a multi-service system with state-dependent distribution of resources for each class of calls. IEICE Transactions on Communications, E97–B(8), 1592–1605.

    Article  Google Scholar 

  17. Iversen, V., Benetis, V., Ha, N., & Stepanov, S. (2004). Evaluation of multi-service CDMA networks with soft blocking. In Proceedings of International Teletraffic Congress Specialist Seminar (pp. 223–227). University of Antwerp: Antwerp.

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

    Article  Google Scholar 

  19. Katehakis, M., & Melolidakis, C. (1995). On the optimal maintenance of systems and control of arrivals in queues. Stochastic Analysis and Applications, 13(2), 137–164.

    Article  Google Scholar 

  20. Koukoulidis, V. (1993). A characterization of reversible Markov processes with applications to shared resource environments. In Ph.D. dissertation, Concordia University: Montreal.

  21. Kuppuswamy, K., & Lee, D. (2009). An analytic approach to efficiently computing call blocking probabilities for multiclass WDM networks. IEEE/ACM Transactions on Networking, 17(2), 658–670.

    Article  Google Scholar 

  22. Kwon, T., Kim, S., Choi, Y., & Naghshineh, M. (2000). Threshold-type call admission control in wireless/mobile multimedia networks using prioritised adaptive framework. IEE Electronics Letters, 36(9), 852–854.

    Article  Google Scholar 

  23. Lee, B., Park, D., & Seo, H. (2009). Wireless communications resource management. New York: Wiley.

    Google Scholar 

  24. Lee, S. S., Lee, J. G., Kim, Y. B., & Kim, Y. S. (2000). An architecture of scalable ATM switching system and its performance. Telecommunication Systems, 14(1–4), 269–290.

    Article  Google Scholar 

  25. Li, X., Toseef, U., Dulas, D., Bigos, W., Görg, C., Timm-Giel, A., et al. (2013). Dimensioning of the LTE access network. Telecommunication Systems, 52(4), 2637–2654.

    Article  Google Scholar 

  26. Litjens, R., van den Berg, H., & Boucherie, R. J. (2008). Throughputs in processor sharing models for integrated stream and elastic traffic. Performance Evaluation, 65(2), 152–180.

    Article  Google Scholar 

  27. Logothetis, M. Vassilakis, V. & Moscholios, I. (2009). Call-level performance modeling and QoS assessment of W-CDMA networks. In J. Feng (Ed.), Wireless Networks: Research, Technology and Applications (pp. 57–90). New York: Nova Science Publishers.

  28. Ma, X., Liu, J., & Jiang, H. (2011). On the design of algorithms for mobile multimedia systems: A survey. International Journal of Communication Systems, 24(10), 1330–1339.

    Article  Google Scholar 

  29. Moscholios, I., Logothetis, M., & Koukias, M. (2007). An ON-OFF multi-rate loss model of finite sources. IEICE Transactions on Communications, E90–B(7), 1608–1619.

    Article  Google Scholar 

  30. Moscholios, I., & Logothetis, M. (2010). The Erlang multirate loss model with batched Poisson arrival processes under the bandwidth reservation policy. Computer Communications, 33(Supplement 1), S167–S179.

    Article  Google Scholar 

  31. Moscholios, I., Vardakas, J., Logothetis, M., & Boucouvalas, A. (2013). Congestion probabilities in a batched poisson multirate loss model supporting elastic and adaptive traffic. Annals of Telecommunications, 68(5), 327–344.

    Article  Google Scholar 

  32. Moscholios, I., Vardakas, J., Logothetis, M., & Koukias, M. (2013). A quasi-random multirate loss model supporting elastic and adaptive traffic under the bandwidth reservation policy. International Journal on Advances in Networks and Services, 6(3&4), 163–174.

    Google Scholar 

  33. Moscholios, I., Kallos, G., Katsiva, M., Vassilakis, V., & Logothetis, M. (2014). Call blocking probabilities in a W-CDMA cell with interference cancellation and bandwidth reservation. Proceedings of IEICE ICTF (pp. 28–30). Poznan.

  34. Moscholios, I., Logothetis, M., Vardakas, J., & Boucouvalas, A. (2014). Performance metrics of a multirate resource sharing teletraffic model with finite sources under the threshold and bandwidth reservation policies. In IET Networks, 2014 doi:10.1049/iet-net.2014.0050, available online: 14 October.

  35. Mundur, P., Sood, A., & Simon, R. (2005). Class-based access control for distributed video-on-demand systems. IEEE Transactions on Circuits and Systems for Video Technology, 15(7), 844–853.

    Article  Google Scholar 

  36. Nasser, N., & Hassanein, H. (2004). Connection-level performance analysis for adaptive bandwidth allocation in multimedia wireless cellular networks. In Proceedings of IEEE International Conference on Performance, Computing and Communications (pp. 61–68).

  37. Ni, J., Tsang, D., Tatikonda, S., & Bensaou, B. (2005). Threshold and reservation based call admission control policies for multiservice resource-sharing systems. Proceedings of IEEE INFOCOM (pp. 773–783).

  38. Ni, J., Tsang, D., Tatikonda, S., & Bensaou, B. (2007). Optimal and structured call admission control policies for resource-sharing systems. IEEE Transactions on Communications, 55(1), 158–170.

    Article  Google Scholar 

  39. Ni, J., & Tatikonda, S. (2005). Revenue optimization via call admission control and pricing for mobile cellular systems. IEEE International Conference on Communications ICC, 5, 3359–3364.

    Google Scholar 

  40. Parniewicz, D., Stasiak, M., & Zwierzykowski, P. (2013). Analytical model of the multi-service cellular network servicing multicast connections. Telecommunication Systems, 52(2), 1091–1100.

    Google Scholar 

  41. Racz, S., Gero, B. P., & Fodor, G. (2002). Flow level performance analysis of a multi-service system supporting elastic and adaptive services. Performance Evaluation, 49, 451–469.

    Article  Google Scholar 

  42. Roberts, J. (1981). A service system with heterogeneous user requirements. In G. Pujolle (Ed.), Performance of data communications systems and their applications (pp. 423–431). Amsterdam: North Holland.

    Google Scholar 

  43. Ross, K. (1995). Multiservice loss models for broadband telecommunication networks. Berlin: Springer.

    Book  Google Scholar 

  44. Simscript III, http://www.simscript.com.

  45. Srikant, R., & Whitt, W. (2001). Resource sharing for book-ahead and instantaneous-request calls using a CLT approximation. Telecommunication Systems, 16(3–4), 233–253.

    Article  Google Scholar 

  46. Stamatelos, G., & Koukoulidis, V. (1997). Reservation based bandwidth allocation in a radio ATM network. IEEE/ACM Transactions on Networking, 5, 420–428.

    Article  Google Scholar 

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

    Article  Google Scholar 

  48. Stasiak, M., Glabowski, M., Wisniewski, A., & Zwierzykowski, P. (2011). Modeling and dimensioning of mobile networks. New York: Wiley.

    Google Scholar 

  49. Tarhini, C., & Chahed, T. (2012). QoS-oriented resource allocation for streaming flows in IEEE802.16e Mobile WiMAX. Telecommunication Systems, 51(1), 65–71.

    Article  Google Scholar 

  50. Theberge, F., Simonian, A., & Mazumdar, R. (1998). Upper bounds for blocking probabilities in large multi-rate loss networks. Telecommunication Systems, 9(1), 23–39.

    Article  Google Scholar 

  51. Tsang, D., & Ross, K. (1990). Algorithms to determine exact blocking probabilities for multirate tree networks. IEEE Transactions on Communications, 38(8), 1266–1271.

    Article  Google Scholar 

  52. Ungureanu, V., Melamed, B., Katehakis, M., & Bradford, P. (2006). Deferred assignment scheduling in cluster-based servers. Cluster Computing, 9(1), 57–65.

    Article  Google Scholar 

  53. Ungureanu, V., Melamed, B., & Katehakis, M. (2008). Effective load balancing for cluster-based servers employing job preemption. Performance Evaluation, 65(8), 606–622.

    Article  Google Scholar 

  54. Vardakas, J., Moscholios, I., Logothetis, M., & Stylianakis, V. (2011). An analytical approach for dynamic wavelength allocation in WDM-TDMA PONs servicing ON-OFF traffic. IEEE/OSA Journal of Optical Communications and Networking, 3(4), 347–358.

    Article  Google Scholar 

  55. Vardakas, J., Moscholios, I., Logothetis, M., & Stylianakis, V. (2012). On code reservation in Multi-rate OCDMA passive optical networks. In Proceedings of IEEE/IET International Symposium on Communication Systems, Networks and Digital Signal Processing 8th CSNDSP’ 2012 (pp. 18–20). Poznan.

  56. Vardakas, J., Moscholios, I., Logothetis, M., & Stylianakis, V. (2012). Blocking performance of multi-rate OCDMA PONs with QoS guarantee. International Journal on Advances in Telecommunications, 5(3 and 4), 120–130.

    Google Scholar 

  57. Vardakas, J., Moscholios, I., Logothetis, M., & Stylianakis, V. (2013). Performance analysis of OCDMA PONs supporting multi-rate bursty traffic. IEEE Transactions on Communications, 61(8), 3374–3384.

    Article  Google Scholar 

  58. Vassilakis, V., Moscholios, I., & Logothetis, M. (2012). The extended connection-dependent threshold model for call-level performance analysis of multi-rate loss systems under the bandwidth reservation policy. International Journal of Communication Systems, 25(7), 849–873.

    Article  Google Scholar 

  59. Vassilakis, V., Kallos, G., Moscholios, I., & Logothetis, M. (2008). On the handoff- call blocking probability calculation in W-CDMA cellular networks. In 4th Advanced International Conference on Telecommunications, AICT 2008 (pp. 8–13). Athens.

  60. Yashkov, S., & Yashkova, A. (2007). Processor sharing: A survey of the mathematical theory. Automation and Remote Control, 68(9), 1662–1731.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ioannis D. Moscholios.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moscholios, I.D., Logothetis, M.D. & Boucouvalas, A.C. Blocking probabilities of elastic and adaptive calls in the Erlang multirate loss model under the threshold policy. Telecommun Syst 62, 245–262 (2016). https://doi.org/10.1007/s11235-015-0056-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11235-015-0056-z

Keywords

Navigation