WGM: Wavelet-Based Gamma Model for Video Traffic in Wireless Multi-hop Networks

  • Hang Shen
  • Guangwei BaiEmail author
  • Junyuan Wang
  • Lu Zhao


While most of the existing literature concentrates on wireless traffic characterization and its effects on network performance, relatively little research work has focused on mathematical modeling and queuing analysis of video traffic in wireless multi-hop networks. The purpose of this paper is to characterize and model wireless multi-hop network video traffic. We begin with thorough analysis and investigations of characteristics of video traffic in typical wireless network scenarios, building upon which we present a novel Wavelet-based Gamma Model (WGM) for wireless multi-hop video streaming. Our analytic and simulation results demonstrate that the WGM provides a flexible and robust means to characterize wireless video traffic, in terms of statistical properties and self-similarity. On this basis, a WGM queuing system is constructed to deduce the theoretical value of buffer overflow probability, delay and delay jitter for wireless media streaming. A series of simulation experiments are conducted to demonstrate the generality and effectiveness of our modeling approach. Our experimental results show that the probability of buffer overflow indicates a hyperbolic decay as the buffer size increases; however, the buffer overflow probability decays exponentially fast, as the sending rate increases. The study also finds that, as the buffer size increases, the delay and delay jitter of video streaming first increase then become stable, but with an increase in the sending rate, both values decrease sharply. We believe that this conclusion could contribute to the design of appropriate network architectures and to elaborate efficient wireless multimedia communication protocols.


Video traffic modeling Self-similarity Wireless multi-hop networks Gamma distribution Wavelet 



This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61502230 and 61073197, in part by the Natural Science Foundation of Jiangsu Province under Grant No. BK20150960, in part by the National Key R&D Program of China under Grant No. 2018YFC0808500, in part by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No. 15KJB520015, in part by the National Engineering Research Center Program of Communications and Networking under Grant No. GCZX012, in part by the Nanjing Municipal Science and Technology Plan Project under Grant No. 201608009. The first author is especially grateful to the Jiangsu Government Scholarship for Overseas Studies assisting his research abroad.


  1. 1.
    Ericsson, A. B. (2017). Ericsson mobility report: On the pulse of the networked society. Ericsson, Sweden, Tech. Rep. EAB-17.Google Scholar
  2. 2.
    Fontugne, R., Abry, P., Fukuda, K., Veitch, D., Cho, K., Borgnat, P., et al. (2017). Scaling in internet traffic: A 14 year and 3 day longitudinal study, with multiscale analyses and random projections. IEEE/ACM Transactions on Networking, 25(4), 2152–2165.CrossRefGoogle Scholar
  3. 3.
    Chaurasia, A., & Sehgal, V. K. (2015). Optimal buffer-size by synthetic self-similar traces for different traffics for NoC. SIGBED Reviev, 12(3), 6–12.CrossRefGoogle Scholar
  4. 4.
    Min, G., & Jin, X. (2013). Analytical modelling and optimization of congestion control for prioritized multi-class self-similar traffic. IEEE Transactions on Communications, 61(1), 257–265.CrossRefGoogle Scholar
  5. 5.
    Lin, S.-C., Wang, P., Akyildiz, I. F., & Luo, M. (2016). Throughput-optimal LIFO policy for bounded delay in the presence of heavy-tailed traffic. In Proceedings of IEEE GLOBECOM (pp. 1–7).Google Scholar
  6. 6.
    Wang, P., & Akyildiz, I. F. (2015). On the stability of dynamic spectrum access networks in the presence of heavy tails. IEEE Transactions on Wireless Communications, 14(2), 870–881.CrossRefGoogle Scholar
  7. 7.
    Kalbkhani, H., Shayesteh, M. G., & Haghighat, N. (2017). Adaptive lstar model for long-range variable bit rate video traffic prediction. IEEE Transactions on Multimedia, 19(5), 999–1014.CrossRefGoogle Scholar
  8. 8.
    Kastrinakis, M., Badawy, G., Smadi, M. N., & Koutsakis, P. (2017). Video frame size modeling for user-generated traffic in an enterprise-like environment. Computer Communications, 109(5), 24–37.CrossRefGoogle Scholar
  9. 9.
    Toral-Cruz, H., Pathan, A.-S. K., & Pacheco, J. C. R. (2013). Accurate modeling of voip traffic qos parameters in current and future networks with multifractal and Markov models. Mathematical and Computer Modelling, 57(11), 2832–2845.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Jin, X., & Min, G. (2007). Performance modelling of priority queuing discipline under self-similar and poisson traffic. In Proceedings of IEEE LCN (pp. 567–574).Google Scholar
  11. 11.
    Adas, A. (1997). Traffic models in broadband networks. IEEE Communications Magazine, 35(7), 82–89.CrossRefGoogle Scholar
  12. 12.
    Willinger, W., Taqqu, M. S., Sherman, R., & Wilson, D. V. (1997). Self-similarity through high-variability: Statistical analysis of ethernet lan traffic at the source level. IEEE/ACM Transactions on Networking, 5(1), 71–86.CrossRefGoogle Scholar
  13. 13.
    Yang, X., & Petropulu, A. P. (2001). The extended alternating fractal renewal process for modeling traffic in high-speed communication networks. IEEE Transactions on Signal Processing, 49(7), 1349–1363.CrossRefGoogle Scholar
  14. 14.
    Mandelbrot, B. B., & Van Ness, J. W. (1968). Fractional brownian motions, fractional noises and applications. SIAM Review, 10(4), 422–437.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Hosking, J. R. M. (1981). Fractional differencing. Biometrika, 68(1), 165–176.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Girma, D., Lazaro, O., & Dunlop, J. (2000). Online video traffic modelling with wavelet transform. Electronics Letters, 36(16), 1368–1370.CrossRefGoogle Scholar
  17. 17.
    Wang, P., & Akyildiz, I. F. (2011). Spatial correlation and mobility-aware traffic modeling for wireless sensor networks. IEEE/ACM Transactions on Networking, 19(6), 1860–1873.CrossRefGoogle Scholar
  18. 18.
    Jin, X., & Min, G. (2009). Modelling and analysis of priority queueing systems with multi-class self-similar network traffic: A novel and efficient queue-decomposition approach. IEEE Transactions on Communications, 57(5), 1444–1452.CrossRefGoogle Scholar
  19. 19.
    Ghosh, A., Jana, R., Ramaswami, V., Rowland, J., & Shankaranarayanan, N. K. (2011). Modeling and characterization of large-scale wi-fi traffic in public hot-spots. In Proceedings of IEEE INFOCOM (pp. 2921–2929).Google Scholar
  20. 20.
    Ma, S., & Ji, C. (1998). Modeling video traffic in the wavelet domain. In Proceedings of IEEE INFOCOM (pp. 201–208).Google Scholar
  21. 21.
    Leland, W. E., Taqqu, M. S., Willinger, W., & Wilson, D. V. (1994). On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Transactions on Networking, 2(1), 1–15.CrossRefGoogle Scholar
  22. 22.
    Crovella, M. E., & Bestavros, A. (1997). Self-similarity in world wide web traffic: Evidence and possible causes. IEEE/ACM Transactions on Networking, 5(6), 835–846.CrossRefGoogle Scholar
  23. 23.
    Bai, G., & Williamson, C. (2004). Time-domain analysis of web cache filter effects. Performance Evaluation, 58(2), 285–317.CrossRefGoogle Scholar
  24. 24.
    Sahinoglu, Z., & Tekinay, S. (1999). On multimedia networks: Self-similar traffic and network performance. IEEE Communications Magazine, 37(1), 48–52.CrossRefGoogle Scholar
  25. 25.
    Karagiannis, T., Molle, M., Faloutsos, M., & Broido, A. (2004). A nonstationary Poisson view of internet traffic. In Proceedings of INFOCOM (pp. 1558–1569).Google Scholar
  26. 26.
    Borgnat, P., Dewaele, G., Fukuda, K., Abry, P., & Cho, K. (2009). Seven years and one day: Sketching the evolution of internet traffic. In Proceedings of INFOCOM (pp. 711–719).Google Scholar
  27. 27.
    Yin, S., & Lin, X. (2005). Traffic self-similarity in mobile ad hoc networks. In Proceedings of IFIP WOCN (pp. 285–289).Google Scholar
  28. 28.
    Tickoo, O., & Sikdar, B. (2003). On the impact of IEEE 802.11 mac on traffic characteristics. IEEE Journal on Selected Areas in Communications, 21(2), 189–203.CrossRefGoogle Scholar
  29. 29.
    Oliveira, C., Kim, J. B., & Suda, T. (2003). Long-range dependence in IEEE 802.11 b wireless LAN traffic: An empirical study. In Proceedings of IEEE CCW (pp. 17–23).Google Scholar
  30. 30.
    Jie, Y., & Petropulu, A. P. (2006). Study of the effect of the wireless gateway on incoming self-similar traffic. IEEE Transactions on Signal Processing, 54(10), 3741–3758.CrossRefzbMATHGoogle Scholar
  31. 31.
    Ge, X., Yang, Y., Wang, C.-X., Liu, Y.-Z., Liu, C., & Xiang, L. (2010). Characteristics analysis and modeling of frame traffic in 802.11 wireless networks. Wireless Communications and Mobile Computing, 10(4), 584–592.Google Scholar
  32. 32.
    Li, X., Lu, H., & Lu, H. (2013). QoS analysis of self-similar multimedia traffic with variable packet size in wireless networks. In Proceedings of VTC Fall (pp. 1–5).Google Scholar
  33. 33.
    Tewfik, A. H., & Kim, M. (1992). Correlation structure of the discrete wavelet coefficients of fractional brownian motion. IEEE Transactions on Information Theory, 38(2), 904–909.MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Ribeiro, V. J., Riedi, R. H., Crouse, M. S., & Baraniuk, R. G. (2000). Multiscale queuing analysis of long-range-dependent network traffic. In Proceedings of IEEE INFOCOM (pp. 1026–1035).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Hang Shen
    • 1
    • 2
  • Guangwei Bai
    • 1
    Email author
  • Junyuan Wang
    • 1
  • Lu Zhao
    • 1
  1. 1.Department of Computer Science and TechnologyNanjing Tech UniversityNanjingChina
  2. 2.National Engineering Research Center of Communications and Networking (Nanjing University of Posts and Telecommunications)NanjingChina

Personalised recommendations