[1] Ji Qijin,. On approximating multifractal traffic burstinesswith Markov modulated Poisson processes [J]. Journal of Southeast University (English Edition), 2004, 20 (4): 436-441. [doi:10.3969/j.issn.1003-7985.2004.04.009]
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On approximating multifractal traffic burstinesswith Markov modulated Poisson processes(
)
用马尔可夫调制的泊松过程近似多分形突发流量研究
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 20
- Issue:
- 2004 4
- Page:
- 436-441
- Research Field:
- Computer Science and Engineering
- Publishing date:
- 2004-12-30
Info
- Title:
- On approximating multifractal traffic burstinesswith Markov modulated Poisson processes
- 用马尔可夫调制的泊松过程近似多分形突发流量研究
- Author(s):
- Ji Qijin
- Key Laboratory of Computer Network and Information Integration of Ministry of Education, Southeast University, Nanjing 210096, China
- 纪其进
- 东南大学计算机网络和信息集成技术教育部重点实验室, 南京 210096
- Keywords:
- multifractal traffic; Markov modulated Poisson processes; queueing delay; packet loss rate
- PACS:
- TP393
- DOI:
- 10.3969/j.issn.1003-7985.2004.04.009
- Abstract:
- We investigate the approximating capability of Markov modulated Poisson processes(MMPP)for modeling multifractal Internet traffic. The choice of MMPP is motivated by its ability to capture the variability and correlation in moderate time scales while being analytically tractable. Important statistics of traffic burstiness are described and a customized moment-based fitting procedure of MMPP to traffic traces is presented. Our methodology of doing this is to examine whether the MMPP can be used to predict the performance of a queue to which MMPP sample paths and measured traffic traces are fed for comparison respectively, in addition to the goodness-of-fit test of MMPP. Numerical results and simulations show that the fitted MMPP can approximate multifractal traffic quite well, i.e. accurately predict the queueing performance.
- 研究了用马尔可夫调制的泊松过程(MMPP)对Internet多分形流量突发行为进行近似建模的能力. MMPP可用于描述适当时间尺度范围内流量的变化以及相关性, 而且它可作为排队系统输入过程得到分析结果. 描述了刻画突发流量行为的重要统计量, 在此基础上给出了一个基于矩的MMPP参数估计方法. 除了对MMPP进行拟合优度检测以外, 本文通过将MMPP的样本过程和实际流量记录输入到排队系统模型中比较其输出结果来研究MMPP对排队性能的预测能力. 数值和仿真实验表明, MMPP能够较好地用于对多分形流量近似建模, 即可以准确地预测网络结点的排队性能.
References:
[1] Leland W E, Taqqu M S, Willinger W, et al. On the self-similar nature of Ethernet traffic(extended version)[J]. IEEE/ACM Trans on Networking, 1994, 2(1): 1-16.
[2] Cappe O, Moulines E, Pesquet J C, et al. Long-range dependence and heavy-tail modeling for teletraffic data [J]. IEEE Signal Processing Magazine, 2002, 19(3): 14-27.
[3] Feldmann A, Gilbert A C, Willinger W. Data networks as cascades: investigating the multifractal nature of Internet WAN traffic [A]. In: Proc ACM SIGCOMM’98 [C]. Vancouver, Canada, 1998. 42-66.
[4] Riedi R H, Crouse M S, Ribeiro V, et al. A multifractal wavelet model with application to network traffic [J]. IEEE Trans on Information Theory, 1999, 46(3): 992-1018.
[5] Riedi R H, Willinger W. Toward an improved understanding of network traffic dynamics [A]. In: Park K, Willinger W, eds. Self-Similar Network Traffic and Performance Evaluation [C]. New York: Wiley, 2000. 507-530.
[6] Abry P, Baraniuk R, Flandrin P, et al. Multiscale nature of network traffic [J]. IEEE Signal Processing Magazine, 2002, 19(3): 28-46.
[7] Norros I. A storage model with self-similar input [J]. Queueing Systems, 1994, 16(2): 382-396.
[8] Erramilli A, Narayan O, Willinger W. Experimental queueing analysis with long-range dependent packet traffic [J]. IEEE/ACM Trans on Networking, 1996, 4(2): 209-223.
[9] Park K, Kim G, Crovella M. On the effect of traffic self-similarity on network performance [A]. In: Proc SPIE Int’l Conf Perf and Control of Network System [C]. Dallas, USA, 1997. 296-310.
[10] Grossglauser M, Bolot J C. On the relevance of long-range dependence in network traffic [A]. In: Proc ACM SIGCOM’96 [C]. Stanford University, 1996. 15-24.
[11] Ryu B K, Elwalid A, The importance of long-range dependence of VBR video traffic in ATM traffic engineering: myths and realities [A]. In: Proc ACM SIGCOM’96 [C]. Stanford University, 1996. 3-14.
[12] Heyman D P, Lakshman T V. What are the implications of long-range dependence for VBR-video traffic engineering? [J]. IEEE/ACM Trans on Networking, 1996, 4(3): 301-317.
[13] Erramilli A, Narayan O, Neidhardt A, et al. Performance impacts of multi-scaling in wide area TCP/IP traffic [A]. In: Proc of IEEE INFOCOM’00 [C]. Israel, 2000, 1: 362-369.
[14] Heffes H, Lucantoni D. A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance [J]. IEEE Journal on Selected Areas in Comm, 1986, 4(6): 856-868.
[15] Gusella R. Characterizing the variability of arrival processes with indexes of dispersion [J]. IEEE Journal on Selected Areas in Comm, 1991, 9(2): 203-211.
[16] Fischer W, Meier-Hellstern K S. The Markov-modulated Poisson process(MMPP)cookbook [J]. Performance Evaluation, 1993, 18(2): 149-171.
[17] Kang S H, Kim Y H, Sung D K, et al. An application of Markovian arrival process(MAP)to modeling superposed ATM cell streams [J]. IEEE Trans on Communications, 2002, 50(4): 633-642.
[18] Akar N, Oguz N C, Sohraby K. TELPACK: an advanced teletraffic analysis package [J]. IEEE Comm Magazine, 1998, 36(8): 84-87.
[19] Cox D R, Lewis P A. Statistical analysis of series of events [M]. London: Methuen, 1966.
[20] Geist R M, Westall J M. Correlational and distributional effects in network traffic models [J]. Performance Evaluation, 2001, 44(1): 121-138.
[21] Auckland Ⅱ trace 20000125-143640 [EB/OL].http: //pma.nlanr.net/Traces/long/auck2.html. 2004-04-26.
[22] Ribeiro V J, Riedi R H, Crouse M S, et al. Multiscale queueing analysis of long-range-dependent network traffic [A]. In: Proc IEEE INFOCOM’00 [C]. Israel, 2000, 2: 1026-1035.
[23] NS2, network simulation 2 [EB/OL].http: //www.isi.edu/nsnam/ns/. 2004-04-26.
Memo
- Memo:
- Biography: Ji Qijin(1974—), male, graduate, andyji@seu.edu.cn.