Abstract
In this paper, we identify the batch Markovian arrival process (BMAP) as an analytically tractable model of choice for aggregated traffic modeling of IP networks. The key idea of this aggregated traffic model lies in customizing the batch Markovian arrival process such that the different lengths of IP packets are represented by rewards (i.e., batch sizes of arrivals) of the BMAP. The utilization of the BMAP is encouraged by the observation that IP packet lengths follow to a large extent a discrete distribution. A comparative study with the MMPP and the Poisson process illustrates the effectiveness of the customized BMAP for IP traffic modeling by visual inspection of sample paths over four different time-scales, by presenting important statistical properties, and by analysis of traffic burstiness using R/S statistics. Additionally, we show that the BMAP model outperforms MMPP and Poisson traffic models by comparison of queuing performance.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Andersson, S., Ryden, T.: Maximum Likelihood Estimation of a Structured MMPP with Applications to Traffic Modeling. Proc. 13th ITC Specialist Seminar on Measurement and Modeling of IP Traffic, Monterey CA (2000) 20.1–20.10
Ash, G.R.: Traffic Engineering & QoS Methods for IP-, ATM-, & TDM-Based Multiservice Networks. Internet Draft draft-ietf-tewg-qos-routing-01.txt (2001)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society 39 (1976) 1–38
Fischer, W., Meier-Hellstern, K.: The Markov-modulated Poisson Process (MMPP) Cookbook. Performance Evaluation 18 (1993) 149–171
Gross, D., Miller, D.R.: The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes. Operations Research 32 (1984) 345–361
Kilpi, J., Norros, I.: Call Level Traffic Analysis of a Large ISP. Proc. 13th ITC Specialist Seminar on Measurement and Modeling of IP Traffic, Monterey CA (2000) 6.1–6.9
Kruse, H., Allman, M., Griner, J., Ostermann, S., Helvey, E.: Satellite Network Performance Measurements Using Simulated Multi-User Internet Traffic. Proc. 7th Int. Conf. on Telecommunication Systems (1999)
Ledesma, S., Liu, D.: Synthesis of Fractional Gaussian Noise using Linear Approximation for Generating Self-similar Network Traffic. Computer Communication Review 30 (2000) 4–17
Lucantoni, D. M.: New Results on the Single Server Queue with a Batch Markovian Arrival Process. Comm. in Statistics: Stochastic Models 7 (1991) 1–46
McCreary, S., Claffy K.C.: Trends in Wide Area IP Traffic Patterns: A View from Ames Internet Exchange. Proc. 13th ITC Specialist Seminar on Measurement and Modeling of IP Traffic, Monterey CA (2000) 1.1–1.12
Nuzman, C.J., Saniee, I., Sweldens, W., Weiss, A.: A Compound Model for TCP Connection Arrivals. Proc. 13th ITC Specialist Seminar on Measurement and Modeling of IP Traffic, Monterey CA (2000) 1–9
Ryden, T.: An EM Algorithm for Parameter Estimation in Markov Modulated Poisson Processes. Computational Statistics and Data Analysis 21 (1996) 431–447
Skelly, P., Schwartz, M., Dixit, S.: A Histogram-Based Model for Video Traffic Behavior in an ATM Multiplexer. IEEE Trans. on Networking 1 (1993) 446–459
Thompson, K., Miller, G. J., Wilder, R.: Wide-Area Internet Traffic Patterns and Characteristics. IEEE Network Magazine 11 (1997) 10–23
Willinger, W., Paxson, V., Taqqu, M.S.: Self-similarity and Heavy Tails: Structural Modeling of Network Traffic. In: A Practical Guide to Heavy Tails. Chapman & Hall (1998) 27–53
Yoshihara, T., Kasahara, S., Takahashi, Y.: Practical Time-Scale Fitting of Self-Similar Traffic with Markov-Modulated Poisson Process. Telecommunication Systems 17 (2001) 185–211
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Klemm, A., Lindemann, C., Lohmann, M. (2002). Traffic Modeling of IP Networks Using the Batch Markovian Arrival Process. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds) Computer Performance Evaluation: Modelling Techniques and Tools. TOOLS 2002. Lecture Notes in Computer Science, vol 2324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46029-2_6
Download citation
DOI: https://doi.org/10.1007/3-540-46029-2_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43539-6
Online ISBN: 978-3-540-46029-9
eBook Packages: Springer Book Archive