Joint modeling of network related events with multi-dimensional Markov Modulated Deterministic Processes

Multiple proposals for modeling networking characteristics have been proposed in the past. However, these proposals have focused in a particular networking characteristic and do not cope with modern requirements for integrated characterization and prediction of network related events. This integrated network characterization should include not only data flow statistics but also higher-level application and protocol statistics and users behaviors (including network actions and mobility profiles). Possible examples of utilizations are the joint modeling of: (i) traffic statistics with lower (wireless) network characteristics (e.g. upload and download packet and byte counts with transmitted and received signal power), (ii) flow statistics with application level statistics (e.g. number of active flows with number of active BitTorrent's multi-source downloads) and (iii) traffic characteristics with network radio statistics and with user location (e.g. amount of generated traffic, receiving signal-to-noise ratio and user distance and angle to a radio base station). Towards this objective, this paper proposes a novel multidimensional discrete Markov Modulated Deterministic Processes (dMMDPs) model, and an associate parameter fitting procedure, that leads to accurate joint estimation of the first and second order statistics of multiple network related events. The procedure matches simultaneously both the multidimensional density distribution function and the autocovariance functions of the univariate marginal statistics. One of the main features of this model is that the number of states is not fixed a priori and can be adapted to the particular dataset and to the network events that are being modeled. The individual autocovariance tail of each univariate marginal statistic can be adjusted to capture the long-range dependence characteristics of the network related events. The procedure then fits the dMMDP parameters in order to match the multi-dimensional distribution, within the constraints imposed by multiple autocovariance matchings. The number of states is also determined as part of this step. As a proof of concept, we applied the inference procedure to a BitTorrent traffic trace, modeling simultaneously the packet count both in the upload and download directions. These two traffic statistics exhibit long-range dependence. Very good results were obtained in terms of approximating the first and second order statistics of the traffic characteristics.

[1]  Kleber Vieira Cardoso,et al.  Accurate hidden markov modeling of packet losses in indoor 802.11 networks , 2009, IEEE Communications Letters.

[2]  Paulo Salvador,et al.  Fitting Self-Similar Traffic by a Superposition of MMPPs Modeling the Distribution at Multiple Time Scales , 2004 .

[3]  Anja Feldmann,et al.  Fitting Mixtures of Exponentials to Long-Tail Distributions to Analyze Network , 1998, Perform. Evaluation.

[4]  Dan Keun Sung,et al.  Two-state MMPP modeling of ATM superposed traffic streams based on the characterization of correlated interarrival times , 1995, Proceedings of GLOBECOM '95.

[5]  Wolfgang Fischer,et al.  The Markov-Modulated Poisson Process (MMPP) Cookbook , 1993, Perform. Evaluation.

[6]  David M. Lucantoni,et al.  New results for the single server queue with a batch Markovian arrival process , 1991 .

[7]  David M. Lucantoni,et al.  The BMAP/G/1 QUEUE: A Tutorial , 1993, Performance/SIGMETRICS Tutorials.

[8]  Yutaka Takahashi,et al.  Practical Time-Scale Fitting of Self-Similar Traffic with Markov-Modulated Poisson Process , 2001, Telecommun. Syst..

[9]  J.B. Evans,et al.  Describing Network Traffic Using the Index of Variability , 2009, IEEE/ACM Transactions on Networking.

[10]  Bo Friis Nielsen,et al.  A Markovian approach for modeling packet traffic with long-range dependence , 1998, IEEE J. Sel. Areas Commun..

[11]  L. Noirie,et al.  CoV(t)-based Traffic and Queuing Modeling , 2008, 2008 Next Generation Internet Networks.

[12]  Gordon K. Smyth,et al.  A Modified Prony Algorithm for Exponential Function Fitting , 1995, SIAM J. Sci. Comput..

[13]  António Pacheco,et al.  Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs , 2004, Comput. Networks.

[14]  Ioan Filip,et al.  Markov models for wireless sensor network reliability , 2009, 2009 IEEE 5th International Conference on Intelligent Computer Communication and Processing.

[15]  Maria Antonieta Garcia,et al.  Modeling P2P-TV Traffic Using Hidden Markov Models , 2009, IEEE INFOCOM Workshops 2009.

[16]  Loon Ching Tang,et al.  Markov-Modulated Processes and Semiregenerative Phenomena , 2009 .

[17]  Hsiao-Hwa Chen,et al.  An Accurate Markov Model for Slotted CSMA/CA Algorithm in IEEE 802.15.4 Networks , 2008, IEEE Communications Letters.

[18]  Stephan Robert,et al.  Which Arrival Law Parameters Are Decisive for Queueing System Performance , 1994 .

[19]  António Pacheco,et al.  Markov-additive Processes of Arrivals , 1994 .

[20]  António Pacheco,et al.  Multiscale Fitting Procedure Using Markov Modulated Poisson Processes , 2003, Telecommun. Syst..

[21]  K. Meier-Hellstern.  A fitting algorithm for Markov-modulated poisson processes having two arrival rates , 1987 .

[22]  P. Skelly,et al.  A histogram-based model for video traffic behavior in an ATM multiplexer , 1993, TNET.

[23]  T. Aaron Gulliver,et al.  A Simple, Two-Level Markovian Traffic Model for IPTV Video Sources , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

[24]  Jean-Yves Le Boudec,et al.  New Models for Pseudo Self-Similar Traffic , 1997, Perform. Evaluation.

[25]  San-qi Li,et al.  On the convergence of traffic measurement and queueing analysis: a statistical-matching and queueing (SMAQ) tool , 1997, TNET.

[26]  António Pacheco,et al.  Modeling Self-similar Traffic through Markov Modulated Poisson Processes over Multiple Time Scales , 2003, HSNMC.

[27]  Jon W. Mark,et al.  Parameter estimation for Markov modulated Poisson processes via the EM algorithm with time discretization , 1993, Telecommun. Syst..

[28]  António Pacheco,et al.  A Hierarchical Approach based on MMPPs for Modeling Self-Similar Traffic over Multiple Time Scales , 2003 .

[29]  Anja Feldmann,et al.  Fitting mixtures of exponentials to long-tail distributions to analyze network performance models , 1997, Proceedings of INFOCOM '97.