%0 Book Section %1 Heyman2001445 %A Heyman, Daniel %A Lucantoni, David %B Teletraffic Engineering in the Internet EraProceedings of the International Teletraffic Congress - ITC-I7 %D 2001 %E Jorge Moreira de Souza, Nelson L.S. da Fonseca %E de Souza e Silva, Edmundo A. %I Elsevier %K itc itc17 %P 445 - 456 %R http://dx.doi.org/10.1016/S1388-3437(01)80142-6 %T Modeling multiple \IP\ traffic streams with rate limits %V 4 %X We start with the premise, and provide evidence that it's valid. that a Markov modulated Poisson process (MMPP) is a good model for Internet traffic at the packet/byte level. We present an algorithm to estimate the size, and parameters, of a discrete \MMPP\ from a data trace. This algorithm requires only two passes through the data. In tandem-network queueing models, the input to a downstream queue is the output from an upstream queue, so the arrival rate is limited by the rate of the upstream queue. We show how to modify the \MMPP\ describing the arrivals to the upstream queue to approximate this effect. To extend this idea to networks that aren't tandem, we show how to approximate the superposition of \MMPPs\ describing the arrivals to the upstream queue to approximate this effect. To extend this idea to networks that arent's tandem, we show how to approximate the superposition of \MMPPs\ without encountering the state-space explosion that occurs in exact computations. Numerical examples that demonstrate the accuracy of these methods are given. We also present a method to convert our estimated discrete \MMPP\ to a continuous-time MMPP, which is used as the arrival process in a matrix-analytic queueing model for performance prediction.

@incollection{Heyman2001445, abstract = {We start with the premise, and provide evidence that it's valid. that a Markov modulated Poisson process (MMPP) is a good model for Internet traffic at the packet/byte level. We present an algorithm to estimate the size, and parameters, of a discrete \MMPP\ from a data trace. This algorithm requires only two passes through the data. In tandem-network queueing models, the input to a downstream queue is the output from an upstream queue, so the arrival rate is limited by the rate of the upstream queue. We show how to modify the \MMPP\ describing the arrivals to the upstream queue to approximate this effect. To extend this idea to networks that aren't tandem, we show how to approximate the superposition of \MMPPs\ describing the arrivals to the upstream queue to approximate this effect. To extend this idea to networks that arent's tandem, we show how to approximate the superposition of \MMPPs\ without encountering the state-space explosion that occurs in exact computations. Numerical examples that demonstrate the accuracy of these methods are given. We also present a method to convert our estimated discrete \MMPP\ to a continuous-time MMPP, which is used as the arrival process in a matrix-analytic queueing model for performance prediction. }, added-at = {2016-07-12T14:53:52.000+0200}, author = {Heyman, Daniel and Lucantoni, David}, biburl = {https://www.bibsonomy.org/bibtex/292953c023c16ae9ccd4eb443f9601b3e/itc}, booktitle = {Teletraffic Engineering in the Internet EraProceedings of the International Teletraffic Congress - ITC-I7}, doi = {http://dx.doi.org/10.1016/S1388-3437(01)80142-6}, editor = {Jorge Moreira de Souza, Nelson L.S. da Fonseca and de Souza e Silva, Edmundo A.}, interhash = {934b63e066c24861d7a6695019075952}, intrahash = {92953c023c16ae9ccd4eb443f9601b3e}, issn = {1388-3437}, keywords = {itc itc17}, pages = {445 - 456}, publisher = {Elsevier}, series = {Teletraffic Science and Engineering }, timestamp = {2020-04-30T18:17:29.000+0200}, title = {Modeling multiple \IP\ traffic streams with rate limits }, volume = 4, year = 2001 }