Modeling multifractal traffic with stochastic L-systems

Salvador, Paulo; Nogueira, António; Valadas, Rui

doi:10.1109/glocom.2002.1189084

Cited by 9 publications

(9 citation statements)

References 12 publications

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“…Accurate modeling of IP traffic requires matching closely not only the packet arrival process but also the packet size distribution. Surprisingly, while the arrival process has received considerable attention [1][2][3][4][5][6][7][8][9][10], very few works have addressed the packet size distribution and, more so, its joint characterization with the arrival process [11,12]. However, as it will be made clear in this paper, a joint characterization is required for accurate prediction of the queuing behavior (i.e., the packet loss ratio or average packet delay observed in a queuing system).…”

Section: Introductionmentioning

confidence: 99%

Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs

2004

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This paper proposes a traffic model and a parameter fitting procedure that are capable of achieving accurate prediction of the queuing behavior for IP traffic exhibiting long-range dependence. The modeling process is a discrete-time batch Markovian arrival process (dBMAP) that jointly characterizes the packet arrival process and the packet size distribution. In the proposed dBMAP, packet arrivals occur according to a discrete-time Markov modulated Poisson process (dMMPP) and each arrival is characterized by a packet size with a general distribution that may depend on the phase of the dMMPP. The fitting procedure is designed to provide a close match of both the autocovariance and the marginal distribution of the packet arrival process, using a dMMPP; a packet size distribution is fitted individually to each state of the dMMPP. A major feature of the procedure is that the number of states of the fitted dBMAP is not fixed a priori; it is determined as part of the procedure itself. In this way, the procedure allows establishing a compromise between the accuracy of the fitting and the number of parameters, while maintaining a low computational complexity.We apply the inference procedure to several traffic traces exhibiting long-range dependence. Very good results were obtained since the fitted dBMAPs match closely the autocovariance, the marginal distribution and the queuing behavior of the measured traces. Our results also show that ignoring the packet size distribution and its correlation with the packet arrival process can lead to large errors in terms of queuing behavior.

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Section: Introductionmentioning

confidence: 99%

Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs

2004

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“…A natural axiom for this model is the average packet arrival rate (computed over all time intervals of interest), which must then be included in the alphabet of arrival rates. This model was introduced in [7].…”

Section: L-systems Backgroundmentioning

confidence: 99%

“…In [7] we have introduced the use of stochastic Lindenmayer-Systems (hereafter referred to as L-Systems) as a model for network traffic. In this paper, we propose a new modeling approach based on stochastic L-Systems, and its associated parameter fitting procedure, which jointly characterizes the packet arrival and packet size processes.…”

Section: Introductionmentioning

confidence: 99%

Joint characterization of the packet arrival and packet size processes of multifractal traffic based on stochastic L-systems

Salvador¹,

Nogueira²,

Valadas³

2003

Providing Quality of Service in Heterogeneous Environments, Proceedings of the 18th International Teletraffic Congress - ITC-18

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Multifractal behavior was recently observed in several traces of IP WAN traffic. This paper proposes a novel multifractal traffic model, which characterizes the joint process of packet arrivals and packet sizes. The construction of the traffic process is based on stochastic L-Systems, which were introduced by biologist A. Lindenmayer as a method to model plant growth. We work with a single L-System alphabet and production rule, where the alphabet is a set of pairs, and each pair element represents a packet arrival rate and a packet mean size. In this way, the traffic model is able to capture correlations between arrivals and sizes, leading to an accurate prediction of the queuing behavior. We provide a detailed comparison with a related multifractal model based on conservative cascades. Our results, that include applying the fitting procedure to real observed data with multifractal scaling behavior on both the packet arrival and packet size processes, show that our L-System based model can achieve excellent fitting performance in terms of first and second order statistics and queuing behavior.

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“…On the other hand, the fitting procedures for MMPPs with an arbitrary number of states mainly concentrate on matching first-and/ or second-order statistics, without addressing directly the issue of modeling over multiple time scales. The application of stochastic L-Systems in the characterization of packet arrival processes was first introduced by the authors in [15], with very good fitting results.…”

Section: Introductionmentioning

confidence: 98%

Modeling self-similar traffic over multiple time scales based on hierarchical Markovian and L-System models

Nogueira

Salvador

Valadas

et al. 2010

Computer Communications

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Modeling multifractal traffic with stochastic L-systems

Cited by 9 publications

References 12 publications

Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs

Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs

Joint characterization of the packet arrival and packet size processes of multifractal traffic based on stochastic L-systems

Modeling self-similar traffic over multiple time scales based on hierarchical Markovian and L-System models

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