On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Analysis, modeling and generation of self-similar VBR video traffic
SIGCOMM '94 Proceedings of the conference on Communications architectures, protocols and applications
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
IEEE/ACM Transactions on Networking (TON)
SIAM Journal on Scientific Computing
Proof of a fundamental result in self-similar traffic modeling
ACM SIGCOMM Computer Communication Review
Fast, approximate synthesis of fractional Gaussian noise for generating self-similar network traffic
ACM SIGCOMM Computer Communication Review
Self-similarity in World Wide Web traffic: evidence and possible causes
IEEE/ACM Transactions on Networking (TON)
Performance evaluation of a queue fed by a Poisson Pareto burst process
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic
Fractal traffic: measurements, modelling and performance evaluation
INFOCOM '95 Proceedings of the Fourteenth Annual Joint Conference of the IEEE Computer and Communication Societies (Vol. 3)-Volume - Volume 3
Modeling multiple IP traffic streams with rate limits
IEEE/ACM Transactions on Networking (TON)
Predicting properties of congestion events for a queueing system with fBm traffic
IEEE/ACM Transactions on Networking (TON)
Performance analysis of a Poisson-Pareto queue over the full range of system parameters
Computer Networks: The International Journal of Computer and Telecommunications Networking
Sample path bounds for long memory FBM traffic
INFOCOM'10 Proceedings of the 29th conference on Information communications
Wavelet analysis of long-range-dependent traffic
IEEE Transactions on Information Theory
A wavelet-based joint estimator of the parameters of long-range dependence
IEEE Transactions on Information Theory
On the correlation structure of the wavelet coefficients of fractional Brownian motion
IEEE Transactions on Information Theory
IEEE Journal on Selected Areas in Communications
On the use of fractional Brownian motion in the theory of connectionless networks
IEEE Journal on Selected Areas in Communications
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The Fractional Brownian motion (fBm) traffic model is important because it captures the self-similar characteristics of Internet traffic, accurately represents traffic generated as an aggregate of many sources, which is a prevalent characteristic of many Internet traffic streams, and, as we show in this paper, it is amenable to analysis. This paper introduces a new, simple, closed-form approximation for the stationary workload distribution (virtual waiting time) of a single server queue fed by an fBm input. Next, an efficient approach for producing a sequence of simulations with finer and finer detail of the fBm process is introduced and applied to demonstrate good agreement between the new formula and the simulation results. This method is necessary in order to ensure that the discrete-time simulation accurately models the continuous-time fBm queueing process. Then we study the limitations of the fBm process as a traffic model using two benchmark models - the Poisson Pareto Burst Process model and a truncated version of the fBm. We determine by numerical experiments the region where the fBm can serve as an accurate traffic model. These experiments show that when the level of multiplexing is sufficient, fBm is an accurate model for the traffic on links in the core of an internet. Using our result for the workload distribution, we derive a closed-form expression for service rate provisioning when the desired blocking probability as a measure of quality of service is given, and apply this result to a range of examples. Finally, we validate our fBm-based overflow probability and link dimensioning formulae using results based on a queue fed by a real traffic trace as a benchmark and demonstrate an advantage for the range of overflow probability below 1% over traffic modelling based on the Markov modulated Poisson process.