On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
Self-similarity in World Wide Web traffic: evidence and possible causes
IEEE/ACM Transactions on Networking (TON)
A Multiplicative Multifractal Model for TCP Traffic
ISCC '01 Proceedings of the Sixth IEEE Symposium on Computers and Communications
Performance Evaluation of Multi-Fractal Nature of TCP Traffic with RED Gateway
LCN '04 Proceedings of the 29th Annual IEEE International Conference on Local Computer Networks
Interaction of TCP flows as billiards
IEEE/ACM Transactions on Networking (TON)
Stability and Ergodicity of Piecewise Deterministic Markov Processes
SIAM Journal on Control and Optimization
Network and user driven alpha-beta on-off source model for network traffic
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Long range dependent trafic
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We consider a family of stochastic processes built from infinite sums of independent positive random functions on R+. Each of these functions increases linearly between two consecutive negative jumps, with the jump points following a Poisson point process on R+. The motivation for studying these processes stems from the fact that they constitute simplified models for TCP traffic. Such processes bear some analogy with Lévy processes, but aremore complex since their increments are neither stationary nor independent. In the work of Barral and Lévy Véhel, the Hausdorff multifractal spectrum of these processes was computed. We are interested here in their Large Deviation and Legendre multifractal spectra. These "statistical" spectra are seen to give, in this case, a richer information than the "geometrical" Hausdorff spectrum. In addition, our results provide a firm theoretical basis for the empirical discovery of the multifractal nature of TCP traffic.