We introduce a general non-Gaussian, self-similar, stochastic process called the fractional Lévy motion (fLm). We formally expand the family of traditional fractal network traffic models, by including the fLm process. The main findings are the probability density function of the fLm process, several scaling results related to a single-server infinite buffer queue fed by fLm traffic, e.g., scaling of the queue length, and its distribution, scaling of the queuing delay when independent fLm streams are multiplexed, and an asymptotic lower bound for the probability of overflow (decreases hyperbolically as a function of the buffer size).

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Keywords Fractal queueing theory, Heavy-tailed distribution, Scaling, Self-similarity
Persistent URL dx.doi.org/10.1016/S1389-1286(02)00300-6
Journal Computer Networks
Laskin, N., Lambadaris, I, Harmantzis, F.C., & Devetsikiotis, M. (2002). Fractional Lévy motion and its application to network traffic modeling. Computer Networks, 40(3), 363–375. doi:10.1016/S1389-1286(02)00300-6