Performance Evaluation 40 (2000) 71–98 Use of α -stable self-similar stochastic processes for modeling traffic in broadband networks  José R. Gallardo a,∗ , Dimitrios Makrakis a , Luis Orozco-Barbosa b a Advanced Communications Engineering Centre — ACEC, Department of Electrical and Computer Engineering, The University of Western Ontario, London, Ont., Canada N6A 5B9 b Department of Electrical Engineering, University of Ottawa, Ottawa, Ont., Canada K1N 6N5 Abstract In this article, we propose a new model for aggregate network traffic. This model, besides reflecting self-similarity and long-range dependence, is able to capture the appropriate level of burstiness of different types of traffic by selecting the proper parameters. Different types of self-similar traffic traces (LAN/WAN, WWW, VBR video) are analysed by estimating their self-similarity coefficient H, as well as the parameters of their marginal distributions. When comparing the real traces with our artificial traces, the agreement, which was evaluated both qualitatively (visually) and quantitatively (by means of the marginal CDF and the periodogram), is better than that achieved with previously proposed models. By analysing different types of traffic traces, the model is shown to be flexible enough to be applied to a variety of communications scenarios. A queue with our proposed traffic as input is analysed. A proof of convergence of aggregate traffic to α-stable processes is also included, as well as the conditions under which the Gaussian assumption is appropriate. ©2000 Elsevier Science B.V. All rights reserved. Keywords: Traffic modeling; α-stable distributions; Self-similar processes; Long-range dependence 1. Introduction The modern telecommunication networks constitute large and complex systems. The always-increasing need of expansion to reach more and more users, and the great degree of sophistication incorporated in the operation of these networks aimed at optimizing the resource utilization, contribute to a permanent increase in complexity. For this reason, simulation is used quite extensively these days in the planning process of telecommunications networks. It is also used to analyse the performance of the various elements of the network under specific conditions. Simulation allows the network designer to draw important conclusions and make the right decisions before major capital investments are made. Theoretical and mathematical  An earlier version of this paper was presented at the Performance and Control of Network Systems II Conference, in: Wai Sum Lai, Robert B. Cooper (Eds.), Proceedings of SPIE (The International Society for Optical Engineering), Vol. 3530, Boston, Mass., 2–4 November 1998. ∗ Corresponding author. Tel.: +1-519-661-2111 ext. 88295, 88243; fax: +1-519-661-3488. E-mail addresses: gallajo@engga.uwo.ca (J.R. Gallardo), dimitris@engga.uwo.ca (D. Makrakis), lbarbosa@uottawa.ca (L. Orozco-Barbosa) 0166-5316/00/$ – see front matter ©2000 Elsevier Science B.V. All rights reserved. PII:S0166-5316(99)00070-X