Proceedings of the 2002 Winter Simulation Conference E. Yücesan, C.-H. Chen, J. L. Snowdon, and J. M. Charnes, eds. A HIGHLY EFFICIENT M/G/∞ MODEL FOR GENERATING SELF-SIMILAR TRACES María Estrella Sousa-Vieira Andrés Suárez-González Cándido López-García Manuel Fernández-Veiga José C. López-Ardao ETSE de Telecomunicación, Universidade de Vigo 36200 Vigo, SPAIN ABSTRACT Several traffic measurement reports have convincingly shown the presence of self-similarity in modern networks, inducing as a result a revolution in the stochastic modeling of traffic. The use of self-similar processes in performance analysis has opened new problems and research issues in simulation studies, where the efficient generation of syn- thetic sample paths with self-similar properties is one of the fundamental concerns. In this paper, we present an M/G/∞ generator of self-similar traces, based on a highly efficient simulation model using the decomposition property of Poisson processes. 1 INTRODUCTION Several traffic measurement studies (Leland et al. 1994, Garrett and Willinger 1994) have demonstrated the existence of statistical self-similarity in modern networks, along with a closely related property called Long-Range Dependence (LRD), that involves non negligible correlations over arbi- trarily large time scales. These findings have contributed to a very important revolution in the stochastic modeling of traffic, since the presence of LRD may have a drastic im- pact on the performance metrics (Likhanov, Tsybakov and Georganas 1995, Erramilli et al. 1996), and the validity of traditional processes, like Markovian or Autoregressive, is in doubt because modeling LRD through these processes requires many parameters, whose interpretation becomes difficult. Because of this, the use of self-similar processes for network traffic modeling purposes is essential, due to their capability to exhibit LRD over all time scales by making use of few parameters (parsimonious modeling). The application of self-similar processes in network simulation studies has opened a wide range of research topics dealing with new problems. One of the most important issues is the synthetic generation of sample paths of LRD processes, since real traces collected by measurements are of limited length and lack the necessary diversity required to make flexible enough simulation studies. A very interesting self-similar process is the occupancy process of an M/G/∞ queueing model, referred to as M/G/∞ process. It belongs to the class of LRD processes when G, the distribution of the service time, is heavy-tailed of infinite variance. Apart from its use in analytical studies, the M/G/∞ process has several important advantages for simulation studies, such as the possibility of on-line generation. Fur- thermore, there exists a trivial method of producing exact sample paths of the process with complexity O(n), being n the length of the sample path: it suffices to simulate the M/G/∞ queue, sampling the occupancy of the system at integer instants. Varying the service time distribution, G, many forms of time dependence can be obtained, which makes this process a good candidate for modeling many types of correlated traffic, such as video traffic (Krunz and Makowski 1998). In Suárez et al. (2002) the authors present a discrete random variable whose distribution (S distribution) is heavy-tailed with two parameters, a feature that enables the modeling of both short-term and long-term correlation behavior of the resulting M/S/∞ process. Despite its high flexibility, the marginal distribution of the M/G/∞ process is Poisson, which is not adequate to model the empirical marginal distribution of some real video sequences. So, we need to transform the Poisson marginal distribution of the M/G/∞ process into a more appropriate heavy-tailed form. However, small values of the arrival rate λ of the Poisson input process are inappropriate for the transformation process (Poon and Lo 2001) and, on the other hand, the complexity of the generator is an increasing function of λ. 2003