A simulation study on the relevant time scales of the input traffic for a tandem network

Network traffic processes can exhibit properties of self-similarity and long-range dependence, i.e., correlations over a wide range of time scales. However, as already shown by several authors for the case of a single queue, the second-order behavior at time scales beyond the so-called correlation horizon or critical time scale does not significantly affect network performance. In this work, we extend previous studies to the case of a network with two queuing stages, using discrete event simulation. Results show that the introduction of the second stage provokes a decrease in the correlation horizon of the input traffic, meaning that the range of time scales that need to be considered for accurate network performance evaluation is lower than predicted by a single stage model. We also resorted to simulation to evaluate the single queue model. In this case, the estimated correlation horizon values are compared with those predicted by a formula derived by Grossglauser and Bolot, which presumes the approximation of the input data by a traffic model that enables to control the autocorrelation function independently of first-order statistics. Results indicate that although the correlation horizon increases linearly with the buffer size in both methods, the simulation ones predict a lower increase rate.