Analyzing the relevant time scales in a network of queues

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 second stage provokes a decrease in the correlation horizon, 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 used 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.