On the efficiency of bridge Monte-Carlo estimator

Long-term correlation is a key feature of traffic flows and has a deep impact on network performance. Indeed, the arrival rate can persist on relatively high values for a considerable amount of time, provoking long busy periods and possibly bursts of lost packets. The authors focus on Gaussian processes, well-recognized and flexible traffic models, and consider the probability that the normalized cumulative workload grows at least as the length $T$ of the considered interval. As $T$ increases, such event becomes rare and ad-hoc techniques should be used to estimate its probability. To this aim, the authors present a variant of the well-known conditional Monte-Carlo (MC) method, in which the target probability is expressed as a function of the corresponding bridge process. In more detail, they derive the analytical expression of the estimator, verify its effectiveness through simulations (for different sets of parameters), and investigate the effects of the discretization step.