On the use of a bridge process in a conditional monte carlo simulation of Gaussian queues

In spite of their low frequency, rare events often play a major role in determining systems performance. In most cases they can be analysed only through simulation with ad-hoc techniques since traditional Monte Carlo approaches are quite inefficient in terms of simulation length and/or estimation accuracy. Among rare event simulation techniques, conditional Monte Carlo is an interesting approach as it always leads to variance reduction. Unfortunately, it is often impossible, or at least very difficult, to find a suitable conditioning strategy. To tackle this issue, the applicability of a bridge process is proposed in the case of queueing systems with Gaussian inputs. In more detail, overflow probability and busy-period length are investigated and the analytical expressions of the corresponding estimators are derived. Finally, the effectiveness of the proposed approach is investigated through simulations.