Large deviations theory and efficient simulation of excessive backlogs in a < e1 > GI < /e1 > / < e1 > GI < /e1 > / < e1 > m < /e1 > queue - Sadowsky, J S (IEEE transactions on automatic control, 1991)
The problem of using importance sampling to estimate the average time to buffer overflow in a stable < e1 > GI < /e1 > / < e1 > GI < /e1 > / < e1 > m < /e1 > queue is considered. Using the notion of busy cycles, estimation of the expected time to buffer overflow is reduced to the problem of estimating < e1 > p < /e1 > (n)= < e1 > P < /e1 > (buffer overflow during a cycle) where < e1 > n < /e1 > is the buffer size. The probability < e1 > p < /e1 > (n) is a large deviations probability ( < e1 > p < /e1 > (n) vanishes exponentially fast as < e1 > n < /e1 > - > {infinity}). A rigorous analysis of the method is presented. It is demonstrated that the exponentially twisted distribution of S. Parekh and J. Walrand (1989) has the following strong asymptotic-optimality property within the nonparametric class of all < e1 > GI < /e1 > / < e1 > GI < /e1 > importance sampling simulation distributions. As < e1 > n < /e1 > - > {infinity}, the computational cost of the optimal twisted distribution of large deviations theory grows less than exponentially fast, and conversely, all other < e1 > GI < /e1 > / < e1 > GI < /e1 > simulation distributions incur a computational cost that grows with strictly positive exponential rate