Before revision:  the optimal average queue length converges to a finite constant, (1-p)/p, as \lambda  1. \to1 We further show that the finite limit of (1-p)/p can be achieved using only a finite lookahead window starting from the current time frame, whose length scales as \log 1/(1-\lambda(\log1{1-\lambda}} ), as \lambda  1. \to1 This leads to the conjecture of an interesting duality between queuing delay and the amount of information about the future.
After revision:  the optimal average queue length converges to a finite constant, (1-p)/p, as \lambda  1. \to1 We further show that the finite limit of (1-p)/p can be achieved using only a finite lookahead window starting from the current time frame, whose length scales as \mathcal{O(\log1{1-\lambda}} ), as \lambda  1. \to1 This leads to the conjecture of an interesting duality between queuing delay and the amount of information about the future.