Queueing with future information

We study an admissions control problem, where a queue with service rate 1 - <i>p</i> receives incoming jobs at rate λ ε (1?<i>p</i>, 1), and the decision maker is allowed to redirect away jobs up to a rate of <i>p</i>, with the objective of minimizing the time-average queue length. We show that the amount of information about the future has a significant impact on system performance, in the heavy-traffic regime. When the future is unknown, the optimal average queue length diverges at rate ~ log _1/1-<i>p</i> 1/1-λ, as λ → 1. In sharp contrast, when all future arrival and service times are revealed beforehand, the optimal average queue length converges to a finite constant, (1 - <i>p</i>)/<i>p</i>, as λ → 1. We further show that the finite limit of (1 - <i>p</i>)/<i>p</i> can be achieved using only a finite lookahead window starting from the current time frame, whose length scales as O(log 1/1-λ), as λ → 1. This leads to the conjecture of an interesting duality between queuing delay and the amount of information about the future.