Queuing with future information

We study an admissions control problem, where a queue with service rate 1 − p receives incoming jobs at rate λ ∈ (1 − p,1), and the decision maker is allowed to redirect away jobs up to a rate of p, 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 ∼ log1/(1−p) 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 − p)/p, as λ→ 1. 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 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.