We study an admissions control problem, where a queue with service rate 1-p receives incoming jobs at rate \lambda\in(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 \log_{1/(1-p) 1/(1-\lambda)} 1{1-\lambda}} , as \lambda\to 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 \lambda %DIFDELCMD < \to %%% 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 %DIFDELCMD < \to %%% 1. \to1 This leads to the conjecture of an interesting duality between queuing delay and the amount of information about the future.
We study an admissions control problem, where a queue with service rate 1-p receives incoming jobs at rate \lambda\in(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 1/(1-\lambda)} \sim\log_{1/(1-p)1{1-\lambda}} , as \lambda\to 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 \lambda %DIFDELCMD < \to %%% \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 %DIFDELCMD < \to %%% \to1. This leads to the conjecture of an interesting duality between queuing delay and the amount of information about the future.
D
\log_{1/(1-p)
A
\sim\log_{1/(1-p)
D
1.
A
.
R
\log 1/(1-\lambda
\mathcal{O
D
1.
A
.