We study an admissions control problem, where a queue with service rate 1βp
receives incoming jobs at rate Ξ»β(1βp,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 βΌlog1/(1βp)β1βΞ»1β, as Ξ»β1. In sharp contrast, when all future arrival and service times are revealed
beforehand, the optimal average queue length converges to a finite constant,
(1βp)/p, as Ξ»β1. We further show that the finite limit of (1βp)/p
can be achieved using only a finite lookahead window starting from the current
time frame, whose length scales as O(log1βΞ»1β), as
Ξ»β1. This leads to the conjecture of an interesting duality between
queuing delay and the amount of information about the future.Comment: Published in at http://dx.doi.org/10.1214/13-AAP973 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org