Queuing with future information
Joel Spencer, Madhu Sudan, Kuang Xu

TL;DR
This paper investigates how future information affects queue management, showing that knowing the future drastically reduces average queue length in heavy traffic, with a finite lookahead window nearly matching full future knowledge.
Contribution
It demonstrates the significant impact of future information on queue performance and introduces a finite lookahead window that approximates full future knowledge.
Findings
Unknown future leads to logarithmic divergence in queue length as traffic intensifies.
Full future knowledge results in a finite, constant average queue length.
A finite lookahead window of logarithmic size achieves near-optimal queue performance.
Abstract
We study an admissions control problem, where a queue with service rate receives incoming jobs at rate , and the decision maker is allowed to redirect away jobs up to a rate of , 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 , as . In sharp contrast, when all future arrival and service times are revealed beforehand, the optimal average queue length converges to a finite constant, , as . We further show that the finite limit of can be achieved using only a finite lookahead window starting from the current time frame, whose length scales as…
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