Queuing with future information

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 $1-p$ 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 $\sim\log_{1/(1-p)}\frac{1}{1-\lambda}$, 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 $\lambda\to1$. 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 $\mathcal{O}(\log\frac{1}{1-\lambda})$, as $\lambda\to1$. This leads to the conjecture of an interesting duality between queuing delay and the amount of information about the future.