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October 2014 Queuing with future information
Joel Spencer, Madhu Sudan, Kuang Xu
Ann. Appl. Probab. 24(5): 2091-2142 (October 2014). DOI: 10.1214/13-AAP973

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 $\lambda\to1$. 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.

Citation

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Joel Spencer. Madhu Sudan. Kuang Xu. "Queuing with future information." Ann. Appl. Probab. 24 (5) 2091 - 2142, October 2014. https://doi.org/10.1214/13-AAP973

Information

Published: October 2014
First available in Project Euclid: 26 June 2014

zbMATH: 1309.60090
MathSciNet: MR3226173
Digital Object Identifier: 10.1214/13-AAP973

Subjects:
Primary: 60K25, 60K30, 68M20, 90B36

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.24 • No. 5 • October 2014
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