Annals of Applied Probability

Queuing with future information

Joel Spencer, Madhu Sudan, and Kuang Xu

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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.

Article information

Ann. Appl. Probab., Volume 24, Number 5 (2014), 2091-2142.

First available in Project Euclid: 26 June 2014

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Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B36: Scheduling theory, stochastic [See also 68M20]

Future information queuing theory admissions control resource pooling random walk online offline heavy-traffic asymptotics


Spencer, Joel; Sudan, Madhu; Xu, Kuang. Queuing with future information. Ann. Appl. Probab. 24 (2014), no. 5, 2091--2142. doi:10.1214/13-AAP973.

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