## Abstract

We study an admissions control problem, where a queue with service rate 1 - p receives incoming jobs at rate λ ∈ (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 ~ log^{1/(1-p)}1 1-λ, as →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 →1. We further show that the finite limit of (1-p)/p can be achieve using only a finite lookahead window starting from the current time frame, whose length scales as O(log 1 1-λ ), as →1. This leads to the conjecture of an interesting duality between queuing delay and the amount of information about the future.

Original language | English (US) |
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Pages (from-to) | 2091-2142 |

Number of pages | 52 |

Journal | Annals of Applied Probability |

Volume | 24 |

Issue number | 5 |

DOIs | |

State | Published - Oct 2014 |

## Keywords

- Admissions control
- Future information
- Heavy-Traffic asymptotics
- Offline
- Online
- Queuing theory
- Random walk
- Resource pooling

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty