### 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) |
---|---|

Pages (from-to) | 2091-2142 |

Number of pages | 52 |

Journal | Annals of Applied Probability |

Volume | 24 |

Issue number | 5 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### 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

### Cite this

*Annals of Applied Probability*,

*24*(5), 2091-2142. https://doi.org/10.1214/13-AAP973

**Queuing with future information.** / Spencer, Joel; Sudan, Madhu; Xu, Kuang.

Research output: Contribution to journal › Article

*Annals of Applied Probability*, vol. 24, no. 5, pp. 2091-2142. https://doi.org/10.1214/13-AAP973

}

TY - JOUR

T1 - Queuing with future information

AU - Spencer, Joel

AU - Sudan, Madhu

AU - Xu, Kuang

PY - 2014

Y1 - 2014

N2 - 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 ~ log1/(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.

AB - 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 ~ log1/(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.

KW - Admissions control

KW - Future information

KW - Heavy-Traffic asymptotics

KW - Offline

KW - Online

KW - Queuing theory

KW - Random walk

KW - Resource pooling

UR - http://www.scopus.com/inward/record.url?scp=84903975922&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903975922&partnerID=8YFLogxK

U2 - 10.1214/13-AAP973

DO - 10.1214/13-AAP973

M3 - Article

AN - SCOPUS:84903975922

VL - 24

SP - 2091

EP - 2142

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 5

ER -