### Abstract

We consider a single server system with N input flows. We assume that each flow has stationary increments and satisfies a sample path large deviation principle, and that the system is stable. We introduce the largest weighted delay first (LWDF) queueing discipline associated with any given weight vector α = (α_{1}, . . ., α_{N}). We show that under the LWDF discipline the sequence of scaled stationary distributions of the delay ŵ_{i} of each flow satisfies a large deviation principle with the rate function given by a finite-dimensional optimization problem. We also prove that the LWDF discipline is optimal in the sense that it maximizes the quantity ^{min}_{i=1, ..., N} [α_{i} ^{lim}_{n→∞} -1/n log P(ŵ_{i} > n)], within a large class of work conserving disciplines.

Original language | English (US) |
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Pages (from-to) | 1-48 |

Number of pages | 48 |

Journal | Annals of Applied Probability |

Volume | 11 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2001 |

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### Keywords

- Control
- Earliest deadline first (EDF)
- Fluid limit
- LWDF
- Large deviations
- Optimality
- Quality of service (QoS)
- Queueing delay
- Queueing theory
- Rate function
- Scheduling

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Annals of Applied Probability*,

*11*(1), 1-48. https://doi.org/10.1214/aoap/998926986