## Abstract

We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partitions the time horizon to intervals in which constant fluid flow rates are maintained. We then use a policy by which the queueing network tracks the fluid solution. To that end we model the deviations between the queuing and the fluid network in each of the intervals by a multi-class queueing network with some infinite virtual queues. We then keep these deviations stable by an adaptation of a maximum pressure policy. We show that this method is asymptotically optimal when the number of items that is processed and the processing speed increase. We illustrate these results through a simple example of a three stage re-entrant line.

Original language | English |
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Pages (from-to) | 233-249 |

Number of pages | 17 |

Journal | Annals of Operations Research |

Volume | 170 |

Issue number | 1 |

DOIs | |

State | Published - Sep 2009 |

### Bibliographical note

Funding Information:Research supported in part by Israel Science Foundation Grant 249/02 and 454/05 and by European Network of Excellence Euro-NGI.

## Keywords

- Continuous linear programming
- Fluid approximations
- Infinite virtual queues
- Maximum pressure policies
- Multi-class queueing networks
- Queueing control

## ASJC Scopus subject areas

- Decision Sciences (all)
- Management Science and Operations Research