### Abstract

A Jackson-like network that supports J types of interactive traffic (e.g., interactive messages) as well as I types of noninteractive traffic (e.g., file transfers, facsimile) is considered. The service-time distributions and the internal routing are homogeneous for all traffic types but can be node (queue) dependent. The problem is to find a scheduling control that minimizes a weighted sum of the average end-to-end delay for the interactive types and at the same time ensures that the average end-to-end delays for the interactive types will be below given design constraints. Conservation laws are first established and shown to yield the base of a polymatroid. The optimal control problem is then transformed into a linear program with the feasible region being the polymatroid base truncated by delay constraints. An optimal control is identified that partitions the traffic types into I + r (0 ≤ r ≤ J) ordered groups and applies a strict priority rule among the groups. An algorithm is developed that does the grouping and solves the optimization problem. A decentralized implementation of the optimal control is also discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 47-53 |

Number of pages | 7 |

Journal | IEEE Transactions on Automatic Control |

Volume | 34 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1989 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Automatic Control*,

*34*(1), 47-53. https://doi.org/10.1109/9.8648

**Optimal dynamic scheduling in Jackson networks.** / Ross, Keith; Yao, David D.

Research output: Contribution to journal › Article

*IEEE Transactions on Automatic Control*, vol. 34, no. 1, pp. 47-53. https://doi.org/10.1109/9.8648

}

TY - JOUR

T1 - Optimal dynamic scheduling in Jackson networks

AU - Ross, Keith

AU - Yao, David D.

PY - 1989/1

Y1 - 1989/1

N2 - A Jackson-like network that supports J types of interactive traffic (e.g., interactive messages) as well as I types of noninteractive traffic (e.g., file transfers, facsimile) is considered. The service-time distributions and the internal routing are homogeneous for all traffic types but can be node (queue) dependent. The problem is to find a scheduling control that minimizes a weighted sum of the average end-to-end delay for the interactive types and at the same time ensures that the average end-to-end delays for the interactive types will be below given design constraints. Conservation laws are first established and shown to yield the base of a polymatroid. The optimal control problem is then transformed into a linear program with the feasible region being the polymatroid base truncated by delay constraints. An optimal control is identified that partitions the traffic types into I + r (0 ≤ r ≤ J) ordered groups and applies a strict priority rule among the groups. An algorithm is developed that does the grouping and solves the optimization problem. A decentralized implementation of the optimal control is also discussed.

AB - A Jackson-like network that supports J types of interactive traffic (e.g., interactive messages) as well as I types of noninteractive traffic (e.g., file transfers, facsimile) is considered. The service-time distributions and the internal routing are homogeneous for all traffic types but can be node (queue) dependent. The problem is to find a scheduling control that minimizes a weighted sum of the average end-to-end delay for the interactive types and at the same time ensures that the average end-to-end delays for the interactive types will be below given design constraints. Conservation laws are first established and shown to yield the base of a polymatroid. The optimal control problem is then transformed into a linear program with the feasible region being the polymatroid base truncated by delay constraints. An optimal control is identified that partitions the traffic types into I + r (0 ≤ r ≤ J) ordered groups and applies a strict priority rule among the groups. An algorithm is developed that does the grouping and solves the optimization problem. A decentralized implementation of the optimal control is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=0024479154&partnerID=8YFLogxK

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U2 - 10.1109/9.8648

DO - 10.1109/9.8648

M3 - Article

VL - 34

SP - 47

EP - 53

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 1

ER -