## Abstract

This paper presents a routing control method for packet-switched networks using an algebraic-topological framework. Our approach is a two-step paradigm. The outer loop control finds the global optimal steady-state routing strategy consistent with the average network inputs and outputs. The inner-loop control corrects for deviations from the steady-state flow by using high-bandwidth, real-time feedbacks of queueing states. The resulting formulation in the algebraic-topological framework allows us to find acyclic (loop-free) stable solutions that are optimal with respect to cost functions. We show how these optimal solutions may be computed using distributed algorithms, where each node updates its own routing table autonomously based on local information. Simulation results for 10-node and 100-node examples are shown to validate the algorithm concept.

Original language | English (US) |
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Pages (from-to) | 241-274 |

Number of pages | 34 |

Journal | Operations Research/ Computer Science Interfaces Series |

Volume | 33 |

DOIs | |

State | Published - 2006 |

Externally published | Yes |

## Keywords

- Algebraic topology
- Distributed control
- Dynamic inversion
- Graph theory
- Quadratic cost function
- Routing
- Steady-state routing strategy