### Abstract

The dynamic assignment model assumes flow moves towards cheaper routes at each time at a rate proportional to the product of the flow along the more expensive route and the cost difference. Therefore it is important for the cost function to be monotone so that convergence to equilibrium will occur. Conditions on the bottleneck output function are given for the bottleneck delay function to be monotone, which will imply monotonicity of the route coat function in the single bottleneck per route case.

It is shown that for reasonable bottleneck output functions, we have monotonicity of the product of link cost with a decaying exponential. This decay-monotonicity transfers to the route cost in certain given circumstances. This will in turn imply convergence of the dynamical system by applying Lyapunov's theorem using the appropriate Lyapunov function. It is then important to note that monotonicity of the route coat function implies decay-monotonicity of the route cost function and hence the convergence result is valid for the single bottleneck per route case with monotone link cost functions.

Original language | English |
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Title of host publication | IEEE 5TH INTERNATIONAL CONFERENCE ON INTELLIGENT TRANSPORTATION SYSTEMS, PROCEEDINGS |

Editors | RL Cheu, D Srinivasan, DH Lee |

Place of Publication | New York |

Publisher | IEEE Press |

Pages | 795-800 |

Number of pages | 6 |

ISBN (Print) | 0-7803-7389-8 |

DOIs | |

Publication status | Published - 2002 |

Event | IEEE 5th International Conference on Intelligent Transportation Systems - SINGAPORE, Singapore Duration: 3 Sep 2002 → 6 Sep 2002 |

### Conference

Conference | IEEE 5th International Conference on Intelligent Transportation Systems |
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Country | Singapore |

Period | 3/09/02 → 6/09/02 |

### Keywords

- convergence
- cost function
- mathematical model
- mathematics
- stability
- telecommunication traffic
- time measurement
- traffic control
- vehicle dynamics
- vehicles

## Cite this

*IEEE 5TH INTERNATIONAL CONFERENCE ON INTELLIGENT TRANSPORTATION SYSTEMS, PROCEEDINGS*(pp. 795-800). IEEE Press. https://doi.org/10.1109/ITSC.2002.1041321