## Development of Dynamic Traffic Assignment Models for Planning ApplicationsAlthough solution algorithms are very well established for LP problems, the size of the problem that can be solved using the LP formulation is still limited by the power of mathematical programming solvers. To relax such limitations, the network structure within the LP formulations is explored to develop decomposition schemes. Such decomposition of the LP formulation can potentially allow us to solve DTA analytically on large size networks. In addition, insights into the problem can be obtained to help better understanding of the behavior of the transportation network under dynamic demand. |

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### Contents

Literature Review | 7 |

6 Decomposition Algorithms in Mathematical Programming | 35 |

Demand Modding for Dynamic Traﬂic Assignment | 41 |

Copyright | |

9 other sections not shown

### Common terms and phrases

applied arrival time based arrival time window assignment model assignment problem Average Travel based demand cell connectors cell representation cell transmission model Chapter combined model computational congestion Dantzig-Wolfe decomposition decomposition algorithm deﬁned demand matrix demand modeling demand pattem Demand Proﬁle departure time based desired arrival destination discussed dual variables dynamic trip entropy estimate exit function FIFO ﬁrst Flow conservation ﬂow pattem impact Indifferent Band interval Lagrangian multiplier Lagrangian Relaxation Late Arrivals linear programming link performance function LP formulation marginal cost master problem min-cost minutes node nonlinear programming Number of Iterations number of vehicles objective function Optimal Dual original problem penalties percentage proposed satisﬁed saturation ﬂow rates scenarios scheduled delays Section simulation-based model solution algorithm solve speciﬁcally sub-problem system performance temporal distribution Test Network time-dependent demand time-dependent departure total system travel total travel traﬁic travel cost trip distribution trip purposes user classes vehicles that arrive Ziliaskopoulos