Linear Programming Formulations for System Optimum Dynamic Traffic Assignment with Arrival Time-Based and Departure Time-Based Demands

The system optimum dynamic traffic assignment problem, in which drivers fix their arrival rather than their departure times, is examined. A model is formulated as a linear program that simultaneously optimizes departure time and route choice. The model applies to multiorigin/multidestination problems, and the first-in-first-out condition is generally observed on the links and nodes of the network. An extension is discussed that accounts for combined departure time– and arrival time–based demand on the same network. The models are tested on an example network, and the results are discussed.