This study develops a predictive continuum dynamic user-optimal model for the simultaneous departure time and route choice problem through a variational inequality (VI) approach. A polycentric urban city with multiple central business districts (CBDs) is considered, and travelers are classified into different classes according to their destinations (i.e., CBDs). The road network within the modeling city is assumed to be sufficiently dense and can be viewed as a continuum. A predictive dynamic user-optimal (PDUO) model has been previously used to model traffic flow with a given traffic demand distribution, in which travelers choose the routes that minimize the actual travel cost to the CBD. In this work, we combine the departure time choice with the PDUO model to study the simultaneous departure time and route choice problem. The user-optimal departure time principle is satisfied, which states that for each origin–destination pair, the total costs incurred by travelers departing at any time are equal and minimized. We then present an equivalent VI and solve it using the projection method after discretization based on unstructured meshes. A numerical experiment for an urban city with two CBDs is presented to demonstrate the effectiveness of the numerical algorithm.
This work was jointly supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China [17208614], the National Natural Science Foundation of China [11272199 and 11672348], the National Basic Research Program of China [2012CB725404], and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) [NRF-2010-0029446].
