A framework for user equilibrium dynamic traffic assignment

Several analytic approaches have been developed to describe or predict traffic flows on networks with time–varying (dynamic) travel demands, flows and travel times. A key component of these models lies in modelling the flows and/or travel times on the individual links, but as this is made more realistic or accurate it tends to make the overall model less computationally tractable. To help overcome this, and for other reasons, we develop a bi–level user equilibrium (UE) framework that separates the assignment or loading of flows on the time–space network from the modelling of flows and trip times within individual links. We show that this model or framework satisfies appropriate definitions of UE satisfies a first–in–first–out (FIFO) property of road traffic, and has other desirable properties. The model can be solved by iterating between (a) a linear network–loading model that takes the lengths of time–space links as fixed (within narrow ranges), and (b) a set of link flow sub–models which update the link trip times to construct a new time–space network. This allows links to be processed sequentially or in parallel and avoids having to enumerate paths and compute path flows or travel times. We test and demonstrate the model and algorithms using example networks and find that the algorithm converges quickly and the solutions behave as expected. We show how to extend the model to handle elastic demands, multiple destinations and multiple traffic types, and traffic spillback within links and from link to link.