A Practical Equilibrium Dynamic Assignment Model for Planners

A Practical Equilibrium Dynamic Assignment Model for Planners


S Gao, J Brandon, A Rabinowicz, Caliper Corporation, US


This paper describes a practical equilibrium dynamic traffic assignment model that can directly replace the static models on existing large regional planning networks, with spillbacks and turn restrictions realistically considered.


It is generally understood that static traffic assignment models can give poor estimates of network link flows and origin to destination travel times. A static assignment model assumes steady-state traffic conditions over the study period, preferably designated as AM or PM peak period or a peak hour. However, during highly congested peak hours, the assumption of steady-state conditions (or that traffic quantities do not change over time) is questionable. Furthermore, static models cannot satisfactorily describe inherently transient queues and spillbacks, which contribute significantly to traffic congestion.

However, it has been difficult to apply dynamic traffic assignment (DTA) methods to networks of the size and geographic scale used in large regional models. Some simplified dynamic models exhibit inconsistent behavior and more elaborate models may require too much memory or have running times that are impractically long. This paper describes a practical equilibrium dynamic traffic assignment model that can directly replace the static models on large existing planning networks. This method incorporates spillback and turn restrictions and should give more realistic assignment results. It takes as input origin-destination (OD) trip departures by time period and outputs dynamic link flows, link costs, spillbacks and other variables of interest.

The DTA model is formulated as a constrained optimization problem whose solution closely satisfies a temporal extension of Wardrop?s first principle (user equilibrium), i.e. all used paths between a given OD pair for the same departure time have the same and minimum experienced travel time. The solution algorithm contains two levels of iterative processes. An outer process solves for a consistent node-time-arrival matrix that governs the dynamic propagation of OD flows in the network (and can be roughly viewed as a temporal extension of the link-path incidence matrix in a static assignment problem); the inner process solves for a user equilibrium for a given node-time-arrival matrix. When both iterative processes converge, dynamic user equilibrium is reached for a node-time-arrival matrix consistent with actual link travel times. The DTA model is also extended to calculate dynamic system optimal solutions.

Application of the model to several large regional networks is described, including the Dallas-Ft. Worth network with more than 4,800 zones, 62,000 links, and 22,400 nodes. An empirical comparison of the static and dynamic models illustrates the differences in results generated by these approaches. An emergency evacuation planning case study is carried out, where emergency management agencies need to designate evacuation destinations and routes to meet system-level objectives, e.g. minimizing total evacuation time.


Association for European Transport