CALCULATION OF DYNAMIC TRAFFIC EQUILIBRIUM ASSIGNMENTS

Abstract

The calculation of dynamic equilibrium assignments of traffic is important in the analysis of congested road networks. The calculations involved are substantially more intricate than are the corresponding ones for static equilibria. Few authors have published details of dynamic equilibrium assignments; where details are given, some fail to achieve a good approximation to equilibrium whilst others generate assignments that are discontinuous in time. This paper addresses the issue of formulating dynamic traffic assignment in a way that is readily solvable and which leads to solutions that are of good quality and hence are plausible. Two aspects of the formulation have been found to be crucial in achieving this: these are the way in which time varying costs and flows are associated with each other in the mathematical condition that is solved for equilibrium, and the assumptions that are made implicitly about the continuity of the assigned flows. Simple test examples are considered that use small networks and simple demand profiles so that dynamic equilibrium assignments can be calculated directly. It is shown that use of the best general formulation will lead to good quality solutions that are close approximations to the known one. However, it is shown that relatively innocuous variations in the formulation, such as inappropriate association of flows with costs or assumption of continuous assignments, can lead to unsatisfactory and noisy solutions that are implausible. This work provides a possible explanation and remedy for the implausible character of many published dynamic assignments. For the covering abstract see ITRD E105584.

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