A link flow formulation and a convergent solution algorithm for the dynamic user equilibrium (due) traffic assignment problem for road networks with multiple trip origins and destinations are presented. The link flow formulation does not implicitly assume complete enumeration of all origin-destination paths as does the equivalent pathflow formulation. Due is a temporal generalization of the static user equilibrium (sue) assignment problem with additional constraints to ensure temporally continuous paths of flow. Whereas sue can be solved by methods of linear combinations, these methods can create temporally discontinuous flows if applied to due. This convergent dynamic algorithm (cda) uses the frank-wolfe method of linear combinations to find successive solutions to due while holding node time intervals fixed from each origin. In due, the full assignment period of several hours is discretized into shorter time intervals of 10 to 15 min each, for which trip departure matrices are assumed to be known. The performance of cda is compared with that of a heuristic solutionprocedure called dta. Cda can be applied to solving due on large networks, and the examples presented show that cda consistently converges to solutions that closely satisfy the due optimality conditions.With computational advances such as parallel computing, cda can be run in near real-time on large-scale networks and used with in-vehicle route advisory systems for traffic management during evacuations and special events. This paper appears in transportation research record no. 1328, Travel demand forecasting: new methodologies and travel behavior research 1991
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