Dynamic user optimal assignment with physical queues for a many-to-many OD pattern

This research extends the dynamic user optimal assignment under the point queue concept so as to deal with physical queues. Given time-dependent many-to-many OD volumes, this paper first shows the formulation of the assignment subject to the flow conservation and the first-in-first-out (FIFO) queue discipline. The optimal condition is then defined and the physical queue propagation based on the kinematic wave theory is discussed. Finally, a solution algorithm is proposed and typical differences between point and physical queue analyses are presented through an example calculation.