The continuous signalized (COS) node model for dynamic traffic assignment

•A specific “cycle-averaged” interpretation of “continuous signal modeling” for time-aggregated of traffic signal boundary conditions and turn movements is presented, which complies with the logic behind it.•Regarding the above-mentioned specific interpretation requirements of a continuous signalized node model are presented and mathematically formulated, which define the continuous signalized (or COS) node model.•A convergent algorithm that solves COS numerically is presented.•Via a series of simple numerical cases it is showed that COS is the only continuous signalized node model that respects all the relevant boundary conditions.