  Dynamic Traffic Assignment (DTA) provides an approach to determine the
optimal path and/or departure time based on the transportation network
characteristics and user behavior (e.g., selfish or social). In the literature,
most of the contributions study DTA problems without including traffic signal
control in the framework. The few contributions that report signal control
models are either mixed-integer or nonlinear formulations and computationally
intractable. The only continuous linear signal control method presented in the
literature is the Cycle-length Same as Discrete Time-interval (CSDT) control
scheme. This model entails a trade-off between cycle-length and cell-length.
Furthermore, this approach compromises accuracy and usability of the solutions.
  In this study, we propose a novel signal control model namely, Signal Control
with Realistic Cycle length (SCRC) which overcomes the trade-off between
cycle-length and cell-length and strikes a balance between complexity and
accuracy. The underlying idea of this model is to use a different time scale
for the cycle-length. This time scale can be set to any multiple of the time
slot of the Dynamic Network Loading (DNL) model (e.g. CTM, TTM, and LTM) and
enables us to set realistic lengths for the signal control cycles. Results
show, the SCRC model not only attains accuracy comparable to the CSDT model but
also more resilient against extreme traffic conditions. Furthermore, the
presented approach substantially reduces computational complexity and can
attain solution faster.
