Traffic flow controlled by synchronized traffic lights in an open and periodic boundaries system

The traffic flow controlled by synchronized traffic lights on a single-lane roadway with open and periodic boundaries is studied. This study is based on a modified version of the Nagel and Schreckenberg (NaSch) (J. Phys. I (France), 2, 2221 (1992)) model recently proposed by Zhu et al. (Eur. Phys. J. B, 57, 103 (2007)) in parallel dynamics, which takes into account the sensitivity of drivers and vehicles. Five traffic lights are placed on the road at equal distances and are synchronized with a cycle time T. The density, flow, and (alpha, beta) phase diagrams are established for different values of T, where alpha and beta are the injecting and extracting rates, respectively, of cars in the traffic lane. In the deterministic NaSch model, the presence of signal lights on the road causes early onset of the high-density region. Additionally, it is shown that the low-density region shrinks with an increase in T, when T is less than a certain value. However, the modified NaSch model shows that the low density phase shrinks even more. Finally, in the presence of traffic lights, a comparison is made between the original NaSch model with a constant braking probability and the modified one.