Effect of bypasses on vehicular traffic through a series of signals

We study the dynamic motion of a vehicle moving through the series of traffic signals on a roadway with bypasses. A vehicle moves on either main roadway or bypass. There are all signals on the main roadway and signals are controlled by both cycle time and phase difference. The dynamic model of the vehicular motion is described in terms of the nonlinear map. The vehicular motion is studied on the roadway with bypasses and without bypasses. The vehicular motion changes highly by the signal control on the roadway with bypasses. It is found that the travel time decreases highly by the use of bypasses for specific values of cycle time but does not change for other values of cycle time. Also, the dependence of the travel time on the cycle time is derived at the green-wave strategy.