Totally Asymmetric Simple Exclusion Process with Entrance Rate sin(x)

In recently, traffic jams have become the focus and one used different approaches to study them. In this paper, the function of sin(x) is used to simulate the enter rate a of the peak period to work. The mean field approach has been used to calculate the phase diagrams and these results were compared with Monte Carlo simulations. They are good agreement. When traffic accidents occur at the exit, the exit rate beta will be less than 1 and traffic jams will occur. Different fixed the exit rate beta is used to calculate the additional energy consumption. The additional energy consumption will increase with the reducing of the exit rate beta.