The investigation of the reentrance phenomenon in cellular automaton traffic flow model

- A new injection strategy in the Nagel-Schreckenberg model with open boundaries is proposed.
- A reentrance phenomenon of the low density phase for high injection rates is found.
- The reentrance phenomenon is due to the frustration of the injected vehicle.
- The in-flow and the system capacity explain the observed phase transitions.

We investigate analytically and by numerical simulations, the reentrant low density phase for high injection rate in the Nagel-Schreckenberg model. It is found that the reentrance phenomenon is a direct consequence of our injection strategy. Indeed, by adopting our injection rule, an injection rate exists, above which the in-flow begins to decrease by increasing the injection rate. In addition, we have studied the extraction rate interval at which the reentrance of the low density phase appears. It is found that this interval increases with increasing the maximal velocity. For the non deterministic case, the reentrance interval shifts to higher values of extraction rate.