The Effect Of On-Ramp And Off-Ramp On The One Dimensional Road With Open   Boundaries
  The effect of one on-ramp (entry) and one off-ramp (exit) is investigated numerically in one dimensional-cellular automaton traffic flow model, with open boundary conditions, using parallel dynamics. Our aim in this paper is to study how the injecting rates $\alpha$ and $\alpha_{0}$ and the extracting rates $\beta$ and $\beta_{0}$ acts on the density and flux of cars in one dimensional road. The priority of occupation at entry site $i_{1}$ (moving at exit site $i_{2}$) is attributed to the particle which entered (absorbed) in the chain. Phase diagrams in ($\beta_{0},\alpha_{0}$), and ($\beta,\alpha_{0}$) plans are established. For $\alpha=0.1$, they show three different topologies in the flow behaviour. The first one correspond to the presence of four regions, by varying $\alpha_{0}$; namely low density phase (LDP), intermediate density phase (IDP), plateau current phase (PCP) and high density phase (HDP). In the second topology the interdmediate density phase disappears. The third topology presents only two regions; i.e. low and high density phases. For small values of $\alpha$, the (IDP) and (PCP) disappears, respectively, by increasing $\beta$. When increasing $\alpha$, the forth topology, corresponding to one phase (HDP), appears for low values of $\beta$ and $\beta_{0}$ 
Abdelaziz Mhirech, Assia Alaoui Ismaili and Hamid Ez-Zahraouy