Off-ramp on Boundary of Totally Asymmetric Simple Exclusion Process with Different Hopping Rates

One-dimensional totally asymmetric simple exclusion process (TASEP) with off-ramp on boundary and different hopping rates (p) under random update rule has been studied in this paper. Here, the off-ramp is on a special site (the left boundary) which can be used to define the traffic diversion rate (q). Comparing with the early studies, the main difference lies in the fact that the phase diagrams and densities are decided by different hopping rates and off-ramp rates. The influences of parameters p and q on the phase diagrams are discussed. When p and q satisfy the relationship $p < 2(1-q)$, the MC phase exists in the system and the region declines when p increase with fixed p. On the contrary, the MC phase vanishes. Interestingly, when q is large enough $(q \rightarrow 1)$ and p is fixed, the HD phase vanishes, too. The result implies that the traffic diversion can reduce the jam on the deceleration road.