Reply to "Comment on 'Analytical investigation of the open boundary conditions in the Nagel-Schreckenberg model' ".

Recent reports [N. Jia and S. Ma, Phys. Rev. E 79, 031115 (2009); T. Neumann and P. Wagner, Phys. Rev. E 80, 013101 (2009)] have different opinions on the exact analytical solution of the inflow in the Nagel-Schreckenberg model with expanded left boundary condition. In the current study, the different implementations of the "expanded left boundary" are proven to cause the confliction. Detailed analyses show that both reports are reasonable, depending on whether the rule "clear the minisystem first" is applied.