  The intersecting pedestrian flow on the 2D lattice with random update rule is
studied. Each pedestrian has three moving directions without the back step.
Under periodic boundary conditions, an intermediate phase has been found at
which some pedestrians could move along the border of jamming stripes. We have
performed mean field analysis for the moving and intermediate phase
respectively. The analytical results agree with the simulation results well.
The empty site moves along the interface of jamming stripes when the system
only has one empty site. The average movement of empty site in one Monte Carlo
step (MCS) has been analyzed through the master equation. Under open boundary
conditions, the system exhibits moving and jamming phases. The critical
injection probability $\alpha_c$ shows nontrivially against the forward moving
probability $q$. The analytical results of average velocity, the density and
the flow rate against the injection probability in the moving phase also agree
with simulation results well.
