A lattice-gas model of biased-random walkers is used to simulate the escaping pedestrian flow under the open boundary condition in corridor. Given that the total number of people is unchanging, we have studied the evolution of pedestrian flow by varying parameters of system size. Relationships between parameters of system size and the transition time are discussed in this paper. Scaling behaviour is found as follows: the transition time tc scales as tc ∝ W-0.85±0.04, and tc ∝ D, where W is the width of corridor, and D is the strength of drift. However, the other parameters are found to have little influence on the transition time.