Abstract: In real evacuation mission, there might be fewer rescue equipments than the number of available evacuation paths. When this situation occurs, a mathematical model is given with objective function minimizing evacuation time and a k-limited flow control algorithm is designed based on flow velocity in this paper. First the feasible path sets would be calculated by sending the largest possible number of evacuees on the shortest path to the nearest destination, and k-shortest paths from it is regarded as the initial solution. Then the algorithm can be realized by updating network according to the flow velocity, in the same time, the path set with minimal evacuation time should be preserved in each iteration. Finally, a numerical example is presented to show the effectiveness and feasibility of this algorithm.

Key words: emergency evacuation, rescue equipments, capacity constraints, dynamic network flow