Dynamic Sign Guidance Optimization for Crowd Evacuation considering Flow Equilibrium

The dynamic exit sign has been verified as an effective means to guide the pedestrian during evacuation. The most critical mechanism with dynamic exit sign guidance is to balance the pedestrian flow on each exit route by optimizing the direction of signs. This paper formulates a bi-level programming model for the direction optimization problem of dynamic signs in buildings. In the bi-level program, the upper-level model is a system optimal model, aiming to minimize the total travel time by optimizing the dynamic sign direction. The lower-level model is a pedestrian assignment model satisfying the dynamic user optimal principle that describes the evacuee exit/route choice behaviour to achieve a balanced pedestrian distribution on the route. A method based on the fundamental diagram, the cell transmission model, and the point-queuing theory is developed to estimate evacuation travel time considering congestion and queuing. A heuristic algorithm is extended to solve the bi-level program. Finally, the proposed methodology is validated with numerical examples. Results reveal that the proposed model can produce the optimal dynamic sign direction, significantly improving the evacuation efficiency.