Modeling and optimization of crowd guidance for building emergency evacuation

Building emergency evacuation has long been recognized as an important issue, and crowd guidance is a key to improve egress efficiency and occupant survivability. Most existing methods assume that crowd behaviors are independent of emergency situations and are fully controllable under guidance. This assumption makes it difficult to capture important features such as stampeding or blocking. In this paper, a probabilistic model is developed to characterize how fire propagation affects crowds in stressful conditions and in turn egress times. This enables the predictions of potential blockings, and provides a foundation to optimize crowd guidance. An optimization problem is then formulated to evacuate as many people and as fast as possible while reducing the relevant risks through appropriate guidance of crowds. To solve the problem, observing that groups of crowds are mostly independent of each other except when they compete for passages, a divide-and-conquer approach is developed. After the nonlinear coupling passage capacity constraints are approximately relaxed, individual group subproblems are solved by using stochastic dynamic programming with state reduction and the rollout scheme. Individual groups are then coordinated through the iterative updating of multipliers. Testing results demonstrate that, compared with the method ignoring crowd behaviors, our method evacuate more people and faster.