This paper is concerned with modeling, analysis and optimization/control of occupancy evolution in a large building. The main concern is efficient evacuation of a building in the event of threat or emergency. Complexity arises from the curse of dimensionality in a large building, as well as the uncertain and nonlinear dynamics of individuals. In this paper we propose relaxation techniques borrowed from queueing theory to address complexity. Then we provide tools to model occupancy evolution during egress, obtain lower bounds on evacuation time, and construct control solutions to instruct occupants in order to efficiently evacuate the building. The control solutions are based on recent generalizations of the MaxWeight policy for decentralized routing. These results are illustrated with the aid of simulations carried out using realistic building models.