Evacuations necessitated by extreme events are usually envisioned as taking place with all people evacuating simultaneously; this leads to premature congestion on the surface streets and excessive delays. With the evacuating load onto the network staggered, the onset of congestion may be delayed, and people can evacuate more quickly. In this study, the problem of scheduling evacuation trips between a selected set of origin nodes and (safety) destinations was considered, with the objective of minimizing network clearance time. A modified system-optimal dynamic traffic assignment formulation is proposed; in it the total system evacuation time, as opposed to the total system trip time, is minimized. An iterative heuristic procedure is used to solve this problem: the method of successive averages is used to find the flow assignments for the next iteration; a traffic simulator, DYNASM ART-P, is used to propagate the vehicles on their prescribed paths and determine the state of the system. Therefore, the simulator serves as a tool to satisfy the dynamic traffic assignment constraints implicitly while evaluating the objective function. The output of this model will be the departure time, route, and destination choices for each evacuee. The output is then aggregated to produce a time-dependent staging policy for each selected origin.