Evacuation Time Estimation Modeling

The mobilization (loading) curve is the cumulative fraction of evacuees who have departed as a function of time after a warning. It is S-shaped because departures are not uniform: a minority leave quickly, the majority depart in a rapid middle phase once the threat is salient and they have mobilized, and a tail leaves late. This pattern reflects how households process warnings and decide to act, as described by warning-response theory. Capturing this curve, rather than assuming instantaneous departure, is what makes an ETE empirically realistic, because the timing of departures strongly shapes when congestion forms and when clearance completes.

In large evacuations, far more vehicles want to use the roads during the peak of the loading curve than the highways can carry. When desired flow exceeds clearance capacity, traffic queues and throughput is capped at capacity, so the bottleneck — not how willing people are to leave — sets the pace of clearance. That is why ETE models couple behavior with a capacity constraint: beyond a point, getting people to decide to leave faster does not help, and only added capacity, phasing, or contraflow shortens the time.

The behavioral component of an ETE — when households decide to leave — is exactly what warning-response models like the Protective Action Decision Model explain. Those models describe how cues, messages, and perceptions lead to the protective-action decision to evacuate and its timing. ETE modeling aggregates these individual decisions into the mobilization curve and then combines it with network capacity. So warning-response theory supplies the micro-foundations of the loading curve, and ETE modeling scales that behavior up to a system-level clearance time.