# How well does population distribution predictÂ evacuation time?

Previously, we tried to predict 90th percentile evacuation time determined from ABM simulation using 90th percentile free flow clearance time . Bigger the city, greater we can expect to be since it would take longer to traverse. Plotting vs produces the figure below. under predicts with a poor fit () but it is clear that is never less than !

Since that did not work out too well, I attempt to predict using the knowledge of how the population is distributed distance from the exit. Imagine that each rectangular block in the histogram below is a horde of agent located distance away from the exit.

Dividing each block of by width of the exit gives us the population per metre width leaving a catchment area. Each population block is of an equal length which we shall call . In this analysis, I have used a granularity of =100m.

We can compute the density using:

From this, we obtain the velocity which has the following relationship with density (Weidmann 1993):

This allows us to calculate the predictive time by doing:

If we plot against , we get:

The fit is much better () in this case. It is even 2x as good a predictor as (*R*=0.31). never exceeds and seems to be closely related to it.

However, what if we plot against ?

Even better ()!

Every city is of a different size. What if we normalise and by ?

For now, normalised seems to under predict normalised with a modest fit ().

Is there anything else that can be done to refine the predictive power of ? We shall see.