# Estimating/predicting maximum of sum process for modeling number of cars on the road?

I have two series of information about (for example) the amount of cars on a two roads over a 1 mile stretch. I have collected 4 outcomes: Number of cars passing through an intersection at 1, 10, and 60 minutes as well as greatest number of cars in the area in the last hour.

I'd like to model the maximum of the sum of the number of cars on both roads in an hour for a given hour.

Adding an example for clarity (as per comments): If (over a 20 minute period, sampled every minutes), my observations are 2,4,7,4,8 and 5,4,3,2,1, the maximum over both roads is 10 (7 + 3), not 13 (5 + 8), because the queue specific maximums happened at different times.

• You should give an example. It took me some minutes to figure out what you mean. Like for 1,3,4 and 4,3,1 it's not 4+4, but 3+3 at $t=2$. – ziggystar Jan 24 '14 at 14:27

If the numbers of cars on either road are not independent, then you will need to merge the road information as a function of time into a 3 column array with a column for time and the corresponding columns for road1 and road2 traffic. You can define a 4th column of roadsum traffic and apply the same smoothing spline methods there.