Need to randomly fade-in/fade-out layers

Hi,

I have a map with dots representing cities.
Between the cities are lines representing communication between them.

Each line between each city is it's own layer.

I would like to randomly fade-in/out each line layer so that some lines are visible and others are not.

I would like the 'fade' to be a set amount (if possible), but the time between fades to be random for each layer.

Is this even possible?

Thanks,

Jim

Reel Inspirations