This may be a bit of a softball question.
I have an intersection that I would like to cross. I can cross the intersection in no time, but I will have to wait at a stop light before I can cross. The waiting time at the light is modeled by a uniform random variable from $[0, b]$.
I also have another option: I can take a bridge to cross the intersection. I can take the bridge any time I want, and don't have to wait for the stoplight. But crossing the bridge will take longer than it would take to walk across the street once the stoplight changes. The time it takes to cross the bridge is $c$.
I was wondering, what is the optimal amount of time to wait at the stoplight before crossing the bridge? What would you try to optimize?