Major thoroughfares in big cities are usually
highly congested. Traffic lights are used to allow cars
to cross the highway or to make turns onto side streets.
During commuting hours, when the traffic is much heavier
than on any cross street, it is desirable to keep traffic
flowing as smoothly as possible. Consider a two-mile stretch
of a major thoroughfare with cross streets every city block.
Build a mathematical model that satisfies both the commuters
on the thoroughfare as well as those on the cross streets
trying to enter the thoroughfare as a function of the traffic
lights. Assume there is a light at every intersection along
your two-mile stretch.
First, you may assume the city blocks are
of constant length. You may then wish to generalize to blocks
of variable length.