The Initial Problem

We have two attitudes: selfish and selfless. The first attitude is expressed as “If only all these drivers would get off the highway, I could be home in seven minutes”. The second attitude can be expressed as “What can I do to help me get me home sooner?”.

• In any event, we are always using 100% safety as a guideline.

That means that I will be using “coming to a complete and controlled stop” as a boundary, rather than “not sliding into the car ahead of me”.

We often need to come to a complete stop in peak-hour highway traffic, but I will show that is caused by drivers not using these basic rules which we will develop). On a two-lane road, one lane each direction, we might have to come to a complete stop if the vehicle ahead of us is involved in a head-on collision.

Our calculations will be based on “coming to a complete and controlled stop”, at which time we are assumed to be safe.

We want to answer the question “What can I do to help me get me home sooner?”, which we will now express in a form that will satisfy the entire population of drivers: “What is the speed at which we should travel to get the maximum number of drivers home in the minimum time?”.

Our solution will work on any stretch of highway, road, avenue or street. I visualize a stretch of 3-lane highway, but you can visualize what you want.

Imagine a stream of cars passing a point on the highway. You are standing well off to the side observing, say, the lane nearest to you. Vroom; whoosh; putt-putt, vrooom. One by one cars slide past you, perhaps one every three seconds. That means that every three seconds a vehicle (and hence a driver) is “getting home”. We want to know the maximum number of drivers per second that can be got home safely.

Rephrasing The Problem

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