Take this hypothetical situation: Joe Commuter is a mild-mannered reporter for a major metropolitan newspaper on his way to work in the city of Metropolis. Every day Joe has to drive from his home downtown to his office uptown. He can take one of two possible routes (downtown-west side-uptown or downtown-east side-uptown), either of which gets him to work in the same amount of time.
His driving time is written as a function of the number of cars on the road, f. For example, three cars traveling a stretch of road marked 10f will each take (10 x 3) = 30 minutes to get to the end. It’s a two-lane road with a traffic light and with a pothole blocking one lane, so cars squeezing over into the remaining lane will slow everything down. If Joe has the road to himself, he can roll along with no one cutting him off and travel the road in 10 x 1 = 10 minutes.
On the other hand, three cars driving a stretch marked f + 50 will each take 53 minutes. This is a clear six-lane highway with no obstructions and thus fewer chances for cars to interfere with one another. If Joe is on this road alone, he’ll make it to the end in 1 + 50 = 51 minutes. Traffic doesn’t make that much difference here; it just takes about 50 minutes to drive the road.
Let’s make Joe Commuter King for a Day and start him driving through Metropolis all by himself. No matter which of the two alternate routes he takes, Joe’s total driving time for getting to work in the morning is (10 x 1) + (1 + 50) = 61 minutes. Since he makes the same commute home after work, Joe is spending more than two hours a day in his car getting hot under the collar.
It would be nice if Joe could zip straight uptown from his home; unfortunately, there are no roads going that way. But what if we paved over a strip of the park in the center of the city and gave him an alternate route to work? Look what happens if Joe zips along the new CrossPark Expressway. His route now goes downtown-west side-east side-uptown, and his total elapsed driving time is a new land speed record of (10 x 1) + (1 + 10) + (10 x 1) = 31 minutes! While not faster than a speeding bullet, this is still half the time it took him to get to work the old way. Joe is a happy man.
Now, though, let’s inject a little reality into Joe’s life. He actually drives to the office when a lot of other working stiffs are clogging the road. In addition to our diagram of the Lone Commuter, we need to see what happens when the rest of society gets involved. You have to remember, says Cohen, stating what might be called his first law of traffic, that most people are traveling when it’s most crowded. And the following example can be read as a parable about the difference between self-interest and the collective good.
Cohen’s second law is Traffic is a noncooperative game. This means that if someone driving from downtown to uptown can switch routes and beat out his neighbor by five minutes, he will. But his fellow drivers will soon catch on, and some of them will also switch routes, until the five- minute edge disappears into a state of equilibrium. This is the natural state of traffic flow, and it means that all commuters traveling a common network of roads from the same origin to the same destination will generally get where they are going at the same time.
What if Joe Commuter is driving bumper to bumper with five other cars? Metropolis has yet to be improved, and there’s a choice of only two routes for getting from downtown to uptown. The network is at equilibrium, with three cars traveling one route and three cars the other, so for each route f = 3. Everyone is creeping along at the same rate, and no one can switch routes without penalizing himself by making the trip longer. Joe’s rush-hour trip now takes (10 x 3) + (3 + 50) = 83 minutes. Joe’s boss, a crusty city editor, doesn’t like him to be late, and Joe is not a happy man.
But hold on to your gearshifts, because we are about to enter the strange terrain of a mathematical paradox. Now, Joe has a rush-hour commute via the new CrossPark Expressway. Remember that when Joe drove it alone, this was the road that cut his travel time in half. But now he is bumper to bumper with his neighbors, choosing one of three alternate routes uptown (downtown-west side-uptown, downtown-east side-uptown, downtown-west side-east side-uptown).
This represents traffic flows at equilibrium. Joe has more choices in a network that he knows should zip him to work before his boss can say Great Caesar’s ghost! Yet look what happens when other people come into the picture.