Applying Metcalfe’s Law to Transit

In the Sunday O, Dylan Rivera’s article about the imminent Green Line opening notes that each time a new MAX line opens, overall ridership on MAX goes up by more than the ridership of the new line:

For example, the Red Line, opened in 2001, initially connected downtown Portland to the airport. So when TriMet extended Red Line service west to the Beaverton Transit Center two years later, planners thought it would add convenience for a sliver of the population. The Blue Line had served the area since 1998, so presumably anyone who wanted to commute on the MAX had already adopted it.

Instead, weekday ridership jumped 49 percent in the corridor.

“We thought we’d already got as many as we could get,” Hansen says. “That kind of a thing almost defies logic. I think we’re going to see more of that throughout the system.”

As a systems engineer by training, I think I see Metcalfe’s law – originally formulated for computer networks – at work. Paraphrased, Metcalfe’s law says that value of a network increases in proportion to the square of the number of nodes.

That means that as we add about 20 new Green Line stations to the existing 75 or so MAX stations (don’t hold me to exact numbers, I did a very quick count), that means the value of the network increases not by 26% (20/75) but by 60% (95^2/75^2 – 1).

Of course I’m not making any numerical claim, because the analogy is not that exact. The ‘distance’ between nodes (stations) is made greater by transfers, etc., so all nodes are are not equally connected as Metcalfe’s law assumes. And to be really accurate, of course we need to factor in the bus network, which is certainly a critical part of the transit network.

But the point I want to emphasize is clear – each addition to the system creates a value much greater than that of the new line itself.

I’m just a computer geek at heart…

58 Responses to Applying Metcalfe’s Law to Transit