The Freeway Congestion Paradox
I’ve gotten some pushback on my claim that adding two congestion-priced lanes to MoPac will increase capacity more than adding two free lanes.
This is the Freeway Congestion Paradox:
Chen and Varaiya, in their article entitled “The Freeway Congestion Paradox,” have demonstrated that, once freeway vehicle density (measured in vehicles per mile) exceeds a certain critical number, both vehicle speed and vehicle flow (measured in vehicles per hour) drop precipitously. They have demonstrated the phonemenon with actual data from a section of westbound I-10 in Los Angeles. Until 5:10 am, a flow of 2,100 vehicles per lane per hour is maintained, at a speed of 58 mph. As density increases after 5:10 am, speed steadily drops, until at 7:00 am speed is a stop-and-go 15 mph, and flow decreases to 1,300 vehicles per lane per hour.
The Federal Highway Administration commissioned a study in 2008 that looked at data from Washington, DC freeways. From the summary:
Highway studies have determined that once traffic volumes exceed the capacity of the roadway, the system can rapidly “break down” to the point where all traffic slows markedly, and the capacity and throughput of the roadway drops precipitously.
They produced neat graphs depicting the drop in capacity caused by stop-and-go traffic, like this one:
This chart pairs vehicle speed and total volume carried (see pp. 15-16 of the report for more discussion). The dots are connected in temporal sequence, so it’s possible to follow the evolution of the traffic jam. The graph has a a random-walk component, but basically it confirms two things. First, low throughput volumes are associated with low speed (i.e., stop-and-go traffic). Second, after the critical threshhold is passsed, it takes traffic a long time to recover.
Here is the same chart, except I have drawn over some of the line segments in red. This shows that once the tipping point is reached, traffic speeds and volumes drop and take a long time to recover. (Just trace the red line segments starting at “A”).
Congestion pricing would have prevented congestion from reaching the tipping point, effectively increasing the highway’s capacity.
Rush-hour traffic on MoPac today is the stop-and-go 15 mph type. Adding a new, free lane would probably shorten the period when the highway is clogged, but it would still be clogged for long stretches of time. During these periods, a new, free lane would carry less traffic than a tolled lane.
When congestion is not bad, the toll should be low. That’s one of the attractive features of variable congestion pricing — the price, in fact, should be zero when the marginal cost of congestion is zero. (According to the Statesman, CTRMA might charge a nominal amount like a quarter to avoid confusing people. Which confuses me.) Put differently, the new lane should “act” like a free lane when traffic is not bad.
