The Triple Convergence

Stuck in Traffic (1992), pp. 27-29, by Anthony Downs


“Nearly every vehicle driver normally searches for the quickest route, one that is shorter or less encumbered by obstacles (such as traffic signals or cross-streets) than most other routes. These direct routes are usually limited-access roads (freeways, expressways, or beltways) that are faster than local streets if they are not congested. Since most drivers know this, they converge on such ‘best’ routes from many points of origin.

The problem is that during the peak travel hours on weekdays, so many drivers converge on these ‘best’ routes that they become overloaded, particularly in metropolitan areas. Traffic on them eventually slows to the point where they have no advantage over the alternative routes. That is, a rough equilibrium is reached, which means that many drivers can get to their destinations just as fast on other roads. At times, the direct road may become even slower than alternative streets, and some drivers eager to save time will switch to them. Soon rough equality of travel times on both types of route is restored at the margin. The opposite happens if travel becomes slower on alternative streets than on the expressway.

Such observations can be made about this equilibrium situation: (1) it tends to recur, because most drivers develop habitual travel patterns; (2) during equilibrium each limited-access road is carrying more vehicles per hour than each normal city street or arterial route because it has more lanes, more direct routing, and fewer obstacles; (3) many drivers time their journeys to miss these periods because they do not like to waste time in heavy traffic; and (4) at the peak of equilibrium, traffic on most expressways is crawling along at a pace far below the optimal speed for those roads, as explained below. Now suppose that the limited-access route undergoes a vast improvement — its four lanes are expanded to eight. Once its carrying capacity is increased, the drivers using it move much faster than those using alternative routes. But this disequilibrium does not last long because word soon gets around that conditions on the expressway are superior.

In response, three types of convergence occur on the improved expressway: (1) many drivers who formerly used alternative routes during peak hours switch to the improved expressway (spatial convergence); (2) many drivers who formerly traveled just before or after the peak hours start traveling during those hours (time convergence); and (3) some commuters who used to take public transportation during peak hours now switch to driving, since it has become faster (modal convergence).

The triple convergence causes more and more drivers to use the improved expressway during peak hours. Therefore its traffic volumes keep rising until vehicles are once again moving at a crawl during the peak period. This outcome is almost inescapable if peak-hour traffic was already slow before the highway was improved. If traffic is going faster than a crawl on this direct route at the peak hour, its users will still get to their destinations faster than users of city streets, which are less direct and more encumbered by signals and cross-streets. Total travel times on these two types of paths will only become equalized if the limited-access roads are so overloaded that vehicles on them are moving at slower speeds than those on normal streets. Triple convergence creates just such an effect during peak hours…

…In any event, expanding roadway capacity does not fully eliminate peak-hour traffic congestion, or even reduce the intensity of traffic jams during the most crowded periods — although those periods will be shorter. In fact, it is almost impossible to eradicate peak-hour traffic congestion on limited-access roads once it has appeared within a nonshrinking community. In theory, such congestion could be eliminated only if the capacity of those roads were increased to the extent that they could carry every single commuter simultaneously at the peak minute at, say, 35 miles per hour or faster. In nearly all metropolitan areas, that is impossible. Therefore, expansions of road capacity — no matter how large, within the limits of feasibility — cannot fully eliminate periods of crawling along on expressways at frustratingly low speeds.”



12 thoughts on “The Triple Convergence

  1. You have absolutely no idea of what you are talking about. What you are talking about is a mathematical ‘theoritcal model of what traffic might look like and act.

    First, fully sixty per cent of all traffic congestion is caused by accidents and breakdowns. That is why all radio traffic reports begin with accidents and breakdowns.

    Second, most drivers have no alternative. They drive what they are assured are the best routes–normally the ‘shortest’ and the limited access freeways. The problem is, once committed to the limited access roadway, you are stuck there. Traffic jam causing accidents are worse of the freeway because the cars are traveling much faster than on other roadways.

    Most traffic, particularly in city centers, is caused by people driving around looking for a place to park. Here in Seattle twenty per cent of downtown traffic is circling, looking for a parking spot.

    As a final note, when I was trained to drive cabs, we were told ‘stay off of the freeway’. Surface streets always keep moving, even if you have to cut across a parking lot to get to another route.

    But seriously, you have no idea of what you are talking about.

    Dick Falkenbury

    1. Thanks for your comments, Dick. It would appear that we will need to agree to disagree. Your views are extremely common, which helps explain why trillions of public dollars have been squandered to make traffic congestion, quality of life, govt and household finances, and traffic crashes much worse over the past several decades.

    2. His theory was mainly related to metropolitan areas and/or central cities. His write-up is for global consumption and is skewed towards Volume of traffic during a particular period of the day relative to highway capacity. When a new four-lane road is built in an area with an existing two-lane road that is usually congested, motorists will like to use the new road to avoid traffic congestion as a result of traffic volume from the old two-lane road. Those who take transits will be willing to drive to take the new four-lane road. Similarly, those who staggered their work hours or travel during off peak hours will be willing to use the new road at anytime. Over the years, the road will also attracts more motorist. Hence, the new road will also experience traffic congestion during the peak hours.

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