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  • Writer's pictureKevin

What makes traffic jam?

In recent days, Los Angeles and the neighboring Orange County passed public measures to tax for roadway expansion projects. The subject is a 13-mile stretch of the Interstate 405 linking Long Beach and Costa Mesa, which consistently ranks in the top five for having the worst traffics in the country. During rush hour, the outbound lanes from LA become stuck as five lanes reduce to four. The havoc predictably lasts 3 to 4 hours on end and wastes 67 years for motorist annually. In response, the solution on the horizon is a $1.7B project that aims to add one extra express lane to both sides of the I-405. This is equivalent to $130 million per mile of construction. That is equivalent to paving the same distance with Farrari’s bumper-to-bumper!

The 13-mile stretch of Interstate 405 in Los Angeles as candidate for retrofit.

Critics of the project believe that roadway expansion has little potential to reduce congestion, as drivers that had been discouraged by long commutes will take the road and fill the newly constructed lanes (as had been seen in the past). Are they right? What is typically referred to is called the Induced Demand, a concept whose result has been qualitatively shown by time-series aerial photos taken since the 1960’s. The photos show that even with a moderate population growth, new highway lanes can never ‘catch up’ to the demand for new cars joining the road. This losing battle has only left cities billions in debt and without a solution in sight. By 2022, when the project completes in 2022, there will be twelve lanes going through the area designated for I-405 expansion.

As the leading cause of death in the world, heart attacks occur in people typically older and overweight. It occurs when the blood stops flowing to the heart causing damage to the muscle. The mechanism relates to a blockage caused by the buildup of plague (e.g., fat and protein) of the vessel wall. The typical remedy uses a stent to prop open the diseased artery. Another is with a bypass surgery to create new pathways for the flow of oxygen to recover muscle cells that were damaged. Prior to these invasive treatments, however, medications such as anticoagulants (e.g., heparin) and nitrates are used to help dilute the blood and relax coronary arteries, respectively. The common objective between both approaches through drugs and surgery is to restore blood flow to the heart muscle ( (i.e., reperfusion therapy).

Akin to blood flow, traffic flow under stress can also coagulate and slowdown. Typically, a bottleneck occurs when there is a local loss of road capacity and/or increase in vehicle density. Physically, this can be due to an accident, roadway construction with reduced lanes, or even with a sudden increase of cars from on-ramp locations. The concept is the same as biology. Flow is impeded by a sudden change in the ratio between capacity and throughput. However, traffic remedies seem to take on the more expensive approach as the first and only solution: roadway expansion. The question that we’d like to answer is: is there a lower cost solution to traffic that corresponds to the use of medication for heart disease? In particular, anticoagulants aims to reduce the blood density by dilution. Perhaps there is a way to diffuse or avert congestions by reducing the density of oncoming traffic. The question that we’d like to answer is:

Is there a low cost solution to our traffic woes more effective than building new roads?

In other words, it would resemble the use of medication for heart disease whose objective is to try non-invasive treatments first before risking having complications with surgeries. What is the proper equivalence of low-cost, low-risk medical treatment to traffic mitigation?

To answer that, let’s look at the way we drive.

The Fundamental Traffic Diagram

Why? To understand how limiting vehicle speeds can improve traffic flow, the key is to understand how a small bottleneck can propagate and build up into long stretches of stop-and-go traffic. Luckily, such transition between free and congested flows is highly predictable. It has been well-documented through traffic data that there exist distinct relationships between vehicle speed and throughput. One is free-flow and the other is congested. The “Fundamental Diagram for Traffic Flow” characterizes these two vastly different regimes simply by the speed and volume (viz., throughput). Namely, the faster, free-flow traffic has the same throughput as slow, congested traffic. The reason is that the former has larger spacing between vehicles than the latter. This equivalent simply occurs naturally given the reaction time of drivers and the common sense of safety.

Also indicated by the traffic diagram is that the two relationships converge at an ideal condition where the highest throughput can be achieved (at approximately 2200 veh/h). The corresponding speed is ~25 mph (or 38–42 kmh as indicated), which is excruciatingly slow compared to the speed limit of most U.S. freeways at 65 mph. The reward is much greater, however; By controlling vehicle speeds en masse close to the said speed, it would be possible to move a lot more cars using existing highways than driving with an uncontrolled, me-first mindset.

Traffic flow simulations make it possible to see the effect of reducing vehicle speeds en masse. The result (1 through 4) shows that congestion can be remediated by limiting the maximum vehicle speeds. Simply by reducing the limiting speed from 75 to 45 mph, the simulation shows that a well-defined bottleneck slowly diffuses and becomes free-flow traffic once more. From the snapshots, one can also observe that vehicle speeds become more uniform. The result is that the average lap time for the faster congested vehicles is 73 seconds, whereas it is 48 seconds for the slower free-flow scenario. That is a 30% reduction in travel time by adjusting the speed limit to maintain free flow.

Time-sequenced closed-loop simulation of traffic flow.

However, this close-ended simulation (i.e., cars traveling in a circle) does not allow for the propagation of the bottleneck to fill the entire track. On open-ended roads, real traffic jams would expand upstream towards the oncoming traffic and greatly limit the overall throughput. Using the Fundamental Traffic Diagram, a free-flow traffic at 38–40 mph yields 2100 vehicles per hour, or ~10 times the capacity of a congested traffic with 200 vehicles per hr. Unfortunately, dense traffics fall into congestion much more readily than maintaining free-flow — it is an unstable condition due to the delay in driver reaction time. At ~2000 veh/hr, this would produce 800% faster commutes for the most problematic corridors such as the Interstate 405.

But is there a density relieve solution cheaper than a line of Farrari’s? Let’s explore that.

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