2010-05-22 Science, Traffic 101 redone.

Traffic 101 redone

Have you ever wondered why the traffic is so slow on a freeway, when the freeway is where the traffic should be fast? Sitting at a dead-stop on the freeway, the meter in the on-ramp to your right flashes green, letting yet another car insert itself into the line of cars in front of you. It is flashing "go" every three seconds while the cars on the freeway next to the on-ramp are mostly stopped. Which brings up the question, "Is there an optimum number of cars which would maximize the throughput of traffic measured in Cars Per Minute (CPM)?"

Two things control the speed of traffic on a freeway. One is the average following distance in seconds (fds) from one car to the next, and the other is the density of traffic measured in cars per mile (cpm). If we use an average following distance of two seconds, assume each car is 12 feet long and have a density of 200 cars per mile, then the maximum speed of traffic is (5280/200 - 12)/2 = 7.2 feet-per-second. That is, the distance between cars in feet, divided by the two seconds the car travels, gives us the speed in feet per second. Because miles per hour is (ft/sec) * (3600sec/hr)/(5280ft/mil), 7.2 feet per second is 4.9 miles-per-hour.

The maximum number of Cars Per Minute (CPM) is absolutely limited by the following distance in seconds. If the fds is two seconds between cars then the number of Cars Per Minute must be less than 30. It does not matter if we make each car zero feet long and travel a hundred miles an hour, fewer than 30 cars per minute will pass any point on the road (in one lane) when the following distance between cars is two seconds each.

Cars Per Minute (CPM) may be calculated as cars-per-mile times miles-per-minute (which is feet-per-second times (60/5280)). The funny thing is, this ends up being the maximum CPM (100%) times the inverse percentage of cars-per-mile. That is, (60/fds) * (1 - cpm / 440). So, every additional 14.66 cars-per-mile is one less Car-Per-Minute of throughput until, at 440 cars per mile (for 12 foot long cars) we have a speed and throughput of zero. No cars can move because they are all bumper-touching-bumper.

fds | cpm | mph. | CPM
----------------------
2 | 025 | 68 | 28
2 | 030 | 56 | 28
2 | 050 | 32 | 27
2 | 100 | 14 | 23
2 | 150 | 8 | 20
2 | 200 | 5 | 16
2 | 250 | 3 | 13
2 | 300 | 2 | 10
2 | 440 | 0 | 0

What does the previous table show us? It shows us that the maximum available throughput for traffic is always achieved at the maximum available speed. The fewer number of cars per mile, the higher the CPM throughput. There is no optimum number of cars to maximize the CPM. It is just a matter of "the fewer the better" up to number of cars able to go the maximum posted speed.

Given a rush-hour density of 150 cars-per-mile for a 5-mile stretch of (one-lane) highway, for a time period of one hour, a total of 1950 cars will be on that road within that hour. At that density the throughput will be 20 Cars-Per-Minute at a speed of 8 miles per hour, and it will take 98 minutes to move all of those cars off of the road.

Given the same 1950 cars at a density of only 30 cars-per-mile, the cars will be traveling at 56 miles per hour and it will take only 70 minutes to move all of the cars off of the road. Or, given the same 98 minutes that we moved 1950 cars at the higher density of 150 cars-per-mile, we could move 2744 cars off of the road if the density were only 30 cars-per-mile.

Which brings us back to "metered" on-ramps. I would like to make the following suggestions:

· Every entrance to a freeway or section of freeway should be metered --- even when the entrance comes from another freeway. On a freeway, there could be holding zones controlled by timed signals which would allow the cars in the zone to turn their engines off for 10 minutes to save gas, before proceeding into the metered zone.

· Like modern "WALK" lights, the meters in the on-ramp should count down the seconds until the next green light. This gives the driver at the front of the line information about how long he will have to wait.

· On-ramp meters should be controlled by radar, measuring the speed of the traffic beside the on-ramp, not by a sensor in the road counting cars per hour. The "Ramp Meter Design Manual" for the state of California apparently uses "Passage Loops: Inductive loops placed downstream of the limit line to detect passing vehicles," to measure "VPH: Vehicles per hour." But VPH gives no clue about how fast the traffic is moving. It cannot tell the difference between light, fast traffic, and heavy, slow traffic. Either way, the VPH can be the same. Measuring actual traffic speed, if the traffic is moving as fast as the posted limit, then the meter may allow more cars to enter the freeway. This will automatically slow down the traffic.

· Metered on-ramps should be allowed to feed traffic into a freeway like a reverse version of water-rights owners pumping water out of a river. That is, each on-ramp should be assigned a specified amount of potential traffic space downstream from its entrance. Upstream on-ramps should not be allowed to fill up the freeway, preventing downstream on-ramps from using their assigned traffic space.

· Outside of each entrance to a metered on-ramp, far enough back where each driver could decide to change lanes and take an alternate route, there should be a sign in lights that says "(freeway) WAIT ## MIN." Like the signs at Disneyland queues which say, "the estimated wait from this point is ## minutes," a wait sign would give drivers the ability to choose how they want to travel to their destination. Do I want to enter the on-ramp and wait 15 minutes, knowing that once I'm on the freeway it will only be another 7 minutes to where I'm going? Or, do I decline to wait for 20 minutes, change lanes and take a local street, knowing I can get there in 25 minutes without using the freeway?

· What if there is more traffic wanting to get onto a freeway, than the best Cars-Per-Minute throughput will handle? In that case, the on-ramp meters should not allow them onto the freeway! If the CPM is already maxed out for the speed limit, allowing more cars into the freeway will overcrowd it, resulting in fewer Cars-Per-Minute throughput. Even if they have to wait 30 minutes to get onto the freeway, people will get to their destination sooner if the freeway is moving traffic at its maximum speed and number of Cars-Per-Minute.