Traffic Flow Theory

Convenience. What does it mean to you? They say time is money, and I agree that sitting in traffic really doesn't constitute the optimal expenditure of your time.

"How much time would you save not having to drive your beloved child to their after school math lessons?" I hear you ask, well I'm glad you did!

I’d like you to consider something. Armed with the most basic equation from Grade 8 Physics, we will work out an estimate of how long you’ll take to stand up from your chair and get into your car. With the help of external PhD Professor Victor Knoop, I will show you that nothing is as simple as it seems regarding real world problems. Now, let’s consider a function t, the time it take you to get into your car to begin your journey which, in a perfect world, should look a little something like this:

Factors to consider:

d – distance to car (in meters)
s – walking speed (in km/h)

we end up with a very basic equation:

t = (d/s)

Assumed distance to vehicle: 45m
Average walking speed of a human: 5km/h

t = (45 / (5000m/3600s)
t = (45m /  1.39m/s)
t = (32s)
t = 32 seconds

Optimally, you’ve wasted half a minute to get to your car, this is without taking into account how long your child will take to get into the car! Many of you reading this will roll your eyes and think “that’s so basic!” and to that I say yes! Math isn’t hard! It’s a summary of this world you already expertly navigate, thus it isn’t hard to see math working but it is hard to learn the language in great enough detail to summarize it precisely and elegantly. Alas, it’s time to ramp it up… Here is an Introduction to Traffic Flow Theory for anyone who wants to truly understand how much time they spend in traffic yearly.

Now you understand what mathematicians do all day. Mathematical researchers summarize this world in math, the background code of the universe. This summary leads to interesting and often depressing studies like the one below, but luckily I won't be adding any days, hours or seconds to your running total of in-traffic time.

Here's an article from CNBC:

"Don’t read this story if you’re stuck in traffic. It will only lead to road rage. The average commuter wasted 42 hours — more than a typical work week — and $960 last year snarled in traffic, according to a recent study from the Auto Insurance Center, an insurance information website. That’s just the average. Commuters in large metropolitan areas, especially Washington, D.C., New York City, and Los Angeles, had it far worse. Commuters in the nation’s capital had nearly double the traffic costs last year, spending an average of $1,834. New York area commuters paid $1,739, while L.A. drivers spent $1,711. Four of the 10 counties with the longest morning drives are in New York. By region, commuters in the Northeast corridor lost the most hours to traffic.

Drivers in D.C. sat for an average of 82 hours in traffic last year, New York City commuters spent 74 hours, and Boston drivers waited 64 hours. Though not to be outdone, the typical L.A. commuter wasted 78 hours in traffic.The Auto Insurance Center analyzed traffic data from INRIX and the Texas A&M Transportation Institute, as well as figures from the U.S. Census Bureau and U.S. Energy Information Service, to determine its findings. The center found the dollar cost of congestion by calculating the value of travel time delay, estimated at $17.67 per hour, and excess fuel consumption using state average cost per gallon of gasoline. While these numbers seem squishy, the Auto Insurance Center may be underestimating the costs of sitting in traffic. Cutting out a daily hour-long commute each way is the equivalent of earning an extra $40,000 a year, according to a 2014 study by researchers at the University of Waterloo in Canada. Think about that the next time you’re waiting for the car in front of you to move."

I’m a self taught mathematician who started studying mathematics when I was 24 years old. I had a basic understanding of high school mathematics at the time, but I never knew the complexity and beauty of math until diving deeper into the history of mathematics. It became an enjoyable pass time and I was asked to help family friends by tutoring their kids. That was 6 years ago now and my hobby has become my business. I’m currently studying multi-variable calculus, discrete mathematics and reading books the following Math related books: “How to Think Like a Mathematician – A Companion to Undergraduate Mathematics” by Kevin Houston, “The Joy of x” by Steven Strogatz and "Introduction to Mathematical Philosophy" by Bertrand Russell.