Traffic Modeling

 

Have you ever been frustrated driving to work because you ended up sitting in a line of stopped traffic and the route you chose was the same one the local radio station suggested as being faster?  Or instead of the trip taking 20 minutes, it ended up taking 55 minutes?  The study of traffic is called traffic modeling and is a valid application of math.

Modeling traffic is done to help pinpoint why traffic slows down, or becomes jammed so cities and states can create better road and highway systems.  It is also used to find the best routes for traveling from point A to point B. The thing about traffic is that it varies from day to day based on signal lights, number of cars, accidents, behavior of the drives and the way the roads are set up and connected to each other.  

There are several methods used to model traffic.  One method is to use fluid dynamics to treat traffic as if it is a flow.  Another uses cellular automata to model traffic flow.  In other words, the roadways are divided up into cells which cars occupy and follow certain rules to explain how cars change location and speed.  Furthermore, traffic modeling uses a certain amount of randomness so they have to apply a type of Monte Carlo simulation to the trials.

Modelers have also used differential equations to model a dynamic system where they calculate how one car changes position constantly in relation to surrounding vehicles and based on the speed limit.  One of the results of traffic modeling is that it is possible to have a traffic jam artificially created by the behavior of drivers and a certain amount of congestion.  If you are on the freeway and someone suddenly hits their breaks, others behind will hit breaks and it can move back a mile or two and you have a parking lot. 

One thing about traffic modeling is that you can read two different reports with two different results.  Unfortunately, traffic modeling is extremely complex because although all roads are connected in some way, what happens in one part can affect the whole.  There are so many different things that can affect traffic.  For instance, one would think that if a person had one more possible route added to choose from to get to work, it might speed things up but in reality, it can actually slow things down without increasing the number of trips someone makes. This means that one small change can have an impact on the whole system.  

Tomorrow, I’ll look at the study of traffic light optimization.  Let me know what you think, I’d love to hear.  Have a great day.