Every year around holiday times, millions of people take to the roads, the skies, and the rails to visit friends and families. Sometimes everything works perfectly: the traffic isn’t too heavy, there are no accidents, schedules are met, lines are short, and the weather cooperates. In my experience, that tends to be more the exception than the rule.

If you think about our transportation systems, there are plenty of places where things can go wrong. One traffic accident on the main road to the airport can disrupt the lives of hundreds, if not thousands, of people. Why is this? What can we do about it?

When I was a teenager growing up north of New York City, I took a summer course at the Polytechnic Institute of New York in Brooklyn. This was a special class for high school science geeks (a label I wear proudly now, though maybe not so much then), that looked at simulation of traffic. For example, suppose you have a traffic light at the intersection of two streets. Your task is to determine how long the light should be red or green in each direction so that traffic moves most smoothly. That is, you would like maintain a reasonable volume of traffic flowing each way, while allowing it to move quickly and safely enough. How complicated could that be?

There are several unknowns and decisions to be made before you can start to get to an answer. How many cars approach the intersection from each direction during some fixed period of time, say, per minute? How does this vary during the day? For how long are drivers willing to wait patiently for the light to go from red to green? How many cars would you like to move through the intersection during each green light?

I didn’t say much about the intersection or the traffic light. What if one road is a one way street and the other is not? Do you want to have one or more right turn arrows? How long should those be green? If this is an existing intersection, do you have the history of accidents (quantitative) and traveler complaints (qualitative)?

By the way, will people be crossing the roads? How many do you need to account for and how long will the “walk lights” permit the crossings?

This is just one intersection! During my summer class all those years ago, we did not look at so many variations. With actual cars and drivers, you must.

With some patience, some research, and some measurement of existing conditions, you can use any one of several simulation software programs to help you model the situation, adjust the various parameters, and come up with a reasonable set of timings.

Unless you live in a town with one traffic light, things get more complicated quickly. Imagine a sequence of traffic lights as you travel down a road. I suspect you’ve heard or even said the phrase “I hit every red light on my way to work today.” That happens then the traffic is not in sync with the lights because of a change in volume (more cars), speed (perhaps an accident), or bad design (light timings that work at Noon may not be optimal for 8 AM).

If you have a light at the bottom of an exit ramp from a highway, you could have traffic backing up unsafely onto the highway if not enough traffic can get off the ramp and onto the local street fast enough. What we have here is the *interaction of complex system*s, and these can be very hard to model and optimize. That said, we can’t just ignore hard problems, because real people have to move through real cities every day and every hour.

Part of the work we do in the Business Analytics and Mathematical Sciences group at IBM Research tackles just such big, complex, intertwined, and sometimes just downright messy problems. We use analytics and statistics to describe what is currently going on and predict what will happen if changes are made. We use the mathematics and algorithms of optimization together with simulation to produce more optimal configurations and test our hypotheses.

If I think again about that simple intersection above, I will need to consider carefully what I’m really trying to optimize. It might be volume and speed as I said above, or it could be pollution or gasoline usage reduction. Ask the right questions and carefully determine what you are really looking to improve first, then let modern analytics and optimization techniques help you understand what steps you need to take to get to that more optimal state.