You are caught in bumper-to-bumper traffic heading south to downtown Chicago on Lake Shore Drive. Tuning your radio to the traffic station, you grit your teeth as you hear that the normal fifteen minute commute time from Montrose Street to Randolph Street has been replaced by forty minutes of torture. With all the time on your hands, you start wondering: "How do they calculate traffic times in Chicago?"
While most people think of helicopters circling high above the traffic, the Illinois Department of Transportation Traffic Systems Center (TSC) uses a different approach. The TSC receives its data from trafficloop detectors embedded in the pavement on the expressways in the Chicagoland area. The trafficloop detectors act like metal detectors and can sense when a vehicle passes over them. This allows the TSC to count the number of vehicles that have passed over each detector as well as how long each detector was occupied. The TSC then uses a simple application of Riemann sums (or probably better numerical approximations such as Simpson's rule)to convert this data into travel times and congestion estimates. The data is updated every minute. (A more extensive explanation for how the system works can be found at the Gary-Chicago-Milwaukee Corridor Home Page .)
We have incorporated this data into a writing project suitable for first-year calculus students studying Riemann sums. Written in the form of a mystery, the project cannot be solved without some mathematical detective work. In an attempt to exonerate the suspect, students must calculate approximate travel times using numerical approximations. They also must present and explain their solution to someone with a limited mathematical background (in this case a lawyer and the jury). In addition to applying calculus to real-world data, this project gives students the opportunity to improve their ability to communicate a mathematical solution to a non-mathematical audience.
The table of sample data for the twenty-one detectors between 95th Street and Roosevelt Road allows students to use twenty intervals in their calculations. To simplify calculations, we suggest that students assume the detectors are more or less evenly spaced. It is also worthwhile noting that the detectors do not register speeds in excess of 55 mph. Students might explore what possible variation in travel times would occur if they considered a maximum speed of 60 or 65 mph for those detectors which indicated 55 mph. In general, the northbound Dan Ryan is most congested in the mornings and early afternoons.