How To Beat Traffic With Math

Tired of being stuck in traffic? One writer broke down his daily Houston commute using a year's worth of detailed data and inferential statistics, and determined how to beat local traffic using nothing but math.. — Ed.

Traffic: the commuter's bane. It plagues major city drivers around the globe and shows no sign of letting up. The average U.S. commuter spends about 100 hours a year just driving to work -– 20 hours more than an average year's supply of vacation. This personal daily grind uses more than 15,000 miles and 1000 gallons of fuel every year, which might not be so bad if much of it wasn't such a waste: 1.6 million hours and 8 million gallons of gas are burned every day in traffic jams across the nation. Traffic even affects your health, raising blood pressure, increasing stress, and producing more Type-A personalities.

How To Beat Traffic With Math

Of course, some places are worse than others. New York tops the list, with Chicago, Newark, and Riverside following, albeit at a distance. L.A. comes in at sixth place, and Houston, where I reside and commute, is fifteenth. Other cities, such as Nashville and Kansas City, Missouri show up much further down the list, but something tells me that even commuters in those relative traffic havens dedicate significant effort and conversation to ‘beating traffic.'

Resources are sometimes available to help in this quest. Houston Transtar provides up-to-the-minute traffic information for all major Houston highways. Average traveling speed and construction and accident information are all available at the click of a mouse, but tips on avoiding the perpetual web of red during the morning and evening rush hours are nowhere to be found. Obvious answers such as public transportation and carpooling are legitimate, but trends show that Americans are meeting the increase in traffic by using such transportation methods less, not more. Also, while online traffic-reporting graphics warn of potential issues, they rarely indicate how long they might persist, leaving the traffic-wary commuter right where he started: guessing.

Tired of the typically inefficient and contradictory workplace chatter on the subject — and feeling the pull of a mild worksheet obsession — I set out to statistically analyze my commute in order to determine how I might minimize my time behind the wheel. If there was a way to figure out how to give myself an advantage over the almost 900,000 other Houstonian workers out there (each of whom averages a 26.1-minute commute), math and a smidgeon of obsessive-compulsive disorder had to be essential ingredients. At the very least, I would be able to ascertain just how much of my commute time was up to me, and how much depended on a "higher power" (e.g., weather, school districts, wrecks, etc.).

How To Beat Traffic With Math

Gathering Data

From March of 2005 to March of 2006, I recorded my departure and arrival times both to and from work, along with whether school was in or out. Other factors, although most likely important, were excluded to keep the scope of the experiment narrow and measurable.

Driving Data
Every morning, I took note of the time on my car clock as I pulled out of my driveway in northwest Houston and then again as I pulled into the parking garage at my office building close to the north-bound frontage road of Sam Houston Parkway and Clay Road In the evening. I followed the same process in reverse. The morning route and evening route differed slightly in length, but data was only recorded when the planned course was followed, allowing for only slight variations.

School District & Government Data
Being suspicious of the influence of the school session, I collected official 2004-2005 and 2005-2006 calendar data from Cypress Fairbanks Independent School District, which covers almost all of my commute route, and took note of all full student holidays (i.e., teacher in-service days, but not student early release days). I also collected official 2005 and 2006 government holiday information from the city of Houston and the federal government, but this proved next to useless as I only commuted to work on one city and two federal government holidays.

Analysis

To set up the gathered information, I first organized the variables into inputs and outputs as shown in Table 1.

How To Beat Traffic With Math

To determine which variables had a statistically significant effect on my commute times, I ran one-way ANOVAs on the discrete variables and plotted smoothed graphs of means for the continuous variables.

Morning Commute ANOVAs

Day of the Work Week

The one-way ANOVA of the morning commute duration versus the day of work week (y1 vs. x1) showed a statistically significant effect. The table in the ANOVA output and the boxplot below confirm that this effect comes on Fridays, where there is a significantly shorter commute time:

How To Beat Traffic With Math

(Click on image to enlarge)

How To Beat Traffic With Math

Month of the Year
The month of the year versus morning commute time (y1 vs. x3) ANOVA results showed even less of an effect:

How To Beat Traffic With Math

Cypress-Fairbanks ISD
Whether or not the local school district was in session proved to be the greatest measured variable in explaining the morning commute time variation (y1 vs. x6):

How To Beat Traffic With Math

(Click on image to enlarge)

How To Beat Traffic With Math

Evening Commute ANOVAs

Day of the Work Week
While the day of the week proved to have a significant impact on the morning commute, the evening commute showed no such relationship (y2 vs. x1):

How To Beat Traffic With Math

(Click on image to enlarge)

How To Beat Traffic With Math

Week of the Month
Again, the week of the month did not explain the commute-time variation (y2 vs. x2):

How To Beat Traffic With Math

(Click on image to enlarge)

How To Beat Traffic With Math

Month of the Year
Another change from the morning results, the month of the year proved to have a significant effect, with February, April, and November showing the longest evening commute times (y2 vs. x3):

How To Beat Traffic With Math

(Click on image to enlarge)

How To Beat Traffic With Math

Cypress-Fairbanks ISD
The school session again showed significant influence, but it was not as strong in the evening as in the morning (y2 vs. x6):

How To Beat Traffic With Math

(Click on image to enlarge)

How To Beat Traffic With Math

Departure Time Analysis
For the continuous variable of departure time, I plotted smoothed curves of the mean commute time at each minute.

The morning departure-time plot shows relatively long commute times until about 7:40 AM, at which time a gradual decrease starts that continues in a largely linear fashion for the next hour. After 8:40 AM, traffic appears to have minimal impact. (y1 vs. x4):

How To Beat Traffic With Math

The evening departure-time plot shows a peak commute time at about 5:10 PM, tapering off linearly through the next two or so hours. Departure times prior to 5:00 PM showed erratic results, but it is obvious that traffic played a decreasing role in evening commute time duration moving back through 4:00 PM, before which its influence is noticeable, but slight. (y2 vs. x5):

How To Beat Traffic With Math

(Click on image to enlarge)

How To Beat Traffic With Math


I usually leave home at 8:00 AM and work at 5:30 PM, but a 30-minute delay of each looks like it would shave five minutes off the morning commute and about 2.5 minutes off the evening one. Additional half-hour delays bring 2.5 minutes of commute time savings in the evening, but little to no savings in the morning. Slightly earlier departure times appear to result in commute-time increases for both trips. Moving back past 4:30 in the evening brings slight improvement in the evening commute, but savings in the morning would most likely require leaving before 6:30 AM.

Conclusions

Given the above data and analysis, what can be done to improve my commute times? Changing my morning or evening departure time looks promising. The best bet appears to be moving my schedule out a half-hour to 8:30 AM and 6:00 PM, bringing significant savings (about 7.5 minutes of commute time per day) without getting too far from normal business hours. Spread out over 50 work weeks, that results in a total savings of over 30 hours a year -– the equivalent of a 38-percent boost to my existing 80 hours of vacation.

Departure time isn't the say-all, however, and making this shift won't always result in a smooth and fast commute. The day of the week in the morning and the month of the year in the evening both have significant impacts, and whether or not school is in session affects both. I could possibly squeeze out a few more minutes of savings by scheduling my vacation days to align with the potentially longest commutes (e.g., non-Friday school days in the months of November, February and April), but the data shows significant variation up and above that described by the measured variables -– much likely due to factors outside of the control of the commuter (e.g., weather, wrecks, breakdowns, response to traffic predictions, etc.).

That said, the commuter may have more control than it appears. Adjusting your commute times and rearranging your vacation schedule will probably help in the meantime, but getting cars off the road is the only sure solution, and one that is within commuters' sphere of influence. It might require punching your "free reign" in the gut, but getting involved in your community by writing your congressperson or attending city council meetings in promotion/defense of improved mass transit could be the most effective way to "curb" your drive times in the long run.

Brandon Hansen, an obvious nerd, is a part owner of — and occasional contributor to — OmniNerd, a place where obsessive geeks can share anything from polls and questions to detailed articles and analysis.

Photo Credits: leungchopan/Shutterstock.com, Shutterstock, Mario Tama/Getty Images