Never Take SR-520

Be sure to subscribe for updates on this and all my other data analysis projects!


Fuel prices have always been higher in Seattle than in many other places in the country. I've been paying around $4.30, and looking at this map from AAA that seems about average for the west coast.
AAA Fuel Gauge Report Map

This year the State Route 520 floating bridge in Seattle become a toll road, after several delays. Besides enabling the automatic tolling service 8 months behind schedule, it's been a rough year for 520. The tolls have been occasionally overcharging drivers, the bridge has been closed many weekends for maintenance (see picture below), and a yacht got wedged under the highway. Yikes.

SR520 closed for weekend
With gas prices climbing, and the 520 tolls due to increase by 2.5% starting July 1st, I thought it high time to finish a post I'd started working on months ago! The premise is simple:
Is it cheaper to take 520, or drive around on I-90?

Tolling prices for weekdays (black) and weekends (blue)

To address this question, we must first understand what the tolling prices are like. Above I have reproduced the weekday and weekend prices as a function of time. You can see the variable price scheme, whereby the drivers in morning and evening rush-hours are relatively fleeced. On the weekends it's a single-peaked distribution, cashing in on (for example) Saturday shoppers headed from Seattle to the popular Bellevue Square shopping mall.

This flat cost is the first part of the equation. Next we need to estimate how fuel efficient your car is, so we can calculate the price of driving the different length routes.




Here I'm showing the fuel efficiency of a car as a function of its speed. The black line describes this efficiency for a fairly ideal passenger car, like my 1999 Honda. The blue line has been reduced in efficiency by 20%, and I believe is more representative of a typical "light SUV", such as the extremely popular (in the northwest) Subaru Outback. I'll be assuming the SUV case below. I don't really know how accurate this data is, but I've assembled it from fueleconomy.gov and I'll let you decide if you think this is a reliable or impartial source.

The last piece of the puzzle is a route to consider! For this example I'll be traveling from UW to Bellevue Square mall. Route A is the direct across 520, route B is the long drive around I-90, via I-5 and I-405. I played with other routes as well, but this is the simplest and most dramatic.

Route A: the direct trip
Route B: the long way around
a


So the game works like this: At every hour of the day, for every speed between 0 and 80mph, I have calculated the cost of going to Bellevue via both routes. The reason I have gone through the silly process of computing cost for every road speed is that I was curious if the distance would be the deciding factor at certain speeds. As such, I apologize if the result figure is complicated. 

Weekday price difference grid, assuming $4.20/gal fuel. Black lines highlight the price
difference over time at 60mph, the nominal speed limit on both roads.
You can almost read off the data from the grid. The color indicates the difference in price between driving around and taking 520. Red indicates that 520 is more expensive. Green to black is I-90 being more expensive, 520 cheaper. The color-bar (legend) at top was capped at $1, but the maximum price difference was actually around $1.80.

The result gives rise to the pointed name I chose for this post: you should (almost) never take SR 520 if you want to save money. The exceptions are:
  • late at night, when the toll is not in effect
  • if you're driving 5mph
  • if your time is worth more than the amount you save driving around. As a graduate student, the choice is laughably clear.
During the off-hours (11pm-5am) you can see the shape of the fuel economy curve quite nicely. Some of that effect can also be seen at the high-speed end. A reminder to you all: going 55mph saves lives and gas, which in turn saves other lives.


It may occur to you (or, it did to me at least) that this result depends on what the price of gas is, and you'd be absolutely correct. So I turned that knob in the model, and found that at ~$7/gallon gas it becomes cheaper to take 520 at all times except rush hour.

The result also depends on your fuel economy in as similar way. I've only explored the case of a small SUV, but consider a semi truck that gets 6-8 miles per gallon! In almost every conceivable scenario it would be cheaper to save a gallon or two of gas and take 520.

Maybe I'm an optimist, or a fool, but it seems like a reasonable proposal for the toll prices would have been to make them price-neutral to driving around. Tolling also increases traffic on other roads, decreasing the profitability some. I did enjoy seeing that the tolls don't affect low income families greatly. I read through a few of the initial reports released about the 520 tolls, but I'm very interested in looking at the traffic statistics and financial data to see if it meets predictions.

Overall I'm struck with how different the data analysis seems to be in this field. Figures don't seem precise, but rather very bold and contrasting. Sometimes this is effective and accurately tells a story better than a very precise figure. Frequently I find the plots burdensome, but that's the subject for another post...

8 comments:

  1. Thank you for taking the time in making such a detailed report!

    As a fellow student (holla, BC) I really appreciate this.

    ReplyDelete
  2. Most of the people crossing 520 make a lot of money - six figures is basically the norm, from the data WSDOT worked with. That's why they're still choosing to use it.

    ReplyDelete
  3. Ben, you raise a great point. This is a subtle means of wealth redistribution by tolling the people who work in Bellevue.

    ReplyDelete
  4. My analytics tools are showing me that I'm getting hits from WSDOT on this post. Let me say a couple things:

    1) Welcome, I'm flattered you folks are reading this
    2) I've long been fascinated by traffic data, and really respect what you guys do!

    ReplyDelete
    Replies
    1. Ben, I take 520 on a bus round trip daily from the eastside to Seattle and back and work for WSDOT. I am not even close to making a 6 figure salary and never will be. I know there are many others in my catagory.

      Delete
  5. Also, you need to consider the impact of traffic on I-90. When the tolls hit, a flood of people decided to now take I-90 no matter what, causing longer commute times when you took that route on top of the extra mileage. If there are accurate estimates of average traffic on I-90 after the toll hits, it would interesting to see how that impacts your numbers.

    It would also be an interesting comparison to look at the scenario of "How much is your time worth if you take 520" and do the same spread across times of the day and speeds of driving. That might validate the assumption that folks who work on the East Side value their time highly.

    Gosh, data is cool.

    ReplyDelete
  6. This is amazing! Thank you! What happens if you factor in wear and tear on your car?

    ReplyDelete
  7. Anonymous above points out accurately that you've missed a huge cost that in fact a whole lot of people miss -- wear and tear. Every mile you drive means your car requires maintenance one mile sooner, and more importantly, every mile you drive is one mile sooner that you have to buy a new car (i.e., it depreciates). You don't notice it because it's a cost you don't actually have to pay right now, but it's just as real. See e.g. this article and the linked pdf: http://newsroom.aaa.com/tag/your-driving-costs/.

    The fleet average cost of depreciation is something like 22c/mile for medium sedans, and maintenance+tires is about 5c. Compare to fuel at $4.20/gallon for a car that gets 20 MPG, which works out to 21c a mile. You state in the post that the maximum cost difference between the two routes (which differ in length by ~8 miles) is $1.80. The extra 27c/mile that your calculation misses actually make the tolled route cheaper!

    You're probably driving a grad student beater car, which pushes the depreciation costs down some, although to some extent this will be countered by higher maintenance costs. I'd make a WAG that the lowest you could get depreciation+maintenance down to would be ~10c/mile, in which case the tolled route is still somewhat more expensive, unless you happen to value your 9 minutes of time at $1.00 or more (which is not unreasonable, even for a grad student!).

    That this article is published on the blog of an astronomer (hello from Berkeley!) goes to show that we're really pretty irrational about the costs of driving. (By the way, I've found several of your other posts fascinating!)

    ReplyDelete

Inappropriate comments, advertisements, or spam will be removed.
Posts older than 2 weeks have moderated comments.
(Anonymous commenting disabled due to increasing spam)

Related Posts Plugin for WordPress, Blogger...