I, like many residents of Victoria, frequently make the trip up island to visit the rugged beauty and outdoors of the north island. Like many, I find my self increasingly frustrated with the traffic lights on a highway.
For those not familiar with Vancouver Island. there is one main artery, highway, running from Victoria, north to Nanaimo. At Nanaimo, this highway (Hwy 1) enters the city to the ferry terminal before continuing across the strait in Vancouver. For those of us who want to continue further north than Nanaimo we more or less stay on the same highway, although it changes names to be Hwy 19.
Although this is a highway, stretching approximately 130 km from the CRD to Parksville and is the main route to travel North/South along the island, it is littered with traffic lights continually stopping traffic and creating congestion along the route.
Finally, in a recent trip, I watched to my horror as I was stopped an astounding 23 times during this stretch for a red light - I figured (as many people say) that I hit every single red light along the route.
Well, in fact, I did not, there are 42 traffic lights along the route between the Goldstream turn off (start of true Hwy at the edge of the city) and the Parksville turn off (where oddly enough, fewer people drive but they have done away with lights in favour of overpasses...). That is I was only stopped by about 50% of the lights.
Regardless this had me thinking about the social cost of these traffic lights due to idling and additional fuel usage through acceleration.
The first thing to determine was the average idling cost. Now there are many different types of vehicle on the road, so utilizing information from Natural Resources Canada to determine the % of vehicle by class (here) - as well as idling information from the US (here) I attempted to link idling information up to vehicle class and determine a weighted average of fuel used while idling. this worked out to a low 0.01884 L/minute. or 0.000314 L/Second
With a loose estimate of idling usage, at a cost of gas currently at $1.36/L this works out to a cost of:
$0.0256/minute or $0.000427/second ... does not seem too horrendous.
Next task then was to determine how much fuel is used every time we need to accelerate back up to speed. Casually googling this information yielded that acceleration can increase fuel consumption by 10-30% ... to pick the middle path, I chose to utilize an increase of 20%.
If acceleration causes an increase in fuel usage by 20%, I needed to figure out what base fuel usage is. utilizing the above date I worked out that the average fuel usage could be expected to be around 11.34 L/100km (remember we have everything from small sub-compacts to Semi trucks driving the road). this yields us an average cost of $15.42/100km
Assuming this 20% increase in fuel usage, and further assuming that it takes us a full Km to get back up to highway speeds from a full stop, this gives us a cost of accelerating at $0.1851 each time we have to stop.
So we have our cost of idling, we have our cost of accelerating. anecdotally I find that on average if I am stopped, I am stopped for at least 20 seconds. extrapolating our previously calculated amounts, this gives me an average cost per redlight of $0.19364 - Just under $0.20 each time we have to stop.
At this point, the whole task seems rather trivial. Even if I was stopped at every red light (42) that would only be an extra fuel cost to me of $8.13.
So turning to the ministry of transportation I collected their traffic volume data for this highway over the stretch of interest (here). I found that on average 26,728.39 vehicles are traveling this stretch on any given day. Now things begin to add up ... but clearly, they are not all stopped at all red lights!
Suppose that a driver has a 20% chance of being stopped by any given traffic light, we can use a binomial distribution to determine how many times these 26,728.39 cars are stopped over their travels.
We find based off this that on an average trip we will be stopped at 10.53 lights (which seems about right from my experience). Further - my event of being stopped 23 times does not even register as a likely outcome!
From this distribution, though we determine that on average on any given day vehicles on whole stop 281,478 times between over this distance.
That is, at an average cost of $0.19 per stop, we have a daily fuel cost of $55,102.04 ... no longer a trivial amount! Extrapolating this out for a full year (365 days) and we have an annual fuel cost resulting from these traffic lights as $20,111,244.60 - that is $20.11 Million dollars a year at present fuel prices.
Add on to this environmental impacts (from burning all this extra fuel) as well as extra transportation time for shipping companies etc. and these red lights turn out to be quite an expensive toll on society!
What are your thoughts on these traffic lights? feel free to comment below.
Update May 2018: the Gas price has increased from $1.36 to $1.55 due to this spike in gas prices - estimated annual cost due to traffic lights has increased to $22,922,044.
