Capacity of Superchargers Using an Erlang-B Model

A capacity model developed over a hundred years ago for capacity of telephone trunks by Agner Krarup Erlang called the Erlang-B model should apply to Tesla Superchargers. See Erlang (unit) - Wikipedia, the free encyclopedia for background.

The biggest error of the Erlang-B model is that it assumes that unserved calls (cars) just go away. However if the blocking rate (the chance of getting a busy signal, or seeing all stalls full) is small, then this is a small error. I did this table using a 2% blocking rate; you have a 2% chance of arriving at the Supercharger and all stalls are full, using the calculator at Erlang B Calculator. Here are the results:


Its interesting to see that the capacity grows faster than the number of stalls, especially at the beginning. Note the capacity going from 1.05 cars being charged to 3.6 when the number of stalls goes from 4 to 8. I hope this means that the long queues at Hawthorne greatly subsided when the number of stalls went from 4 to 8.

Perhaps Farmington, NM will be the first 2-Stall Supercharger... The capacity of a 2-stall setup is pretty small, but maybe that is enough for Farmington.

donauker said:

Actually Milford CT Northbound and Milford CT Southbound are each 2-stall Superchargers

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Interesting...have you ever seen a queue there are 2 cars in the 2 stalls at the same time?

jkirkebo said:

I think the failure risk of a single SC site is too big. One SC down, no stalls available. One SC is currently down at Lillehammer, but there are 3 more so still 6 stalls available.

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I agree completely. Also, the real, very-low-queue-probability capacity of a 4-stall station is 5x that of a 2-stall station; see the chart above. It seems that Tesla is making the minimum size of a station, 4-stalls/2-cabinets. The exception so far is Madison, WI. It looks like the mall there limited Tesla to 3 stalls. It looks like Tesla is compensating by putting in 3 cabinets to reduce the charge time on each of those 3 stalls.

Doug Martoccia said:

Wouldn't the blocking rate vary per site? I've seen blocking at Gilroy and heard that blocking is a problem at Hawthorne.

It would be possible to estimate total SC use for future SCs. San Juan Capistrano will probably move up to the top five once built and will probably see higher blockage, even with a large number of stalls. None of the mid-west SCs will ever amount to much use. They are really only there for show.

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Exactly! The capacity at each Supercharger site has to be tailored to the demand at that particular site. Gilroy is at a perfect place to top off into or out of the Bay Area, so it will get a lot of traffic. Hawthorne is an anomaly. It is not placed as Tesla described, between cities, but is right in a city that does not have a lot of Superchargers in the area. This puts a double heavy load on the site. It was placed there as a show piece for Tesla at their Hawthorne facility and next to Space X. To take care of this, Tesla is adding capacity which is very much needed.

Communications engineers have looked at historical usage, current capacity overloads, and predictions of future need to install adequate capacity for over a century. The Erlang models and queueing theory are big part of that. Tesla just needs to stay ahead of the curve with more sites, more stalls at sites that are getting crowded, faster charging to make the service time shorter, and incentives to move your car when the charging is done.

Many of the mid-west and other remote sites will rarely, if ever, get crowded. They are there for connectivity, which is fun, makes the car more useful, and is good PR. It looks like the minimum site is going to be two Supercharger Cabinets feeding four stalls. That gives some redundancy if one Supercharger Cabinet fails, a very good practice.

With all of the talk of queues at some Superchargers, see Interesting night at the Supercharger, I decided to see if there was available information that could let us see how close some of the existing Superchargers are to having queuing problems from over use, and then see if that correlates with TMC user observations.

I hope that someone at Tesla is tracking busy hour utilization and comparing that to Erlang models to stay ahead of capacity problems. All they need to do is track stall utilization as a function of time of day, day of week, special days, etc. to see when the Supercharger sites are starting to reach capacity. In addition, tracking full utilization times with short times between one car disconnecting and another connecting are good indications of a queue forming.

We don't have this info, but a few of us have taken a picture of the Hawthorne Supercharger Dashboard that shows total MWh usage by site in the last 30 days. Below is a picture that I took on March 12.
View attachment 45086


If I make some assumptions, I can get an estimate of busy hour usage and compare that to usage that would create a 2% blocking rate, the rate where short queues will occasionally form, or at the threshold of queues being annoying.

A few assumption/estimates: I will assume that the average power draw per stall is 60 kW. Telecommunications engineers have long used the rule of thumb that busy hour usage is 1/5 of average daily usage or a day's usage is the equivalent of 5 busy hours. The period for the Dashboard picture is 30 days. Multiplying these together says that a fully utilized stall will draw 9 MWh in a 30 day period.


If we fold this into the table at the start of this thread, we can calculate the energy usage in 30 days for a Supercharger at a busy hour blocking rate of 2% for various number of stalls available:


Now, if I read the actual 30-Day energy use from the March 12 Dashboard Picture above, we can compare that to 2% threshold usage. The last column displays that as a percentage ratio. More than 100% says the Supercharger is operating beyond a 2% blocking capacity.


Remember that this is all based on some pretty broad assumptions, but perhaps it can provide some insight to what is going on. Here are some of my interpretations. I would love to hear other thoughts.

• Hawthorne - This site is way over a threshold capacity. It is so far over capacity, I would expect more complaints. My guess is that its urban usage is really spread over more than 5 busy hours a day. At any rate, Tesla needs more stalls at Hawthorne and more Superchargers in the area very soon!
• Fremont - We don't hear much about queues at Fremont. I think this is because a lot of the use is the factory for new cars, and that use is spread over 16 hours a day.
• Gilroy - Good thing they have 10 stalls there!
• Oosterhoot - Getting close to capacity. What are observations from locals?
• Vacaville/Harris - Will need capacity in the future. Maybe Roseville will take some pressure off of Vacaville.
• Tejon - Are queues starting to appear on occasion?
• Folsom/Barstow - We know about many reported queues at Barstow. How is Folsom?

Doug Martoccia said:

I suspect that opening Superchargers in Oxnard, SJC, and along the 5 will reduce significantly reduce congestion at Hawthorne. Adding capacity helps with frustration, but adding additional sites is a greater good because it can significantly reduce detours and enable trips that are impossible today without relying on slow Level 2 charging.

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I wholeheartedly agree. More Superchargers are great in terms of convenience to find one close, but infrastructure efficiency goes up with more stalls. As more Teslas hit the road, I think the 10-12 stall Supercharger site will be more and more common, as well as seeing more Superchargers in general.

Absolutely, San Juan Capistrano, Oxnard, Indio, and the second LA site, will all take pressure off of Hawthorne.

PaulusdB said:

Usage is quite well spread over daytime and evening hours.
McD and the other restaurant there are open for business till midnight.
Queueing has been reported to take place, though.

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So I went the other way and put the actual usage into the Extended Erlang-B model and got a 0.6% probability of a queue at Oosterhout with the March 12 numbers. Within measurement error, 0.6% is pretty close to "has been reported"... :wink:

What is interesting is that usage at Oosterhoot increasing by 30% would increase the queue probability by more than a factor of 3. It's a very sensitive, non-linear function as you start reaching capacity. If I were Tesla, I would be planning more stalls at Oosterhoot, or more Supercharger sites in the area, soon!