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Superchargers and queueing theory

Has anybody seen an academic style analysis on the Supercharger model, where queueing theory is applied in order to determine how well it's going to work as a function of total cars sold?

This is not my area of expertise, but I am guessing that this branch of science should be able to tell us how many Supercharger stalls are needed as a function of Teslas being driven, such that it is more likely than not that a charging stall is available upon arrival there.

Gas stations work because of their quantities (about 125,000 in the US) and short visit intervals (less than 5 minutes/car right?)...

Things are fine now, but what about in 1 year, 2 years, 3 years; especially when certain collective actions are known to occur, like thousands of people from Atlanta heading to the Gulf Coast at the same time on Memorial Day weekend.

If anyone can point me to a quality analysis I'd be interested!


I have been asked to participate in a survey in the past. I think it was probably done by ChargePoint or PlugShare. First I think we need to have more supercharges before this type of questions can be efficacious.

I'm not so sure about that... the science needed to make accurate predictions may already exist.

There is another part of the equation. I read here that when all stalls in an SC site are active that the draw per car slows down a bit (or somewhat noticeably). Some drivers reported seeing charging speed up when others unplugged. Did I understand this correctly? It is like the SC unit can throttle itself during a charge when all are underway (and not based on the final 20% which is charged more slowly).

One thing I noticed on the SuperCharger LCD screen display that was shared on a few sites recently. The average charge was in the 30-40kWh range and not a full charge. Seems like folks would typically want to roll in for a nice 30 minute charge of 30-40 kWh and roll out.

I'm sure a great model could be created, but doubt we would learn anything from it.

If Tesla builds and expands superchargers based on demand, there will be limited or no queues - just like gas stations.

If Tesla does not build and expand superchargers based on demand, there will be long queues and frustration.

No model needed to figure that out.

The good news is they have detailed data on supercharger usage, so they know the utilization and when they are at capacity.

"how many Supercharger stalls are needed as a function of Teslas being driven, such that it is more likely than not that a charging stall is available upon arrival there.

Gas stations work because of their quantities (about 125,000 in the US) and short visit intervals (less than 5 minutes/car right?)..."

Well, I'd rather look at things differently. Electric cars can be charged really anywhere. At home, at a shopping mall, at work. There is no limit. Charging technology as well as charging points will keep pace with the number of cars, and sometimes exceed them.

Current confusion on standards will not last for too long and from that point on, things will move much faster than even today.

My worry is this - queuing theory will tell us that the number of stalls required to handle peak rates of use will be prohibitively expensive because of long interval times.

Yes, Tesla monitoring the data is a good thing; certainly glad they are doing that. But if queuing theory tells us that an interval time increase by a multiple of 4 (20 mins vs 5 mins) requires a stall count increase by a multiple of 16 then maybe there is a problem.

In the special case of many people going the same route at the same time, like Memorial Day weekend, planning the Supercharger build out to meet AVERAGE demand will still result in a big problem.

I'm going to start reading this and see if I can wrap my mind around it as everything I've stated above is just "gut feeling" -

@Al1 - good points. You're right. The domain of this discussion is limited only to long trips... and then maybe even only to long trips during peak demand. And that's a nice advantage over ICE right off the bat. Even still, I wanted to explore the idea a little bit.

@bonaire "I read here that when all stalls in an SC site are active that the draw per car slows down a bit (or somewhat noticeably)."

There are two stalls per Supercharger module, which depending on Supercharger module is either 90 kW (old), 120 kW (newer), 135 kW (near future).

For a 120 kW module, the understanding (which can always change), is the first car of the pair of stalls gets the full 120 kW (assuming the charge is not near full and they have v5.0+ software). When a second car connects to the second slot of the same Supercharger, it will get 30 kW, and the first one gets cut back to 90 kW. As the first car gets near full and the charge rate is reduced to protect the battery, the remaining power is diverted to the second car so it starts charging faster.

When you drive up, if possible, pick an empty stall where both the "A" and "B" of the same Supercharger are empty. It doesn't matter if you pick A or B. This way, you'll get the fastest charge, and not slow down another car. The stalls are normally marked as 1A, 1B, 2A, 2B, although a rare few are not marked.

Well, dagnubbit, you are confusing me yet again!

I thought it was "pick the other number" not "pick the other letter"...

I believe it was @nickjhowe that put this to rest, but it was excepting one SC (maybe in FLA ?).

My answer to that is that I'll just travel off-peak and leave the weekends to you folks.
I don't need no stinkin' queueing theory to figure that out.
;-) :-)


"I don't need no stinkin' queueing theory to figure that out."

LOL - you're a man of pragmatism.

This is an interesting problem to consider. Not every problem needs to have a practical application.

The model has a large number of parameters, but perhaps we can simplify it a bit to approximate a solution.

I do agree that "average demand" doesn't tell us much. As they say, if you threw all the mountains into all the lakes, Switzerland would be flat.

The problem is not unlike memory and processor capacity planning on servers. Must sleep now though.

TM is planning and emplacing according to peak demand. SCs are neither convenience nor time nor financial substitutes for home charging for the owner. Overnight 20A+ charging is the best deal on all counts.

There's a non-linear multiplier of sorts involved, though, because the pleasure of driving and using a Tesla will increase the per capita frequency of long road trips, according to experience to date. As SCs make that more feasible, the effect will be enhanced. A positive feedback factor.

But no runaway disaster is in the works. Building and operating SCs is a net benefit to TM, in every sense and dimension.

As jbunn said, there must certainly exist math models for queuing in servers, telephone exchanges etc. have been around for decades at least.

This looks like a good phD dissertation. Time to get TM to get an interested Stanford grad student on this one.

At some point free market forces must take over.

Better software for finding and reserving a charger on the fly or even scheduling charge location based on availability.

Business figuring out that charging gives you a customer that will be around for at least 30 minutes and it is worth the cost of an SC or two to attract the Tesla's.

I will not be surprised if some national chains negotiate some kind of license or exclusive use agreement with Tesla that speeds the rollout of more chargers. Like Apple and AT&T did on the iPhone initial release.

Yep, competitive fee-based superchargers from other licensed companies will be the ultimate solution to complement TM's superchargers. That, combined with apps for reserving and for monitoring availability. Perhaps charging rates will be adjusted depending on demand or time of day. And it is also true that EVs have many multiples of more places to charge than ICEs.

So you should always be able to find an open supercharger even during peak demand on Memorial Day. Just expect to use a private one and pay a higher rate than usual.


"My worry is this - queuing theory will tell us that the number of stalls required to handle peak rates of use will be prohibitively expensive because of long interval times".

Unfortunately I don't remember details of that theory. But like any other theory there are key assumptions to revisit before throwing in the numbers. Or conclusions may prove wrong.

Comparing to ICE cars is not apples to apples comparison. You can't fill your ICE car while sleeping, with EV you can. That takes a lot of cars off from charging stations. Than most likely queuing theory assumes there are no alternatives. If you need to call, you need to call. And your call has to go through existing lines, until they are extended. Most likely you can't make your calls shorter either. E. g. you can't identify idle lines and send some bites through them to rebuild the message in the end (I believe that came with internet, and that's how VOIP almost sent land lines to a museum in a matter of few years).

With superchargers before calculating your limits you's have to consider: ability to increase number of stalls, ability to add a station just one mile from existing one, it could be commercial technology by Tesla or comparable one offered by a retailer who wants to attract customers to his shop. You can't do that with oil station can you? You wouldn't allow a stinky oil-station next to your world's biggest wine store with collections from most exotic parts of the world and some bottles worth a few thousand dollars.

Also remember with ICE is filling time is pretty much set. With electric charges you can't make that assumptions, they keep improving at astounding speed. And then remember what Elon said?

Your ultimate choice will be between FREE (if you value your dollars) and battery swap (if you value your time more). That was pretty much Tesla's response to concerns what happens if there are too many electric cars?

PS: Remember your shopping experience at an oil station? You can buy coffee, ice-cream, drinks. In other words items, that don't require a lot of thinking. Because nobody will spend at your store more than five minutes.

Now imagine selling your product requires no less than half-an-hour of your client's attention. How can you make people come and visit your store and spend more time in it? Well, there is your answer! Charging stations!

In my opinion, superchargers are there to provide a capability but not necessarily to be able to sustain all predicted demand. In other words, the superchargers allow Tesla to say "a Tesla Model S can travel from DC to Boston". Soon they will be able to say that it can travel cross-country.

As far as the academic question, this would be a M/M/s queuing model (if anyone wants to look it up). Like some have suggested, this is routine analysis that can even be done with a simple spreadsheet. However, my guess is that Tesla is simply deciding on what to build based on customer demographics, not on usage forecasts.

To @Al1's point, a couple of weeks ago, I found myself at a truck stop in Alabama out of pure coincidence. It was very eye-opening. The place was like a combination amusement park and shopping mall. I had no idea truck stops were so cool(!). It occurred to me that's the future of the supercharging station and it would not surprise me if truck stops were the first to capitalize on this. So @Al1 and @Roamer are on to something.

[sorry this is of the original topic]

@TeslaTap/NKYTA - you are both right - you said the same thing a different way.

Each SuperCharger location contains one or more SuperCharger units. Each Unit is rated 90, 120, 135 kW and feeds two pods (the place where you plug in the car)

Each pod has number (1 to N) identifying which SuperCharger feeds it, and an A or B indicating which one of the pair it is. For most SC locations the pods are paired along the row (1A, 1B, 2A...); one SC location (Silverthorne??) is known to have 1A, 2A, 3A 4A, 1B, 2B, 3B, 4B).

Not sure I agree 100% with @TT. What I was told is that the amount of charge each car gets when both slots on a pod are occupied depends on the SOC of each car. Low SOC gets more kW. I do NOT know what happens if a low SOC car plugs into a pod that already has a high SOC car connected.

Regardless of the sequence, the rule is the same. If you can find a number where both A and B are free, use one of those.

I've been wondering about the time-of-day effect on SC demand. Whenever anyone asks me about the range of the MS and I tell them, including the availability of SCs, the instant response is always something like "That solves it. You can just have lunch while your car is getting recharged". Of course if a large proportion of users feel this way, lunch-time will be a zoo eventually.

I'm about to travel from the SF Bay Area to Southern California on Monday, so I guess I'll be able to report on the lunch-time demand in Gilroy and / or Atascadero.

The sc queuing problem is similar to the gas station on the turnpike model.

Whoops didn't finish. If you are pn the turnpike, you can choose other alternatives, but it's a pain. During peak periods, it gets crowded, but they have a small number of queues. Also, if you haven't noticed, gas pumps slower when there are a lot of cars sucking from the same underground tank. On memorial day weekend you could spend a considerable amount of time filling up on the turnpike.

Truckstops must accommodate drivers who have spent a long time behind the wheel. They need every kind of service and amusement, and spend a great deal on fuel. It makes sense the stops are so built up.

One thing I remember from queuing theory is that average traffic load does not mean uniform distribution. Even outside of peak times, traffic comes in bursts.
That is why you usually get to the line in the grocery store at the same time as several others. When there is no line at the checkout, well, there is hardly anyone there to see it.
Superchargers will have this same lumpy distribution, so to keep peak lines reasonable, they will be idle most of the time.

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