A few days ago, I calculated regional rail operating costs from first principles, as opposed to looking at actual operating costs around the world. Subway operating costs in the developed world bottom at $4-5/car-km (and Singapore, near the bottom end, has long cars), and I wanted to see what the minimum achievable was. I tweetstormed about it two days ago and was asked to turn it into a full blog post. It turns out there is a vast difference between the operating cost of base service and the operating cost of the peak. The cost of rolling stock acquisition and maintenance may differ by a factor of five, or even more for especially peaky operations. The reason is that there are about 5,800 hours of daytime and evening operation per year but only about 1,000 hours of peak operation. Acquisition and maintenance costs seem to be based exclusively on time and not distance traveled, so this is about a factor of five difference in cost per hour (or kilometer) of operation: $5/car-km for the peak, or $1/car-km for the base.
The cost of acquisition of trains is pretty easy to calculate, since a large number of orders are reported in trade magazines like Railway Gazette and Rail Journal. The cost of a single-level trainset should be taken to be $2.5 million per 25-meter-long car, a length typical of American and Nordic trains, though on the high side for the rest of Europe. This is based on German orders of high-performance EMUs from 2014, 2016, and 2017, rated per meter of car length. In the US, the cost of single-level EMUs is similar, but the trains are heavier and lower-performance: the LIRR and Metro-North M9 is $2.7 million per car, and SEPTA’s defective Silverliner V cost $2.3 million per car. Bilevels cost more, and, as I complained at the beginning of this month, Paris has some comically expensive bilevels, approaching $6 million per 25 meters of car length on the RER D and E. American one-off orders are expensive as well: Caltrain’s KISS order is $5.7 million per car for the base order and $4 million per car for the option; in countries that import trains from the usual factories rather than making manufacturers open new domestic plants, the KISS is cheaper, down to about $3.2 million per car in Sweden.
I consolidated this list of costs to one tweet: $2.5 million per 25-meter car if you’re good at procurement, $5 million if you’re bad. The rest of the analysis assumes agencies are good at procurement, so a car is $2.5 million. This is a capital cost, but it’s still a marginal cost of operations, since higher frequency requires more trains at the end of the day; it’s not like investments in physical plant, which may or may not be necessary depending on the precise infrastructure situation.
Depreciation on $2.5 million over 40 years, and 4% interest, add up to $162,500 per year. Here I’m making an assumption that the lifespan of a train is the same no matter how long it runs. This seems justified: peaky American trains, traveling less than 100,000 km per year, don’t last longer than their less peaky counterparts in Europe. London aims at reducing its peak-to-base ratio to not much more than 1; judging by annual train-km and the number of trainsets, Underground trains travel 127,000 km a year, whereas the same analysis on the New York City Subway (using NTD data) yields 86,000 km. But in both cities, trains typically last about 40 years.
In Japan, the situation is different – trains only last 20 years. This is not because they run all that much (the peak-to-base ratio on the Tokyo rail network is about 2, and the average speed is 30 km/h except on a few express lines), but because the trains are designed to be lighter, cheaper, and lower-maintenance, at the cost of lasting only half as long. I’m not including Japanese costs in this analysis, because I can’t find any numbers for procurement costs, let alone maintenance costs, except for Shinkansen – and high-speed trains cost a multiple of regional trains (in Europe, about $5 million per 25-meter car).
Now, if acquisition ends up costing about $160,000 per year for a car, maintenance adds another $70,000-100,000. This is harder to ascertain, but there are occasional maintenance contracts, or purchase + maintenance contracts. An Alstom Coradia Nordic maintenance contract works out to about $70,000 per 25 meters of train length annually. Another Alstom contract, for British trains manufactured by CAF for $3.3 million per 25 meters of train length, is $550,000 per 25 meters of train length over 6 years; half of the trains are EMUs, the other half are unpowered cars (the diesel locomotive’s maintenance is not included in the contract). Two more contracts covering purchase plus maintenance, one by Bombardier and one by Stadler, are consistent with annual maintenance costs in the $70,000-100,000 range.
That the maintenance cost is priced per year, independently of distance driven, suggests that distance driven plays a limited role. The Bombardier contract involves a consortium with specified service, but the other contracts separate maintenance from operations, and were maintenance cost based largely on distance, operators could easily run more service and offload the cost to the vendors. This is not necessarily true everywhere, and Adam Rahbee (profiled in CityLab) told me that New York City Subway maintenance costs scale with distance driven, so running trains more often off-peak wouldn’t improve per-km operating expenses. But it does seem to hold at least in European regional rail maintenance contracts.
The upshot is that adding maintenance and depreciation and interest on rolling stock acquisition works out to about $250,000 per 25 meters of train length. So it’s now left to compute costs per car-km.
Base service for 16 hours a day works out to 5,800 hours a year. But rolling stock availability is less than 100% because of routine maintenance needs. In its proposals for high-speed rail in the US, SNCF said that it cycles TGVs for maintenance on weekdays in order to be able to run maximum service during the weekend travel peak: for example, in its Midwest proposal, it says on PDF-p. 60 that off-peak availability is 80% and peak availability is 98%. The 80% off-peak availability figure assumes one fifth of the trains are undergoing maintenance each weekday; but for service provided without a peak, it’s possible to also do maintenance on weekends, raising availability to 6/7, or about 86%, giving about 5,000 hours a year. If commuter trains average 50 km/h, the cost is $250,000/(5,000*50) = $1/car-km.
Peak service only allows a fraction of this usage level. Rolling stock availability can approach 100% if maintenance is kept to the off-peak period, but this only squeezes an extra 1/6 improvement in vehicle-km per year, nowhere near enough to offset the fact that the peak is short. When I write commuter rail schedules for the US I assume a 6-hour peak, entering the CBD between 7 and 10 in the morning and leaving between 5 and 8; however, actual peaks are much shorter, especially in the morning. The RER A has about 2.5 peak hours per day. One MBTA commuter train, the Heart-to-Hub nonstop service between Worcester and Boston, only runs for an hour a day in each direction. Metro-North’s New Haven Line schedules suggest a short peak period for each train as well. A 4-hour peak corresponds to 1,000 hours a year, assuming 250 weekdays excluding holidays.
Of note, it doesn’t matter too much whether the peak is unidirectional (inbound in the morning, outbound in the afternoon) or bidirectional, except when the train’s one-way travel time is much shorter than the peak window. A bidirectional 6-hour peak, with 3 hours in each direction, only allows trains to run the full 6 peak hours if the one-way trip time is 3 hours or if there’s enough reverse-peak service to allow the train to do multiple runs. On Heart-to-Hub this doesn’t matter because it consists of exactly one roundtrip, but on Metro-North, it does matter: the peak lasts about 2 hours in each direction, but there’s almost no supplemental reverse-peak service, and the one-way trip time ranges from 30 minutes to just over 2 hours, with an average of a little more than an hour, so each train can only run about 2.5 hours of peak service on average. The assumption of 4 hours of peak service per weekday is generous for an American operation.
With 1,000 annual hours of peak service and 50 km/h average speed, $250,000 in maintenance costs translates to $5 per car-km. Heart-to-Hub averages about 70 km/h, but only gets about 500 annual hours, boosting costs to $7/car-km.
In practice, all-peak and all-base rail operations only exist as edge cases: the only urban rail service without a peak that I know of is the Helsinki Metro, which runs every 5 minutes all day, whereas peak-only rail operations, such as Vancouver’s West Coast Express, tend to have so little ridership that they’re irrelevant to any discussion of modern regional rail. Switzerland tries to run the same frequency all day based on its clockface schedule plans, but peak trains are longer, so from the perspective of train maintenance there is often a hefty peak-to-base ratio there.
A mixed operation can be analyzed as a weighted average of peak and base costs. A good rule of thumb is that the overall cost can never be higher than the cost of the base times the peak-to-base ratio, because ultimately introducing extra peak service multiplies costs by the peak-to-base ratio while also increasing train-km (and of course increasing capacity when it is most constrained, significantly increasing ridership and revenue).
A peak-to-base ratio of 2, which seems typical of operations in Tokyo and is a little bit on the high side on the RER (in both Tokyo and Paris train lengths are the same throughout the day), means 5/6 of train-km are the base and 1/6 are supplemental service over the 4-hour peak, combining to a weighted average of $1.67/car-km. But the peak-to-base ratio on the New Haven Line is 5, which means the base contributes 5/9 of train-km and not 5/6, yielding only 90,000 annual km per car (in fact, the NTD suggests the actual figure is about 97,000, not including locomotives). Were maintenance costs on Metro-North similar to those of routine European operations, this would be about $2.70/car-km.
It’s important to note that rolling stock is just one of several costs of rail operations. Evidently, Metro-North costs $10/car-km to operate, and while its rolling stock maintenance appear higher than the European norm, procurement costs aren’t, and high maintenance costs can push it from $2.70/car-km to maybe $4/car-km. There’s a lot of extra expense on top of that. Among the other costs, infrastructure maintenance, including stations, has the same implication as rolling stock: the costs are insensitive to train-km, and they’re also relatively insensitive to the total amount of peak service provided. Crew costs in contrast mostly scale with train operating hours – a higher peak-to-base ratio does make it harder to schedule crew for optimal efficiency, but the difference is not so stark. And energy costs scale linearly with the number of train runs in service. So it’s not really true that the peak is five times as expensive to run as the base; I would guess the figure is about three times as expensive, from some data on other costs that isn’t strong enough for me to commit it to a blog post.
That said, rolling stock really does cost five times as much at the peak than off-peak. This implies that places that can’t control their rolling stock costs should aim at reducing the peak-to-base ratio whenever possible, including the RER (because of high procurement costs, especially on the RER A) and American rail operations (because of high maintenance costs on the LIRR and Metro-North, and high procurement cost of anything that requires setting up a new factory because of Buy America regulations).
The RER is not the LIRR or Metro-North. The total operating costs of the Metro and the RATP portions of the RER are together about $6 per car-km (this is one of the systems labeled “EU” in London’s benchmarking report), and unless the Metro is unusually cheap to operate, which would be surprising, the costs of both systems have to be about the same. Depreciation and interest on RER A rolling stock procurement costs alone is about $350,000 per 22.5-meter car, which works out to about $1.50/car-km base and $7.50 peak. Today’s peak-to-base ratio of 2 means that this capital cost adds about $2.50/car-km, or about 40% of operating and maintenance costs; this could be cut back to $1.50 if RATP ran off-peak and reverse-peak service at the same frequency as the peak. Boosting off-peak frequency to where the peak is today, about 25 trains per hour, would still have pretty full trains within the city and its innermost suburbs, if not near the ends. And it would cut unit capital costs by about 1/6 of present-day operating costs, while also allowing a supplementary cut in direct unit operating costs (namely, maintenance) of about 3%. In reality, Francilien tax money goes to pay for both capital and operating costs, so combined this cuts ongoing unit costs (i.e. excluding new tunnels) by about 17%, by running more service for not much more than today’s costs.
In an environment in which costs are dominated by capital acquisition, it makes sense to operate expensive machinery for as many hours as possible. This means running maximum service whenever possible, subject to spare ratios and maintenance needs. Even if the off-peak trains are mostly empty, the marginal cost of rolling stock for such service is free, and the other costs are still on the low side; adding more runs throughout the day has low enough operating costs ($1/car-km for rolling stock procurement and maintenance, again) that trains don’t need to be full or even close to full to socially and economically justify extra service.