Base Train Service is Cheap, Peak Train Service is Expensive

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.

29 comments

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  2. ckrueger99

    How do labor costs figure into the analysis? The conductor issue is a major one for US regional rail especially.

  3. Christopher Parker

    You’ve made a very strong argument for a higher peak hour fare. Let the off-hour fare serve those who need a lower fare and let the rush-hour folks pay some of the impact they create. Create an incentive to shift travel.

    You’ve also made a strong case for all-day service, so long as the infrastructure is built and available (which leaves out freight railroads used at off-peak times for freight).

  4. Joey

    As Clem Tiller recently reported, CalTrain is now planning 6 TPH peak with 8 car trains / 3 TPH off-peak with 4 car trains.

    Your analysis would suggest that (1) CalTrain should run more off-peak service (duh) and (2) There might not be much value in running shorter trains off peak (interesting).

    Maybe labor does factor in though – IIRC CalTrain’s work rules base the number of conductors per train on the number of cars, so running longer trains requires more conductors.

    • Alon Levy

      The MBTA’s contract with Keolis says there should be a conductor per fixed number of passengers, IIRC 300. There are also issues with manual door opening, but Caltrain won’t have that problem. Frankly, a modern regional railroad doesn’t have either problem, because practically nobody still uses conductors (Americans are a big exception), and even fewer places still use manually-operated doors.

      • Nathanael

        DLR in London, of course, uses conductors (“captains”) but no drivers, which has a lot to be said for it — unlike automated cars, which are still fantasy material, automated trains are well-developed technology.

  5. Joseph

    Your calculations here would mean that the number of kilometers traveld has little to no effect on total maintenance and equipment costs. This seems hard to believe. Cars and trucks depreciate mainly per mile, don’t they? And a plane’s lifespan is closely tied to total flight hours. I also don’t see where the per-hour / per-mile labor costs were accounted for.

    • Alon Levy

      Cars have gas engines, which are responsible to a large share of maintenance costs. The same issue affects diesel trains – my understanding (i.e. I heard it from railfans) is that the biggest maintenance item is the diesel engine, and the same is true of buses. This also explains why diesel trains have a fraction of the mean distance between failures of electric trains. Without such an engine stressing the systems, maintenance is less sensitive to whether the vehicle is in operation, and to how fast it is. Evidently, faster trains don’t depreciate faster than slower trains, and trains that have a high peak factor don’t depreciate slower than trains with a low peak factor.

      I expected maintenance to mostly track v-km, but once I started looking at maintenance costs I saw all these contracts that specify cost and time period but say nothing about frequency, even in situations in which the operator can make big decisions either way. The Coradia Nordic maintenance contract is for provincial regional rail services, in which local authorities can make sweeping decisions about peak and off-peak frequency.

      • Eric

        How DOES a train degrade over time in a way that’s not sensitive to the amount of use it gets? Does it rust?

          • Colin V. Parker (@ColinVParker)

            So your theory is that dust, when inside the bearing, causes wear relatively quickly, and that the dust takes many years to migrate through the various covers and mitigation schemes? If rust mattered you’d expect huge variation depending on typical moisture levels, right? Does your data although for that type of comparison?

          • Alon Levy

            It doesn’t, it’s not nearly granular enough.

            For what it’s worth, ICE inspection schedules are per km, not per period of time. But the most routine inspection (every 4,000 km) involves emptying waste collection, which sounds like something that needs to be done on a regular basis even if the train only runs at rush hour; the other checks also involve looking for problems that could come from weather and erosion. This is nearly half of the scheduled maintenance time.

          • F-Line to Dudley

            The traction motors providing propulsion to the wheels are the primary component susceptible to dust. Most rolling stock on all rail modes–tram, metro, EMU/DMU, locomotives (any: electric, diesel, dual-mode)–manufactured prior to ~1995 use DC traction motors (regardless of whether source power is AC or DC electrification, or fossil fuel prime mover). From the late-90’s and turn of the century on new orders have used AC traction almost exclusively. Brief explainer here on how the motors work, and the key differences between AC and DC: http://www.northeast.railfan.net/diesel_faq.html.

            On DC motors a wire brush is needed to kinetically transfer power to spin the motor (video here of one in action on a Melbourne tram: https://www.youtube.com/watch?v=0Am7BXcRvd0), making the motors very maintenance-intensive and susceptible to environmental conditions like debris buildup, overheating, and sucked-in snow/ice. So much so that the main motors are paired with separate blower/scrubber motors simply for the sake of keeping the main motor clean and temperature-controlled. Even a well-maintained DC motor with frequently-changed brushes is going to suffer attrition in reliability from the cumulative effects of dust, with attrition on one motor accelerating attrition on all of other traction motors on the railcar or locomotive that have to work in tandem. And if it’s a multiple-unit train, heavily-worn propulsion on one self-propelled car is going to take its toll on the other cars in the MU fleet through same forces of overcompensation over time. So even though individual traction motors are considered semi-“consumable” parts individually replaced many times during a railcar’s lifespan, wholesale system replacements of propulsion components end up one of the biggest costs for midlife fleet overhauls because of the cumulative drag motor wear exerts on overall reliability: motor-to-motor, then car-to-car. You can trace it all back to dust and weather.

            The move to AC traction motors changes the game considerably. AC traction does away with the entirety of the brush mechanism for an entirely solid-state energy transfer via magnetic fields. They’re more expensive up-front because of the additional transformer infrastructure required to power the motors; DC motors require far less in way of support systems. But AC motors are are MUCH simpler to maintain, much longer-lasting, can run in wider temperature extremes (and thus be pushed to higher performance limits), and are much less susceptible to environmental attrition because that big Achilles heel–the mechanical brushes–is gone. It took awhile for the technology to get efficient enough to displace DC traction in production rolling stock, so it’s only been in the last 20 years that AC has become widespread. First in trams/metros/MU’s in the late-90’s, then locomotives from the early-00’s on. Very few new-from-ground-up DC traction railcars or locomotives are produced at all today, except to serve smaller niche customers who are still maintaining all-DC rosters and don’t have the maintenance bandwidth to fragment their motor types yet.

            However, rolling stock is rebuildable again and again and again so DC traction isn’t going away at all. It’s probably only been the last 2-3 years that AC traction even topped 50% share of worldwide rolling stock despite that being just about the only thing produced new for 20 years now. Economic pros/cons for rebuilding vs. buying new are still extremely individualized by application, and there are too many unrelated compelling reasons to rebuild “It Just Works™” old stock for change in motor tech alone to trigger a mass purge.

            Tracing attrition rates is going to be murkier and more complicated for the next 20 years with today’s pronounced split in worldwide AC vs. DC traction usage than it used to be when DC had a near-total hegemony. You have an enormous worldwide installed base of DC with an enormous maintenance supply chain keeping it stable and cost-controlled. But then AC, despite its hands-down technological advantages, is still featured in a lot of first-generation vehicles (now 5-, 10-, 15- years old) that packed a lot of less-proven new tech–usually computers, not motors–under the hood, with lots of proprietary first-time supply chains. Those first-gen vehicles often end up pricier to maintain and may not have the same longevity in rebuild as an nth-generation DC traction railcar. The actual economic “proof” of AC’s better attrition rate comes from the 2nd/3rd-generation production runs that are only now being ordered from the factory, so it’ll take a couple more decades of gradual overchurn to show itself macroeconomically. Eventually you’ll be able to make clear predictions of maintainability and attrition economics distinct from today’s rolling stock figures because propulsion systems factor that hugely in the equation. But it’s going to take a very, very long time for this major tech shift to cycle itself completely through worldwide because railcars have such inherently long service lives compared to other modes.

    • mdahmus

      Cars don’t depreciate mainly per mile unless excessively used. This is a fiction most people believe solely due to the fact that the IRS treats depreciation that way (they pretty much have no choice).

      Take a look at Kelly Blue Book at a 10 year old Honda Civic with 10,000 and 150,000 miles on it and tell me how much depreciation you think was time versus miles after that.

    • Ian Mitchell

      Planes depreciate mainly from pressurization and landings. They also depreciate from cold flow (creep), which comes from the transition between surface temperatures to the sub-stratosphere and back.

      This is correlated with flight hours, but isn’t the same.

      The delta flight from Philly to JFK on a 757, less than 100 miles long, puts much of the same wear and tear (thus depreciation) on the plane as Aer Lingus’ 3000-mile 757 jaunt from Hartford to Dublin.

      • Untangled

        Yes, that’s why you see planes running long-haul flights that are quite old still in service, yet newer planes which run short-haul flights are being retired.

  6. Eric

    You should divide this (and your other posts) into sections, i.e. “Rolling stock”, “maintenance”. I think you scare off some readers by giving them a 2300-word wall of undifferentiated text.

  7. adirondacker12800

    A $1 km car with 20 people on it costs 5 cents a passenger. A $5 km car with 200 people on it costs 2.5 per passenger. Pesky passengers. On a passenger railroad. Increase the frequency from once an hour to four times an hour and double ridership, it’s 10 people on a car at 10 cents a passenger. Pesky passengers.

    ….. East Side Access is costing an outrageous amount of money. 10,000 people at peak, which is probably low, would need 5 lanes of very crowded highway. They wouldn’t have anyplace to park. Not that if 10,000 cars were added to the Upper East Side during rush hour, they would be able to get to the parking…. if it existed. Getting some employers to change their business hours to 9PM to 5AM would solve a lot of problems. Pesky employers. And their customers.

    And energy costs scale linearly with the number of train runs in service.

    Maybe for diesel trains but commercial electricity customers don’t pay flat rates. Railroads are big customers and can negotiate rates but they aren’t flat. Apparently the constraint on the Harlem Line is the capacity of the substations. Volts time amps equals watts. It’s why they went from 600 volts to 750 volts for the M1s. Air conditioning had something to do with too. Air conditioning, pesky passengers. They want heat in the winter too. There are constraints on how high the voltage in wire can be before it starts arcing. And the amount of amps you can shove through it before you need thicker wires or more closely spaced substation. Pesky electricity and it’s weird stuff like Ohm’s law. …it’s really inconvenient that the sun is out in on summer afternoons increasing the load on the air conditioning. Pesky passengers wanting windows in their trains that let the sun in increasing the cooling load. During the peak of usage. When rates for commercial customers are high. They get home and want to reheat dinner in a microwave oven extending peak demand. Very likely in an air conditioned kitchen. Pesky.

      • anonymouse

        I think the two of you are agreeing with each other? If energy costs scale nonlinearly, then the marginal peak train is much more expensive on that front than the marginal off-peak train, both because of substation capacity issues and because of potential time of day pricing for power.

        • Alon Levy

          Well, in the morning peak there isn’t a lot of power demand… peak power demand is in the evening, starting around the tail end of the afternoon peak.

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  9. Manuel

    Depreciation costs depend on time, maintenance costs depend on time AND on distance. Wheels and brakes’ wear, for instance, depend exclusively on distance. If you subcontract maintenance on a time-only basis, you should be sure you’ll be paying the subcontractor’s risk factor, which, almost by definition, will be heavy

  10. Michael

    Have you considered doing a break even analysis? For example, what you describe here is consistent with intuition. It’s intuitive that running 2/hr all the time would be less expensive than a 50/50 blend of 4/hr & 0/hr (kinda like MBTA commuter rail current state…)

    But could we run 3 per hour at the same cost as a current 4/0 scheme?

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