Category Archives: public transport

How to account for higher quality of service in Benefit/Cost Analysis

I recently had an twitter and email conversation with Benjamin Ross about rail vs. bus benefit/cost analysis (BCA).

The problem is that conventional BCA in practice does not consider the quality differences of different modes, focusing primarily on travel time, monetary costs, and monetized externalities. Assuming everything else were analyzed correctly, this leads us to over-invest in low quality modes and under-invest in high quality modes, from a welfare-maximizing perspective.

Let’s start with a few premises

1. The value of time (value of travel time savings) of each user differs because of a variety of factors. Everyone is in a hurry sometimes, and so has a higher value of time (willingness to pay for saving time) when time-strapped than at other times. Some people have more money than others, and so find it easier to pay to save time. The related notion of value of travel time reliability (VTTR) is reviewed here.

2. We don’t actually know user value of time. (An alternative approach evaluates just based on travel time, and assumes everyone is equal, since time is just as fast for rich and poor people.  For instance Carlos Daganzo and his students (e.g. Gonzales) optimize in terms of time, and convert monetary and other costs into time, referring to value of time as a politically determined variable. E.g. section 2.3.2 here. developing a temporal value of money rather than a monetary value of time. This is not standard in transportation economics.)

3. We  assume the value of time of all users is the same in a Benefit/Cost Analysis because the alternative would bias investment toward users with a high value of time. E.g. wealthy people in the western suburbs would get more investment than poor people in the city because they have a higher value of time, which is politically unacceptable to admit, as they did not pay proportionate to their value of time (since transportation funding on major roads comes predominantly from gas taxes. In contrast for local roads it comes predominantly from property taxes, which of course are paid for more by the wealthy).  For a market good this is not a problem (rich people pay for and get better goods and services all the time, otherwise why be rich). We do BCA because transportation is a publicly provided good.

4. We have models which purport to know people’s value of time and do use that in forecasting travel demand. The ratio of coefficients to time costs and money costs is implicit in the mode choice model. The value of time is usually in practice estimated from revealed preference data, but values have a wide range depending on location and methodology.

5. Travel demand models are highly inaccurate, etc., for a variety of reasons.

6. If these models were correct, the log-sum of the denominator of the mode choice model multiplied by the value of time (determined by the coefficients on time and cost in the model), with a little math, gives you an estimate of Consumers Surplus. This estimate is not usually used in practice, as no one outside of economics and travel demand modeling believes in utility theory.

7. Benefit/Cost Analysis is much simpler (and more simplistic) than travel demand modeling, and uses travel time savings and monetary cost in estimating Consumers Surplus.

8. BCA doesn’t actually estimate CS, just change in CS, since we don’t know the shape of the demand curve, but can estimate small changes to the demand curve and assume the curve is linear. Those doing BCA often use the rule of 1/2 to find the area of the benefit trapezoid)


Multiply the area by the Value of Time to monetize. This is shown in Figure 1.


9. This assumes the value of time experienced is the same independent of how it is experienced. Yet people clearly would pay more for a better experience. That doesn’t show up unless you have multiple demand curves (see below), and that is never done except by academics.

10. The travel demand model gives you an alternative specific constant (ASC), which says all else equal, mode X is preferred to mode Y, and will tell you how much additional demand there will be for X than Y under otherwise identical circumstances (namely price and time).

11. Empirical evidence suggests the ASC is positive for transit compared to car (all else equal, people like transit over car. Car mode shares are higher in most US markets because all else is not equal).

Usually the ASC is higher for new rail than new bus, since trains are a nicer experience. This is sometimes called the rail bias factor.

For instance Table 3 below reproduces values the FTA accepts for rail bias factors according to the linked report. The implication is that people would be willing to spend 15-20 minutes longer on a commuter rail than a local bus serving the same OD pair and otherwise with the same characteristics (except for the quality of the mode).

Much of this is just a question of modeling specification though, so e.g. the rationale includes things that (a) can be modeled and specified (but aren’t typically), and (b) may be improved for bus routes. Recent research says this number can be brought down a lot by better specification.


Constant Range (relative to Local Bus)


Commuter Rail

15 – 20 minutes

Reliable (fixed‐guideway), vehicle and passenger amenities, visibility, station amenities, etc.

Urban Rail

10 – 15 minutes

Reliable due to dedicated, fixed‐guideway, well‐identified, stations and routes, etc.


5 – 10 minutes

Reliable when running on semi‐dedicated lanes, often times uses low access and especially branded vehicles

Express Bus

‐10 to 10 minutes

Non‐stop, single‐seat ride, comfort, reliable when running on semi‐dedicated lanes

Infrequent off‐peak service, unreliable when subject to road congestion


12. The Consumers Surplus from a mode choice model would reflect this with higher utility when rail is available than if bus were available.

13. The Consumers Surplus from BCA, using the rule of 1/2,  would be higher for a rail line (Figure 2) than a bus line (Figure 1) because the demand is higher.


14. The CS from BCA would not reflect fully the quality difference. It should be shown as moving the demand curve outward. The benefit from the red area (Figure 3) is missing.





15. The red area is impossible to estimate with any confidence, since the shape of the curves outside the known area (before and after) is unknown. I drew the total consumers surplus as a triangle (and the change in CS as a trapezoid) (Figure 3), but this is misleading. Certainly it is positive.

16. If it were a triangle, and the Demand curves were parallel, some geometry might reveal the shape, but we also don’t know the lines are parallel. In reality they surely aren’t. The high value of time folks (on the left) might be willing to pay a lot more for the improved quality than the low value of time folks on the right.

Ben Ross proposes to improve BCA and develop an adjustment factor to account for the differences in quality  between modes. He suggests we look at the number of minutes it takes to get a number of riders for each mode.

I have mathematized this. So Rq=Crail,q – Cbus,q, where R is the travel time difference at some number of riders q, and Cm,q is the travel time (cost) at which you would get q riders on mode m. 

To illustrate:

If 1,000 people ride the bus at 10 minutes and 1,000 people ride the train at 12 minutes, Ben proposes the extra pleasure (or lessened pain) of taking rail is equal in value to a time savings of two minutes.

At a given margin, this is probably approximately correct. That is, the  marginal (the 1,000th) train rider is willing to take (pay) 12 minutes 12 minutes while the 1,000th bus rider insists on 10 minutes.

The problem we are trying to construct an area (the benefit). There is no guarantee that R is constant.

  • The 2,000th rail rider might insist on 11 minutes, while the 2,000th bus rider requires 8 minutes. R2000= 11-8 =3 ≠ 12-10.
  • The 10,000th rail rider might be willing to pay 3 minutes, while the 10,000th bus rider requires -3 minutes (you have to pay them 3 minutes to ride the bus). R10000=3–3 = 6.

Now we could try to find the “average” value of R, or the value of R for the average rider.  So let’s say you have forecast 30,000 riders for a line, then you try to find R for the 15,000th rider, and apply it over the whole range.

(What travel time do you need to get only 15,000 bus riders and 15,000 rail riders, this will be much different than the actual travel time you are modeling, and it will be a higher travel time, so the model will require some adjustment to obtain this number).

This again assumes distance between the curves is fixed. Unlike the rule of 1/2, which is meant to be applied over a small area, so the curvature doesn’t really matter, the assumption here is this applies over the whole demand curve, where differences in curvature might be quite significant.

If we used the model to trace out the demand curves, we could then integrate (find the red area), but this is data that is not generally obtained or reported to the economist doing the BCA. The modeler could compute this of course if they wanted to, with a bunch of model runs, but the modeler could just use the log sum, and no one believes the model or in utility or understands log sums. So the economists takes the forecast in its reduced form, and treats the method for getting it as a black box (or magic).

So is the approximation R reasonable? Is using this value better than using the implied R of 0 which is currently done?

As Ben notes,

All we really have is our one Alternative Specific Constant. It’s tough enough to draw a single value of that constant out of the available data, we surely can’t measure its dependence on income, walkability, etc.  What we actually know is the size of the rail preference under the conditions where the data was collected that the constant was calibrated against, not under the conditions that the model is simulating.
The hard part is scaling from measurement conditions to project conditions, but there are only a few simple alternatives (per trip, per mile, per minute) so if you don’t know which is right you could show results for all of them (and accept that reality may be in between).

I don’t see how this is different from the money value of time.  Doesn’t it involve the same kind of approximation?  And an assumed method of scaling?  Measured under one set of conditions, used under different conditions.


I don’t think I would trust using the model to trace out the demand curves.  The delta we’re looking at is ultimately derived from that Alternative Specific Constant.
When you only have one measured data point, drawing curves inevitably pulls in assumptions that tend to get insufficient examination and can easily introduce subtle (or not-so-subtle) errors.  The only robust conclusions are the ones that you can connect directly to your measured data point.  In my opinion (derived mostly from other kinds of models, but very strongly held) the best way to proceed is to treat your measured data point as a constant, multiply it by the relevant parameters, and go straight to an answer.  Then adjust it for whatever important factors that you can point to and explain in words why your measurement didn’t account for them and why your correction is appropriate.
You can certainly compare the calculation to a black-box model that solves partial differential equations (or in the transportation case a giant matrix), but you shouldn’t believe any model results whose cause you can’t explain convincingly after you get it.  (yes, the model sometimes detects your erroneous intuition, but most of the time it’s the model that is wrong).

Transit Station and Stop Design and Travel Time Perceptions

Eric Roper at the Star Tribune writes:
Study: Transit amenities affect perceived wait times

Eric Jaffe at CityLabs writes: A Basic Shelter Can Make the Wait for the Bus Feel Shorter:Twin Cities riders believed transit arrived more quickly at shelters or stations compared with stops at curbside signs.

I mentioned the Minnesota Daily piece earlier in the week

Both are about our (Guthrie, Fan, Levinson) unpublished, unreleased study on transit amenities: Transit Station and Stop Design and Travel Time Perceptions. I would say more, but it is unpublished and unreleased.

Three on Green Line / Green Lights

Updated 9/18/2014 with MPR article

Fred Melo writes in the Pioneer Press about Always Green Traffic Control “Green Line: Inventor proposes using timing, speed to improve travel time

“Ultimately, the decision whether or not to implement a system such as this along the Green Line would need to be made by Metro Transit’s project team,” said Kari Spreeman, a spokeswoman with the St. Paul Department of Public Works.

David Levinson, an engineering professor at the University of Minnesota who specializes in transportation issues, has blogged about “Always Green” on his website,

“It’s an interesting idea,” Levinson said. “Even if the total travel time is the same in both cases, it’d be better than going fast and then stopping. You might even save some time. After you stop, you have an acceleration-deceleration loss (in travel time).”

Levinson acknowledged one drawback, however. “It’s never been tested,” he said.


Tim Harlow at the Star Tribune writes in his column The Drive: Nick Musachio and the Always Green Traffic Control

David Levinson, a transportation expert at the University of Minnesota, says the Always Green Traffic Control has potential.

“I think it would work best for isolated intersections on rural expressways, but there is no reason it couldn’t work in an urban area,” Levinson said. “Static speed signs have been used for decades on Connecticut Avenue in Washington, D.C. Something dynamic should do even better. I do believe it warrants a field test.”

Musachio faces the challenge of getting somebody to do just that. He’s been bending ears of the St. Paul Public Works Department, but so far they have not bitten.

“In theory the system could work, but it has not been tested in a real environment. Until that happens, we won’t consider it,” said city spokeswoman Kari Spreeman.

Marion Renault at MPR writes “Inventor says synchronized lights could boost Green Line travel time” [I hope by "boost" she means reduce.]

“You can either change the lights to match the vehicles,” said David Levinson, a civil engineering professor at the University of Minnesota. “Or you can change the vehicles to match the lights.”

Levinson said keeping cars moving at a steady speed is optimal for traffic flow. But he said it takes a lot of coordination and a tightly-maintained fixed traffic system to create a grid of alternating, forward-moving platoons of cars and trains.

Previously here and here and here.

New London buses

Part 6: Political parties, three-axes, and public transport – A summary

By David Levinson and David King.

A comment on power: politics maximizes the ideal subject to the real

To be clear, everyone near power is instrumental – the Democrats favoring rail and construction in general due to  the association with unions and Republicans with their association with “free” roads, or Paul Weyrich with his justifications for suburban commuter rail.  Merriam Webster defines instrumentalism as  a doctrine that ideas are instruments of action and that their usefulness determines their truth. Thus it represents a situation, where values are an instrument to build a coalition to obtain power, as opposed to using power to support core values.  The Libertarians and Greens are purer of heart as they are farther from actual power. (And perhaps they are farther from actual power because they are purer of heart. The causality is mutual.)


Get on the Bus
Get on the Bus


Despite the transportation logic,  trains are more politically popular. A new train on new track in an exclusive right-of-way is a more comfortable ride than a bus on beat-up pavement shared with cars, trucks, and other vehicles.

People riding buses are unhappier with their commute than commuter train riders in Montreal (though about the same as Metro riders). Walking and biking make their commuters happier still.  By implication Greens are happiest with their non-motorized travel.

The unhappiness with bus use is for a variety of reasons. In part poor people (are rightfully) not as happy about the state of reality than those with more resources and opportunities. In part bus riders are likely less happy because of the stigma associated with buses and because of the underfunding of buses due to that stigma.

While that may seem like bad news for an argument about investing more in buses, we think it is an opportunity. It is the mode most easily improved. Thus it is where happiness can be most readily increased by reorganization and increases in service, better integration of information technology,  and enhancing the environment around stops and stations. We should increase the dignity of riding the bus.


Bus has received far less attention than rail. In the Twin Cities, the number of planners and engineers, leave aside dollars, per bus rider falls far short of the number per rail rider. In addition to high level design questions, attention to local details does matter, and does pay off. Attention is required.

New London buses
New London buses

Typically, bus/rail comparisons contrast existing local buses, which are old, noisy and slow,   with new trains. New beats old.  Where buses have been used to provide high quality, speedy, quiet (electric), lane separated transit in good markets they perform really well. Finding ways to make buses work requires cooperation of the bus operator (public or private) and the infrastructure provider (almost always the public).

The land use argument is one of choice. Zoning can be changed without building rail, but no one seems to be doing that. Economic development effects have been demonstrated for significant bus improvements.

There is so much more than can be done with buses, and can be done within a year, that it is depressing (if not insane) so few even try.

Take away a few parking spaces, and even some general purpose traffic lanes, and put some paint on the road (reallocating road space to buses), then see how people like the new bus versus the old bus.

Reallocate transit dollars and see how many new high frequency bus services can be deployed for the same resources otherwise dedicated to a short  rail corridor that .

The mainstream political parties tend to exist for political purposes more than for pursuing a coherent set of policies. The evidence suggests no one in power actually wants less public spending, and arguments are about marginal increases in spending. Yet most of the public is far more interested is being able to get around affordably and easily, reaching their valued destinations, than what technology is used.

Political Parties, Three-Axes, And Public Transport

  1. Part 1: Introduction
  2. Part 2: Why Democrats Should Like Buses
  3. Part 3: Why Republicans Should Like Buses
  4. Part 4: Why Libertarians Should Like Buses
  5. Part 5: Why Greens Should Like Buses
  6. Part 6: Summary
London Green Bus (Country Bus)

Part 5: Why Greens should like buses

By David Levinson and David King.

I don't need a war to power my bicycle. Bumper sticker on car.
I don’t need a war to power my bicycle. Bumper sticker on car.

Greens are most associated in the US with non-motorized transportation. As pedestrians ourselves, we see the many advantages. While many more people could walk than do, and many others could re-arrange their home and work locations over time to enable one or more members of their household to walk or bike, getting people to move home or change jobs to minimize travel costs is a big ask. Creating new (and re-creating existing) urban places (instead of new suburban places) aligns with the philosophy of some Greens. Economic development and real estate  tend to be local issues, and downtown real estate in particular is now an odd ally of the Greens.

The next best thing to minimizing distances through changes in relative location and land use is getting people to their destinations in an energy efficient way.

While Greens don’t fit cleanly on the three-axis model, it is probably most related to Social Justice/ Equality, but extending the object of Justice from People to the Environment as a whole (that is valuing the environment for its own sake, not just for the sake of future humans).

Why Greens should want to invest in buses.

Energy use per passenger-km by mode. Source Transportation Energy Data Book, USDOE Energy use per passenger-km by mode. Source Transportation Energy Data Book, USDOE. Figure 27-8 in The Transportation Experience

  • Buses (when more fully occupied) are more energy efficient than other modes, and electric buses show promise to improve this even more. (In practice as shown in the adjoining figure, buses are less energy efficient than cars on average, due to low occupancies in off-peak and suburban services, though the marginal passenger incurs almost no additional energy consumption.)
  • Buses (and vans) are community transportation where people can meet their neighbors and the driver.
  • Rail construction (or any infrastructure construction) is highly disruptive to fragile eco-systems and highly energy intensive, so the payback period for CO2 emissions may be decades, if at all. If you think that CO2 is something to worry about, improving bus service in a matter of months should be far more valuable than potential reductions more than a decade away.
  • Making buses work better adheres to the adage used about housing that the greenest houses are existing houses. The greenest transport is more intensively using existing transport. Even with new rails, existing roads will remain. We should use them wisely.

Political Parties, Three-Axes, And Public Transport

  1. Part 1: Introduction
  2. Part 2: Why Democrats Should Like Buses
  3. Part 3: Why Republicans Should Like Buses
  4. Part 4: Why Libertarians Should Like Buses
  5. Part 5: Why Greens Should Like Buses
  6. Part 6: Summary
Buses are franchised out in London, and in many places have exclusive lanes

Part 4: Why Libertarians should like buses

By David Levinson and David King.

Today libertarian (if not “Libertarian”) transportation policy (best represented by Reason) favors moving towards road pricing, public private partnerships, contracting out, HOT lanes, and privatization as strategies, but doing so intelligently. All of this will have the consequence of raising the cost of travel by automobile and result in fewer vehicle miles traveled than current policies. It also suggests that if auto travel is more expensive, the use of other modes will increase. One of those other modes is buses.

Libertarians uphold the value of “Liberty”, freedom of action. Providing mobility for those without effective options increases overall freedom.

Buses are franchised out in London, and in many places have exclusive lanes
Buses are franchised out in London, and in many places have exclusive lanes

Why Libertarians should support buses.

  • Buses are more easily contracted out or franchised to private firms in a competitive way than infrastructure itself, which is embedded capital subject to natural spatial monopolies. The evidence for the ease of contracting is the extent of contracting (many non-US cities already contract out or franchise bus services).
  • Bus routing and scheduling is also more dynamic and adaptable to actual and changing needs given an environment with ubiquitous roads and evolving land uses.
  • Buses can take advantage of High Occupancy/Toll lanes, and integrated busways/HOT lanes are useful for suburb to city radial commuting markets, sharing the fixed costs of expensive facilities over more users than exclusive transit ways, without a time penalty.
  • Buses enable people without other options to travel farther than no motorized transport at all, increasing freedom.


Political Parties, Three-Axes, And Public Transport

  1. Part 1: Introduction
  2. Part 2: Why Democrats Should Like Buses
  3. Part 3: Why Republicans Should Like Buses
  4. Part 4: Why Libertarians Should Like Buses
  5. Part 5: Why Greens Should Like Buses
  6. Part 6: Summary
Buses are coldly efficient.

Part 3: Why Republicans should like buses

By David Levinson and David King.

Today Republicans are associated with roads (and “free” roads at that). The reasons we hear from politically connected folks are their constituency drives cars, and they don’t want to subsidize inefficient “toy” trains. The business community, traditionally Republicans, does support transit investment as a public amenity they don’t have to pay for.

Buses are coldly efficient.
Buses are coldly efficient.

It should be noted the late, racist, Republican,  rail-advocate Paul Weyrich continues to be trotted out by “conservatives“. Weyrich was embraced by the rail community despite admitting his “sordid grab bag of lamentable beliefs”.  His argument was that trains serve white middle class republican voters, so (a) Republicans should support their constituency (not much about actual core values of balancing budgets or efficiency required), and (b) rail advocates should accept the support as the coalition to build trains needed to be large due to their large public cost.

To the extent Republicans uphold the value of “Fraternity” and support the existing “Social Order” they should endorse buses.

Why Republicans should like buses

  • Buses are much less expensive to build than rail, and thus much more cost effective per passenger served in most markets. If you are a Republican who wants to provide public services (that is, you believe in governing as the outcome of victory), you want to provide them effectively.
  • Bus transit helps more lower income workers get to jobs than a similar investment in rail in most places. Employed people have a stake in the system.
  • Republicans can foster the many private bus operators serving US cities, including many of the suburban bus companies.
  • By supporting buses Republicans can show that they care about an actual problem their constituents have and work to improve how bus service is supplied.

Political Parties, Three-Axes, And Public Transport

  1. Part 1: Introduction
  2. Part 2: Why Democrats Should Like Buses
  3. Part 3: Why Republicans Should Like Buses
  4. Part 4: Why Libertarians Should Like Buses
  5. Part 5: Why Greens Should Like Buses
  6. Part 6: Summary