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).

One Way to Deal With a Desire Line |

Soon enough it will be Winter. Again a landscape covered with white powdery snow will reveal where travelers want to go. The first figure is an aerial shot of the former environment around the McNamara Alumni Center on the University of Minnesota campus. The second figure is in front of (behind) McNamara . Though there is a sidewalk just on the right of this image, pedestrians prefer the straight line path between the Scholars Walk and the diagonal path across Walnut from Beacon Street to the intersection of Oak Street and Washington Avenue. And why shouldn’t they? It’s cold outside. The extra few feet (extra few seconds) are not worth it, even for a cleared path.

In this Aerial photo via Google Maps you can see what the scene looked like before the recent "improvements". Pedestrians could walk diagonally across Walnut to the Scholars' Walk
In this Aerial photo via Google Maps you can see what the scene looked like before the recent “improvements”. Pedestrians could walk diagonally across Walnut to the Scholars Walk

The 2009 Campus Master Plan for the University of Minnesota is a very clear document regarding transportation. It prioritizes pedestrians, as is completely appropriate for a campus. There is nothing about “modal balance” or other nonsense. [I was involved with the development of transportation elements of the plan. I am also an employee of the University.]

Guideline 35 says:

Develop pedestrian connections that will:

  • Continue to share corridors with other modes of movement along streets or paths;
  • Enable pedestrians to take the most direct route between major destinations;
  • Prioritize pedestrian movement over other modes of travel whenever possible.

Guideline 57 says:

Design signature streets to accommodate all modes of
travel, with walking as the highest priority followed by bicycling, transit, and private vehicles.

So you would think when a desire line emerges, it would be considered for improvement since it is evidence of a direct route. Certainly you would think direct paths would be preserved rather than removed.

Desire line at McNamara Alumni Center
Desire line at McNamara Alumni Center

Sadly, this desire line used to be the regular sidewalk path until recent landscaping work done at the McNamara Alumni Center. But the people (well about 20% of the people based on my springtime count) could not be kept down by a mere four inches of concrete, they rebelled, in the typically passive-aggressive Minnesota way, by walking across the desire line rather than the rat run of the planner, especially in Winter when the curb is so conveniently hidden under snow, but even in summer, when there were dying plantings showing the ineffectiveness of the curb.

Still, I complained to campus facilities staff about the remodeling (1) making it a worse pedestrian condition, and (2) flying in the face of the campus master plan.

I am told this change was to slow down bicyclists coming from Washington Avenue to the Scholars Walk. I personally never noticed much of a bicyclist problem on the Scholars Walk, and there is Beacon Street right next door (and now Washington Avenue Mall a block away) so I doubt this will continue to be a significant problem. But perhaps a regent encountered a bicyclist.

I am also told that this was not a University of Minnesota, but a University of Minnesota Foundation decision. See the distinction? Me neither, and I work there. They share the domain and the Foundation Board is in part appointed by the Regents. I am sure this is important for tax purposes or some such.

A tree! That's how we solve a desire line.
A tree! That’s how we solve a desire line.

Staff said they would try to get this fixed. In spring I even met onsite with a campus planner, who agreed there were better solutions. This summer there was to be work here (to fix some poor construction in the remodel I am told), so there was an opportunity to rectify the situation.

Thus I am surprised to see at the end of this past summer a tree planted where once there was a path, and later a desire line despite curbs aimed nominally at slowing bicyclists and actually just extending the trip of pedestrians (if not increasing the likelihood of their tripping). Now I like trees, but I don’t see them being planted in the middle of streets. So why is it planted where once there was a sidewalk?

Sidewalk at McNamara
Sidewalk at McNamara 1
Sidewalk at McNamara 2
Sidewalk at McNamara 2

Here we have a tree giving the figurative finger to pedestrians who want to take the most direct route between major destinations (like the Stadium Village Campus Connector Bus Stop on Oak Street and the East Bank of Campus, for instance) in direct contravention of the guidelines of the University’s officially adopted plans.



1. If 1200 people  are each delayed three seconds, that is 1 person hour per day that is lost. I don’t know the pedestrian count, but that seems the right order of magnitude. (I know, this is America, and we don’t value the pedestrian’s time).

Desire Line at Nano Building
Just for Future Reference: Another Desire Line at Nano Building leading from the Rec Center

A clean well lighted place for cars

Go to here

The Transportation Experience: From Steamboats to Streetcars.

I will be giving a Seminar in Civil and Materials Engineering  at University of Illinois at Chicago on October 3, 2014 at 11:00 AM. The Talk is in 1047 Engineering Research Facility (ERF).

The Transportation Experience: From Steamboats to Streetcars.

Abstract: The talk explores the historical evolution of transportation modes and technologies. It traces how systems are innovated, planned and adapted, deployed and expanded, and reach maturity, where they may either be maintained in a polished obsolesce often propped up by subsidies, be displaced by competitors, or be reorganized and renewed. An array of examples supports the idea that modern policies are built from past experiences. The planning (and control) of nonlinear, unstable processes is today’s central transportation problem, and that this is universal and true of all modes.

The talk is based in part on the book: The Transportation Experience

Autonomous Vehicles: The Legal and Policy Road Ahead

I will be at Autonomous Vehicles: The Legal and Policy Road Ahead.

October 31, 2014


Cowles Auditorium
Hubert H. Humphrey Center
301 19th Ave. So., Minneapolis, MN 
University of Minnesota


Register online to attend–early registration ends Oct. 17

The event will feature:

  • Karlyn Stanley, RAND Corporation senior researcher, who will discuss the opportunities and challenges that lay ahead for autonomous and automated vehicles and the legal, regulatory, and policy frameworks responsible for their oversight and governance.
  • Bryant Walker Smith, University of South Carolina law professor, who will address the legal, ethical, and policy issues surrounding automated driving.
  • A panel discussion led by Senator Scott Dibble, Santa Clara University law professor Dorothy Glancy, and University of Minnesota professor David Levinson. The panel will explore the impacts and implications of autonomous vehicles for society.
  • Minnesota Secretary of State Mark Ritchie, who will close the conference by addressing opportunities and visions for Minnesota.
  • Breakout sessions exploring industry and design perspectives, civil liability and insurance, criminal liability, regional and city planning perspectives, and ethics, equity, and access.

For a detailed event program and speaker information, please visit the event website.

Land Value Capture Presentation

I talked about Land Value Capture at the Railvolution Conference yesterday. The presentation is here. Our reports are here.

Value Capture Flowchart
Value Capture Flowchart


The forgotten discovery of gravity models and the inefficiency of early railway networks

Andrew Odlyzko finds the earliest use of gravity models for travel demand and spatial interaction in his new working paper “The forgotten discovery of gravity models and the inefficiency of early railway networks“, moving the clock a few years earlier.

Abstract. The routes of early railways around the world were generally inefficient because the prevailing doctrine of the time called for concentrating on provision of fast service between major cities and neglect of local traffic. Modern planners rely on methods such as the “gravity models of spatial interaction,” which show the costs of such faulty assumptions. Such models were not used in the 19th century.
The first formulation of gravity models is usually attributed to Henry Carey in 1858. This paper shows that a Belgian civil engineer, Henri-Guillaume Desart, discovered them earlier, in 1846, based on the study of a unique and extensive data set on passenger travel in his country. His work was published during the great Railway Mania in Britain. Had the validity and value of this contri- bution been recognized properly, the investment losses of that gigantic bubble could have been lessened, and more efficient rail systems in Britain and many other countries would almost surely have been built. This incident shows society’s early encounter with the “Big Data” of the day and the slow diffusion of economically significant information. The methods used in the study point to ways to apply methods of modern network science to analyze information dissemination in the 19th century.

ISYE Faculty Opening at University of Minnesota

The Department of Industrial and Systems Engineering at the University of Minnesota, has a faculty opening.


Department of Industrial and Systems Engineering University of Minnesota
Faculty Opening

The Department of Industrial and Systems Engineering at the University of Minnesota invites applications for a tenured or tenure-track faculty position starting in Fall 2015. Applicants at all ranks will be considered. We seek candidates with a strong methodological foundation in Operations Research and Industrial Engineering, and a demonstrated interest in applications including, but not limited to: business analytics, energy and the environment, healthcare and medical applications, transportation and logistics, supply chain management, financial engineering, service operations, quality and reliability. Applicants should also have a strong commitment to teaching, to mentoring graduate students, and to developing and maintaining an active program of sponsored research. Applicants must hold a Ph.D., or expect to complete their degree before Fall 2015, in Industrial Engineering, Operations Research, Operations Management or a closely related discipline. Senior applicants should have an outstanding track record of research and teaching accomplishments.

The University of Minnesota is located in the heart of the vibrant Minneapolis-St. Paul metropolitan area, which is consistently rated as one of America’s best places to live and is home to many leading companies. The Department of Industrial and Systems Engineering is the newest department within the College of Science and Engineering at the University of Minnesota and is growing rapidly. Additional information about the department can be found at

Applicants are encouraged to apply by November 15, 2014. Review of applications will begin immediately and will continue until the position is filled. Applicants interested in meeting with current Industrial and Systems Engineering faculty members at the 2014 INFORMS Conference in San Francisco should apply by October 19, 2014. Additional information and application instructions can be found at Candidates may contact the chair of the search committee at The University of Minnesota is an equal opportunity educator and employer.

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.