Distance-Normalized Ridership

One of the most frequent criticisms of Dallas’s light rail implementation is that it carries comparatively few riders for the amount of track that has been built. This is then followed by either criticism of suburban-oriented transit generally, or by praise for Houston’s more urban-centric system.

Recently, it occurred to me to look up the ridership per mile of the Shinkansen network. Using annual figures (since the Shinkansen has a different weekly distribution than commuter-oriented LRT), the bullet train carries 340 million people over 1484 miles of track. DART carries 28.5 million people over 85 miles of track.

That gives the Shinkansen an annual ridership per route mile of 229,101, while Dallas clocks in at 336,096.

Is Dallas’s light rail 50% more effective than the bullet train? It is if you use the same math Houstonians have been using to argue why our system is better than the big D’s.

Clearly, a new metric is needed. I propose that we evenly weight both speed and ridership density. Density, because a system that serves denser-developed areas is more effective than one that serves a few desolate park and ride lots. Speed, because a system that gets you there faster is better than one that’s slow.

Distance-Normalized Ridership takes passenger volume, divides by system length, and then multiplies by space-mean speed. If all other factors are held constant, this number can be raised by an increase in ridership, an increase in average speed, or a decrease in total system length. This also captures one of the most basic tradeoffs in transit planning; do we have more stops, and serve a greater area? Or do we have fewer stations, to provide a faster trip? Finally, Distance-Normalized Ridership also has the advantage of being constant across Metric and Imperial units, because the distance factors cancel each other out. I propose that Distance-Normalized Ridership be expressed in units of riders per hour squared.

To show how this works, let’s look at Houston and Japan.

The combined ridership of the Tokaido, Sanyo, and Kyushu Shinkansen lines between Tokyo and Kagoshima is 219,513,000 passengers per year. This line stretches across 1326 kilometers and takes approximately 6.5 hours to traverse, for an average speed of 204 kilometers per hour.

Dividing 219,513,000 into 1326 yields 165,545 annual riders per kilometer. Further division yields 18.95 hourly riders per km. Multiplying this figure by 204 km/h yields 3866 riders per hour squared, which sounds like a reasonable number. The statistics for the Tokaido Shinkansen alone are 6337 riders/hr2, reflecting the much higher ridership density on that segment.

As of this writing, Houston MetroRail carries 45,751 riders on an average weekday, plus 18,656 on Saturday and 14,494 on Sunday. This adds up to 261,905 every week, or 1,559 per hour. Dividing 1,559 into the system’s 12.8 mile length yields 122 hourly riders per mile, and multiplying by its average speed of just over 15mph yields 1871 riders/hr2.

These numbers make intuitive sense. Japan’s Shinkansen is twice as effective as MetroRail, and the core Tokaido Shinkansen is twice as effective as the network as a whole. The figures are small enough to not be unwieldy (e.g. we’re not talking millions), yet large enough that we can get a reasonable degree of accuracy without using a decimal point.

So what about Dallas? I’m not going to compute them for this post. First, because I’m more interested in proposing a new metric than in producing yet another 713-214 comparison. Second, because I’m unsure of how to weight Dallas’s various lines. DART’s slowest segment also has the most interlining, and how you weight that is a major determinant in systemwide average speed.

What I’d really like is for some outside party – say, Greater Greater Washington’s Matt Johnson – to tally up the distance-normalized ridership for Dallas, Washington, and a number of other systems. I have a feeling WMATA would score fairly decently, given that system’s relatively high speeds.

6 thoughts on “Distance-Normalized Ridership”

  1. I find it interesting that this metric has units similar to that of acceleration. Riders per hour is straightforward, but riders per hour per hour is normally the unit you would use for the rate of change of your ridership. I suspect the difference between the units comes from different origins of your time measurement–for instance, work and torque have the same units (N-m), but the lengths being measured are perpendicular.

    [(R/hr)*(km/hr)]/(km) = (R*km)/(hr^2) / km — I don’t think R*km/hr^2 is terribly meaningful.

    For km/h, that is the distance each rider travels in an hour, while the other km comes from the system’s length.

    km/hr/km is the inverse of time it takes for a vehicle to travel the length of the system, in units of 1/hr. In other words, it’s the number of times a vehicle could traverse the network in a single hour.

    R/hr * km/hr/km == R/hr^2. Riders per hour is how many people get on the network in an hour.

    R/hr^2 can be visualized as filling all the vehicles of a network up, and driving them from one end to another. Each time they reach the end, the people get off and then get on again. On a shorter network, with the same number of people, you reach the end more often. With faster vehicles, you reach the end more often. With more people on your vehicles, you get more boardings.

    This is somewhat awkward to visualize.

  2. I like this idea, but if you’re going to bring speed into it, you might need to weight things by the number of passengers on each segment, especially if there are big differences in speed. For example, with Dallas, trains might be going 55 mph way out in the suburbs where there are few riders, but slow downtown where the trains are full. The full slow section obviously matters more than the empty fast section, something not captured by an overall average speed. Likewise, ideally you could even capture things by time of day, because low speeds due to congestion impact more people during rush hour than they do late night, the same way an on-time departure makes a bigger impact during rush hour. This would require a lot of data but there’s no technical reason agencies shouldn’t be able to get a lot of it pretty easily.

  3. I find this an interesting measure; thank you for leading me to it. Some slightly different choices of normalized variables could give you significantly more informative comparisons. Adding in distance traveled and/or revenue as inputs enables one to analyze

    1. Passenger miles (kilometers) traveled
    per Mile (km) of Alignment or Track
    per Year (month, day, hour, …) of elapsed time

    2. Revenue accrued
    per mile (km) of alignment (track)
    per unit of elapsed time

    3. Passenger boardings
    per Mile (km) of Alignment/Track
    per Year (month, day, hour, …)
    which can also be analyzed in terms of
    Average Distance Traveled per passenger.

    Note 1: The choices of mile or km, alignment or track, and unit of time must be adhered to in any given analysis, or comparisons will not be consistent and thus lacking in information.

    Note 2: For these measures the average is the most appropriate measure rather than the median, because the average preserves the relationship Distance times Fare equals Revenue.

    Handy point for comparison: Assuming average fares of 16 cents (US) per passenger mile, which yield average revenue of 21 cents per passenger mile, and assuming that break even includes covering capital and depreciation of the fixed plant and the rolling stock (but NOT stations), the break even load factor for high speed (400km/hr) rail in the US and Canada is about 6.5 million passenger miles per mile of alignment per annum. Note also that the percentage of cost covered increases with speed, so that for slower speeds, break even is not possible.

    Note 3: Were one to do an analysis based on the population density through which a given alignment passes, one would need to use census tract data … Conflating passenger load per alignment/track mile with population density through which the alignment passes would seem to confound analysis.

    Note 4: In rereading your text, I suspect some of your data is per track mile and other is per alignment mile. A given alignment mile can be served by anywhere from 1 to n tracks where n for passenger rail has a mode of 2 and is usually less than 5. So, the choice of units is significant.

  4. Based on my personal spreadsheet,

    Dallas DART: 1079 riders/hr2
    Houston Metro: 1850 riders/hr2


    I used NTD annual ridership, and calculated average speed as the total scheduled travel time for each unique section of track, divided by the total system track length.

    Dallas DART: 26 mph average speed
    Houston Metro: 15 mph average speed

    Dallas’ significant speed advantage doesn’t outweigh Houston’s 2.9x ridership/mile advantage.

    Results for a few other systems:

    DC WMATA: 8,981 riders/hr2
    NYC Subway: 24,806 riders/hr2
    San Francisco BART: 6,920 riders/hr2
    San Jose VTA: 533 riders/hr2
    Seattle Link: 2,237 riders/hr2
    Portland MAX: 1,938 riders/hr2

    In general, the variation in ridership density between US rail system is far greater than the variation in speed, so systems with high ridership will come out ahead of faster low ridership systems. A weighting factor could be applied to the speed term, but then you have an abstract scoring value without clearcut units.

    1. Thank you.

      I prefer the unweighted metric, since it keeps the percentages interchangeable – a 10% increase in ridership is equal to a 10% increase in speed. If you want to argue for Dallas-style rail, all you have to do is point to the system map. (There’s something intrinsically aesthetic about a bunch of different colored squiggly lines radiating out from a central core.)

      Besides, all of your numbers seem essentially “right” to me. Houston is playing in the same league as Portland. Seattle does a bit better, since it’s basically a heavy rail system with a piece of token street running so y’all can take pictures of townhomes with trains in front of them and say “transit oriented development!” BART comes in below DC, but not horribly so, NYC is in a league all its own, and San Jose isn’t something we discuss at the dinner table.

  5. This is a subject where the ridership data available does not permit us to meaningfully evaluate and compare transit systems, modes of transit particular to a system, individual lines, or segments along a line. What we have to work with are boarding and disembarkation numbers for each station, but what we lack is information that would indicate the statistical distribution of trip lengths to/from each node in the system. This means that a short trip between the TMC and outlying parking lots is counted as having the same utility as a trip between the apartments near the Astrodome and an office building downtown, but that’s obviously not the case.

    At a systematic level, viewing ridership in terms of vehicular boardings as being unequivocally good is a perverse incentive that may encourage system design that requires a greater frequency of transfers between transit vehicles even if that has the effect of inconveniencing riders and prompting some of them to commute by other means.

    If we’re going to compare the performance of transit systems then I prefer to compare Census data on workers’ commuting methods for appropriate geographies and then statistically adjusting that for the effect of urban density and travel times to work by various modes. That gives a better (albeit not flawless) indication of a transit agency’s market share.

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