Getting Charlie off the MTA: a multiobjective optimization method to account for cost constraints in public transit accessibility metrics

ABSTRACT

Most analyses of accessibility by public transit have focused on travel time and not considered the cost of transit fares. It is difficult to include fares in shortest-path algorithms because fares are often path-dependent. When fare policies allow discounted transfers, for example, the fare for a given journey segment depends on characteristics of previous journey segments. Existing methods to characterize tradeoffs between travel time and monetary cost objectives do not scale well to complex networks, or they rely on approximations. Additionally, they often require assumed values of time, which may be problematic for evaluating the equity of service provision. We propose a new method that allows us to find Pareto sets of paths, jointly minimizing fare and travel time. Using a case study in greater Boston, Massachusetts, USA, we test the algorithm’s performance as part of an interactive web application for computing accessibility metrics. Potential extensions for journey planning and route choice models are also discussed.

KEYWORDS:

• Pareto-optimal solution
• multiobjective optimization
• fares
• accessibility
• public transit
• equity

Acknowledgements

Road basemap $\copyright$ OpenStreetMap contributors.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Conveyal Analysis; source code available at https://github.com/conveyal.

2. If such systems do exist, users would likely be clever enough to discard their tickets when advantageous. While many airline contracts of carriage disallow throwaway ticketing ploys, we are unaware of any transit agencies that have codified such restrictions.

3. One might guess that the allowance is $\mathrm{\infty }$ because one can save $2 at each subsequent boarding, but this is actually false; the user can save $2 at the next boarding over paying the full fare, but if they were to instead pay the full fare, they would receive the transfer allowance at the next boarding. Thus, regardless of how many vehicles have been ridden, after the first vehicle is ridden, the fare paid and the maximum transfer allowance are both $2.

4. For instance, consider a system where at each bus boarding you get a transfer slip to board one additional bus, and after that you must pay full fare again. Thus, the transfer allowance afforded by a single bus journey prefix is the same as that afforded by a bus $\to$ bus $\to$ bus journey prefix, although the fare for the latter option is higher. While these options would be incomparable under Lo et al.’s framework, our framework can compare them (and will only retain the three-bus journey prefix if it is better in terms of time than the one-bus option).

5. Owen and Jiang’s method is slightly different from ours; they produce an accessibility figure for each minute, and average them, while we produce a specific percentile of travel time across all possible departure times for each origin-destination pair and use that to calculate accessibility. We believe Owen and Jiang’s findings are still relevant. For more discussion on the tradeoffs between these two methods, see Conway et al. (2017, 2018).

6. Boston also has a long history of activism surrounding transit fares more generally, as evidenced by the iconic protest song ‘M.T.A.,’ which bemoans the fate of a traveler, Charlie, who lacked the subway exit fare and ‘may ride forever ‘neath the streets of Boston.’ Originally written to protest a subway fare increase, the song is now arguably part of the New England vernacular (Dreier and Vrabel 2010).

7. Our algorithm cannot fully model the CharlieCard transfer discount system, because it violates the nonnegativity of transfer allowances assumptions specified in Equations (5) and (6). For instance, a user making a Local Bus $\to$ Inner Express Bus $\to$ Subway journey will pay $6.25 ($1.70 local bus, $2.30 upgrade to express bus, and $2.25 for the subway), but if they were to discard their transfer allowance after the first ride they would pay only $5.70 ($1.70 local bus, $4 express bus, and a free transfer to subway). A user could also achieve this price if they rode a second local bus before boarding the express bus, expending their transfer allowance. The consequence of this violation is that a small number of lowest-fare trips that rely on such ploys may not be found. We suspect few users rely on such trips. This is a specific idiosyncracy of the MBTA fare system and does not undermine the correctness of the algorithm in more common situations where transfer allowances are nonnegative.

8. https://github.com/conveyal/r5/blob/95d076896e0a076207ced83742deb8fb620127df/src/main/java/com/conveyal/r5/analyst/fare/BostonInRoutingFareCalculator.java.

9. https://openstreetmap.org; data $\copyright$ OpenStreetMap contributors.

10. https://lehd.ces.census.gov/data/#lodes.