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On March 16th, the two downward escalators between the mezzanine and sub-mezzanine at the University of Washington Link Station failed. With only elevators available to move people into the station for four hours, a line snaked around the station. On April 4th, a presentation to Sound Transit’s Operations Committee reviewed the event and discussed changes that could be made to prevent and mitigate future outages. While the presentation recognized the poor customer experience during the event, it described the impact in a strictly qualitative fashion.

This is a quantitative assessment of the escalator outage event. Any mitigation or preventative measure is going to have a cost to put in place. Without the ability to assign a cost to the event, it would be difficult to understand which actions should be on the table.

This assessment uses a measurement called Spontaneous Accessibility, published in this year’s Transportation Research Record. At a high level, this measurement describes how well an individual can make an unanticipated, unplanned transit trip throughout a given area. From a technical standpoint, it divides an area into a high-resolution grid of sectors. For each sector it computes, for every minute of a time window, the number of other sectors that can be reached within 30 minutes using transit and walking. This yields a heat map of how easily reachable each sector is, as well as a Network Accessibility Ratio that measures the proportion of time-origin-destination combinations that can be reached within 30 minutes against the total number of combinations. By making modifications to the modeled transit network and calculating the change in the Network Accessibility Ratio, it is possible to make a quantitative assessment.

To model the outage, Spontaneous Accessibility was computed under two circumstances. The first considers the scheduled transit service within the city of Seattle on March 16th, between 3:30 PM and 7:30 PM. The second uses the same temporal and spatial parameters, but eliminates the University of Washington stop from southbound Link trains. This is not a perfect model of the outage, as customers could still reach trains at UW Station after a substantial wait. Nevertheless, to a person arriving at the station and viewing a long line, the station may be considered effectively unreachable. This analysis yielded a change in Spontaneous Accessibility of -0.339%. A maximum reduction of 12.3% was observed in the vicinity of the Capitol Hill Link station, with other measurable reductions clustered largely around Link stations and a portion of the Aurora Avenue corridor. This Spontaneous Accessibility map shows the distribution of impact.

To extract a meaningful cost from the change in Spontaneous Accessibility, it is necessary to bring in some additional data. Over the four-hour period of the outage, there were 1988.28 vehicle-hours of in-service trips serving the city of Seattle. Using King County Metro’s $140.86 cost per vehicle-hour figure as an estimate for operating costs across all transit providers, the cost of in-service trips for the four hour window was approximately $280,069. In the same period, the Network Accessibility Ratio for the unimpaired network would have been 0.10378. Thus $280,069 was necessary to sustain a 0.10378 Network Accessibility Ratio in Seattle over those hours. When impaired, Seattle had a 0.10342 Network Accessibility Ratio. Sustaining this for four hours should cost approximately $279,097. Thus, from a Spontaneous Accessibility standpoint, the cost of the outage was $972.

It is important to be cognizant of aspects of the measurement that may distort this value. Because Spontaneous Accessibility is an isochrone-based measurement, it is not sensitive to the outage’s impact on trips that initially would have taken longer than 30 minutes. Spontaneous Accessibility measurement also acts as though riders have perfect knowledge of the transit network. Actual riders may not be aware of the other options that they have for completing their journeys, and thus may queue at the station instead of finding alternatives. Even if riders were to have this knowledge, Spontaneous Accessibility does not incorporate vehicle capacity, and thus would not account for alternate routes becoming congested as riders switched to them. Particularly thorny in this case is that Sound Transit would largely be relying on King County Metro to absorb that missing capacity.

Any attempt at assigning a single cost to an event is going to have limitations, and this is a basic one using publicly available data, open source software, and back-of-the-envelope math. At this point, however, it describes the impact more quantitatively than Sound Transit has put forth at this time. Sound Transit plans to evaluate certain mitigations by the next Operations Committee meeting on April 20th. These will surely have a price, and it will certainly be interesting to see how they compare to this assessment of the UW escalator event’s cost.

8 Replies to “The UW Escalator Event: A Quantitative Analysis”

  1. It sounds like Sound Transit has to wait until a citizen calls them to report the escalators are out. Why don’t the escalators have an automated system that notifies Sound Transit immediately when the escalators stop? My goodness, for a few hundred bucks a home alarm company could install this just like they did at my house to notify the police when an intruder breaks in. Am I missing something?

    1. Hi Peter,
      The timeline in the main page post (https://seattletransitblog.com/2018/04/13/st-exploring-new-escalator-strategies/) gives a good high-level ordering of the events and the Sound Transit presentation has many more details and is surprisingly watchable and well-paced (https://livestream.com/accounts/11627253/events/3731004/videos/172834237/player?width=640&height=360&enableInfo=true&defaultDrawer=&autoPlay=true&mute=false). In this case, a security officer, not a citizen, reported the escalators out. Though there was some delay routing and handling this report, much of the delay came from getting a technician on-site, which is, unfortunately, a very hard problem to automate!

      I’m not a mechanical engineer, so I can’t speak to the feasibility or price of detecting an escalator in a permanent fault state. Nor can I speculate if this would be more or less reliable than occasional checks by a security officer. I avoided talk of specific preventative measures or mitigations in this post. While it shows great civic engagement to think up solutions, I think that this need to come second to a cost analysis of the problem itself.

      Thanks for your comment!

  2. Do you happen to know why they don’t encourage people to walk down the escalators like stairs? There must be some kind of safety break.

    1. Hi Mary!
      Nothing legally prevents it, but the manufacturer and the American Society of Mechanical Engineers do not recommend it. One mitigation that was proposed in the presentation is allowing them to be used as stairs, but only when all escalators in one direction are unavailable and only with the supervision of staff at both ends of the escalator (to redirect those who might not be able to handle the step height to other means of conveyance).

  3. You have to be kidding. The “cost’ of this outage is not extra operating bus-hours for Metro. It is the sum of the self-determined value of the time lost by the thousands of riders of Link riders who were delayed.

    And conceivably — if it were to happen a few more times in the near future — reputational damage to Sound Transit and Link. Obviously such costs are incalculable except in hindsight, but they are potentially enormous.
    .

  4. Hi Richard,
    Thanks for your comment, no kidding! Based on it, though, I’m afraid I might have made my point unclearly. Let’s try to get to an understanding.

    The cost that I’m arriving at is not the cost of extra operating hours. I’ll go into why I use the operating cost figure later in this response, but I first want to focus on why I do see this as at least a partial cost of time lost by riders. When it comes down to it, a Network Accessibility Ratio is just a measurement of how many points on a map are reachable within a time threshold. If a change in NARs is strongly negative, that means many fewer points will be reachable within a time threshold. An event that strongly reduces Network Accessibility is one that has the potential to impact many riders, and thus one that is going to drive up the time-lost cost that you reference.

    Is a Spontaneous Accessibility-based cost an all-inclusive, irrefutable measurement of the cost of an event? Absolutely not. I do think it’s better than not having any quantitative measure of cost. Which is a worse outage, for example: no downward escalator access at UW Station or a disabled vehicle on the tracks in SODO forcing single tracking between Stadium and ID? With a Spontaneous Accessibility measurement you can give each event a relative cost very easily. If the bar for a cost measurement is one based on each individual rider and their subjective notion of how much they’re inconvenienced, I’m afraid we would have no way of judging which event was worse. I don’t see how an agency could prioritize and make determinations about future mitigations and preventative measures if there is no way to compute some form of cost.

    To return to your point about extra operating bus-hours, I wanted to clarify my use of this figure. I am not trying to calculate how much bus capacity/cost would be necessary to mitigate this outage. Spontaneous Accessibility can be thought of as a measurement of the convenience an agency provides to those within an operating area. The transit agencies spend money to provide some amount of convenience per unit time. The per vehicle-hour operating cost is just a vehicle for computing a total cost for some time window, that can then be re-expressed as a cost per level of convenience-hours. If the level of convenience is impaired, a transit agency is overpaying for convenience-hours. The cost is from an agency’s perspective: it is the overpayment they are making for the actual service provided. It might be better to think about as a floor (and perhaps I should have expressed it that way in the original post!). You right that if these events happen often, there will be indirect costs through changes in rider behavior and trust as well. Nevertheless, I would still assert that being able to assign a cost to the loss of efficiency is superior to not being able to assign a cost at all to a more inclusive measurement.

    Thanks again for your thoughtful and critical comment, and hope this clarification can help us come to a better understanding of each other’s positions.

  5. well… we know that the City of Seattle says that the bare minimum that people should value their time at is $15.00/hour. (minimum wage. There are people who value their time higher than that of course.)

    i don’t have a count of the people that were delayed, but let’s say it was 2000. If they were each delayed by 30 minutes then that tells me the ‘cost’ was at least $15,000.00, and then you can add your $972 on to that for a total of $15,972.00.

    but in fact Metro didn’t add any buses so really, what is this $972.00 a cost of? Who paid it?

    And as Mr. Bullington points out the cost to the agency’s reputation is incalculable.

    1. Hi jas,
      I think it’s great and useful to have multiple quantifications of the situation. I personally would not be as comfortable making the count and time-valuation assumptions that you did. I’ve tried to stick to data that is attributable to some agency or individual, whether that’s the service operating cost, or the street map data that feeds into the Spontaneous Accessibility calculation. But there’s nothing wrong with another viewpoint, and I think we’re all better for your sharing of it.

      With regards to your second point about cost, first of all, thank you, you’ve forced me to think about a point of contention that I’ve done a poor job answering up until this point. I hope I can do your question justice. The cost is not a cost in the sense that it’s additional money paid. It’s a cost in that the same amount of money is being paid, but the amount of product received is lower. In this case the product is the capability to move people (measured by Network Accessibility Ratio). The cost is collectively borne by everyone who pays for the transit agencies in Seattle to operate, not because they’re paying more, but because they’re receiving less.

      And of course, the cost to the agency’s reputation is important and quite hazy. My nature is to calculate what I feel I can quantify with some certainty rather than speculate on costs that I don’t have a good handle on. This will of course result in a less broad assessment of cost, but I think should engender more confidence in the elements of cost that are covered.

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