All posts by Matt Laquidara

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.

Earlier this week on the main blog, Zach posted about, and Metro responded to, potential problems with weekend service in Northeast Seattle after the Bus2Link restructure. Coincidently, I had started generating isochrone maps originating at one of the locations called out in the aforementioned posts, Roosevelt and 65th. Unfortunately, these maps and their scores largely support Zach’s contention, that while weekday service has allowed more destinations to be reachable more often, weekend service has in fact suffered.

This post will share a set of three maps apiece for weekday, Saturday, and Sunday service. The first two maps are a side-by-side comparison of pre-restructure and post-restructure service at Roosevelt and 65th. The third map is the difference between the first and second maps. For those unfamiliar with the isochrone maps and scores I’ve generated in previous posts:

1. The maps are centered at a single starting point, in this case Roosevelt and 65th.
2. For every minute of the day, a map is generated at that point in time. The presence of a dot at a bus stop signifies that there is at least one point in time when that bus stop can be reached within 30 minutes, by starting at the origin point and using some combination of public transit and walking to get there.
3.  For the comparative maps, the color of the dot depends on how many points of time in the day that one could start at the starting point and reach that point. Colors range from navy blue for points that be reached infrequently to hot pink for points that can be reached often.
4. The comparative maps have two scores associated with them. The first is a count of the stops reached. The second sums the number of times per day each stop can be reached, thus favoring networks that allow a broad number of destinations to be reached regardless of the time of day. I refer to this score as the “reachability score” throughout this post.
5. For the difference maps, the color of the point signifies whether the point can be reached more or less often after the restructure. White dots signify no difference, more strongly black dots show an increase in reachability, more strongly red dots show a decrease.

Let’s get to the data:

Weekday

Comparative map

Difference map

The reachability score shows a 4% increase, largely on the back of large frequency gains within Northeast Seattle. The 62 and the more frequent buses on the north/south corridors appear to be excelling at improving mobility within this region.

This improvement is pulled down by a reduction in the number of times destinations in Montlake, Eastlake, the Denny Triangle, and  the northern part of downtown can be reached in under 30 minutes. The decline of reachability in Montlake can be attributed to the split of the 45 from the 48. The reliability that the split offers likely outweighs the disadvantages (as these maps use Metro’s schedule data, there’s no accounting for  congestion or accidents). The decline in the latter two areas represents a more concerning situation. Neither of Metro’s suggested options for getting downtown—the 45 to the Link nor a one seat ride on the 62—allow one to get to downtown within 30 minutes as often as the prior network did. These routes are less direct than the deleted 66, and their higher frequencies do not offset that. Of course the 30 minute time limit is arbitrary—perhaps at 31 minutes the situation changes entirely—but some cutoff had to be made.

Nonetheless, the weekday system’s increased score represents an improvement in general mobility. If nothing else, the map demonstrates a more coherent system: destinations fairly close to Roosevelt and 65th are reachable far more often than they previously were. But a coherent network is small consolation for anyone whose access to downtown has been impaired.

Saturday

Comparative map

Difference map

The reachability score on Saturday shows a 5% decrease. The general look of the difference map is the same: improvements in Northeast Seattle offset by decline in Montlake, Eastlake, the Denny Triangle, and the northern part of downtown. The reason for the decline, in spite of the superficially similar map, appears to be the shorter span of service for Northeast Seattle routes on Saturdays versus weekdays. In this case, Metro’s cache of remaining service hours may help close this gap.

Sunday

Comparative map

Difference map

The reachability score on Sundays shows a 6% decrease. While the same successes and concerns of the weekday and Saturday map are clear, a new set of issues has arisen. The north/south arterials show a reduction in reachability north of 80 Street NE, particularly 15th Ave NE and 5th Ave NE. This is not unexpected: though route 62 has the same 15 minute frequency, the connecting north/south lines suffer from frequency degradation on the weekends. Expectedly, the maps confirm that Zach’s general assertion, infrequent transfers perform worse than infrequent one-seat rides, holds true in this specific case.

Overall, I feel it must be underscored that five out of the seven days of the week, on the days when the most people use transit, the Northeast Seattle restructure lets people get to more places at more times of day. Metro should be lauded for not just making a drastic change, but a beneficial one. Metro should also be lauded for its quick, but measured, response to concerns. Hopefully data such as these scores and maps, can help target future responses and avoid gross overreactions such as a total rollback. And of course, the entire restructure can’t be judged just by reachability from Roosevelt and 65th, I hope to continue this series of Northeast Seattle maps with the other locations cited in the previous posts.

Entering the first work week with ULink open and the Link Connections restructures in place, there will be a flood of anecdotes about whether or not the changes are working. Eventually, ridership numbers will serve as a more concrete measurement of the efficacy of the changes to the transit network. Until then, it’s still possible to take some cursory measurements of the potential for rider benefit using the isochrone map generator that I posted on the blog two weeks ago. Whether these measurements of transit network potential measure anything real and important is another story. You be the judge!

Below are three sets of two maps apiece. As a recap of how these maps work:

1. They’re centered at a single starting point.
2. If a bus stop can be reached within 30 minutes by some combination of public transit and walking, there’s a dot at that point.
3. The color of the dot depends on how many times of day that one could start at the starting point and reach that point. This is in rainbow order, with bright red signifying small numbers and dark violet signifying high numbers.

The first map in each set is generated over the full day of March 17, before the opening of ULink. The second map in each set is generated over the full day of March 31. For each map, two “scores” are included. The first is a counter of the number of stations reached. The second sums the number of times per day each station can be reached, thus favoring networks that allow a broad number of destinations to be reached regardless of the time of day. Both of these scores are fairly flawed, but can be useful when used comparatively and viewed with healthy skepticism. Let’s get to the data:

Start point: Capitol Hill Station

Before: static map; station count: 1774 weighted count: 994130

After: static map; station count: 2375 weighted count: 1291599

Scrollable, zoomable maps (your browser may hate you for this)

Given 30 minutes of transportation time, reaching UW from Capitol Hill was reasonably achievable (at least according to published schedules) before ULink. While improving upon this already good reachability, what really shines through is how much more feasible it is to reach points north and west of the university within 30 minutes. A similar pattern holds for downtown: reaching it within 30 minutes was already nearly a given, but shaving time off the journey allows better chances of reaching West Seattle, not to mention the destinations directly served by the Link. One thing I specifically wanted to observe was any impact of the reduction of the 43 bus. This map shows improved reachability in its corridor, but might not tell the whole story: 30 minutes seems like a generous time allowance for Capitol Hill to Montlake and this map says nothing about reaching downtown from Montlake. But those are maps for another day.

Start Point: UW Station

Before: static map; station count: 2014 weighted count: 758513

After: static map; station count: 2543 weighted count: 1324769

Scrollable, zoomable maps (your browser definitely hates you now)

The weighted count score and the map both make it easy to see a large increase in destinations reachable within 30 minutes. Even with suboptimal station placement, the bus connections appear to work well enough to make locations varying from Lake City to Sand Point to Westlake reachable at many more times in the day. The reachability improvement to downtown is staggering, though it is important to keep in mind that this map does not measure reachability from a portion of the campus where the now-truncated 70-series expresses had a nearby stop. Again, a map for another day.

Start Point: Beacon Hill Station

Before: static map; station count: 1912 weighted count: 989892

After: static map; station count: 1891 weighted count: 1015671

Scrollable, zoomable maps (your browser would have already killed you, but ran out of memory to do so)

I generated this map because I wanted to show the impact of ULink and Link Connections in a neighborhood to which they did not directly pertain, and I already had an existing Beacon Hill Station map. (The limiting factor on why I can’t be generating these maps every second of every day is a daily quota on looking up the walking distance between locations.) There’s a marked improvement in reaching the immediate vicinity of the new stations. The spread of improved reachability around them is weaker than I expected, but I would want to do more analysis before ascribing this to bad bus connections rather than simply running out of time taking the Link. Another interesting component is the decreased station count score. I suspect this is merely the result of some adjustment of the Link schedule so that it no longer aligns as perfectly with some runs of the 41 and 11 buses.

I am hoping to generate more of these comparative maps in the next couple of days. If you’d like one of your neighborhood, give it a shout out in the comments and I’ll do the best I can. I’d also be interested in any comments or issues with methodology or results; if you find this week that this data doesn’t match your observations, we ought to work together to figure out why!

I became fascinated with public transit planning at the beginning of the outreach process for Link Connections. By the time Alternative 3 came out, I was drawing lines all over maps of Capitol Hill, attempting to design a better network. What I soon realized, though, was that I had no reason to believe that my designs were any better that Metro’s alternatives, nor could I defend them against potential objections. So I scrapped those half-finished plans and sought to develop a tool that would allow some semblance of objectively measuring a hypothetical transit network. What I ended up with is an isochrone map generator; you can see an example of what it generates given a 30 minute range starting from Beacon Hill Station.

I suspect isochrone maps can be a useful tool for transit planning. They can help sell a reluctant community on a beneficial restructure. Showing isochrone maps of before and after the restructure provides a visual demonstration that while the specific routes traversing that community may change, the restructure allows more destinations to be reached at more times of day. That is a difficult assertion to communicate with route maps, even ones that show frequency. By generating isochrone maps from a variety of starting points, revisions of a transit network can be objectively compared by calculating a score derived from counting the number of points reachable within some amount of time, weighted by the percentage of the day when those points can be reached. Furthermore, generating isochrone maps can highlight the needs of transit riders unlike ourselves. By tweaking the generator in ways such as halving the walk speed, limiting the walking distance, or prohibiting transfers of a certain length after dark, it can produce maps that emulate the characteristics of other riders. By seeing their view of the transit network, we can evaluate the impact of restructures with less intrusion of our own biases.

I’m surprised King County Metro does not use isochrone maps publicly in its restructuring process. Perhaps there is a lack of tools; other than Mapnificent—which undermines its utility by making simplifying assumptions about transfer timing—I haven’t found others. But perhaps they simply aren’t compelling in practice. To figure that out, I’d like to give the readers, writers, and commenters on this blog an opportunity to make use of the map generator. The articles and comments here contain an abundance of restructuring ideas large and small. I welcome anyone in this community to propose any restructure experiment that they feel would benefit from having isochrone maps generated. I can only process a limited number of requests, so priority will be haphazardly based on personal interest and ease. (Providing modified versions of Metro’s general transit feed specification files makes life easiest, but simple changes like eliminating a route or comparing the regional impact of an existing restructure are fairly simple for me to do.) Nonetheless, I’d encourage erring on the side of putting forth ideas. After all, if isochrone maps can make our arguments more logically grounded and ideas more worthy of actual implementation, finding a way to generate them is time I’d consider well spent.