Tuesday, September 26, 2017

Route Contributions Revisited

In the last blog post, I considered how a route-oriented measurement of Spontaneous Accessibility could be more illuminating to planners than ridership-based measurements of route productivity. The post analyzed some routes that King County Metro labeled as the most unproductive in their system, and found a variety of clues about their lack of productivity by measuring Network Accessibility Contribution. This post views those previous results in a broader context.

In this analysis, I selected every King County Metro route that met two criteria: the route must run entirely in Seattle, and it must not have changed substantially in routing since the ridership data published in the 2016 Service Evaluation was collected. I selected August 31, 2017 as a typical weekday and, for each route, calculated a 2000-sample Sampled Network Accessibility Contribution where the change was to delete the route. For each of these contributions, I negated the measurement, so that it is the accessibility gain of the route existing rather than the (negative) benefit of its non-existence, and divided it by the total amount of vehicle hours that service on the route requires. The lack of this additional step was mentioned as a weakness of the analysis in the previous post. Measuring the contribution on a rate basis rather than an absolute one allows the contributions of routes of very different lengths, spans, and frequencies to be compared fairly. The results are shown in the two charts below.



There are several noteworthy conclusions. The previous post established low absolute SNAC measurements for routes 47 and 99. On a rate basis, these routes similarly provide extremely low value. This additional information confirms that these routes have a low SNAC for reasons other than their short length. Poorly performing routes 24 and 33 are above average in terms of their rate-basis SNAC. This is a challenging situation to rectify: the routes allow trips that other routes are unable to provide. Nevertheless, riders are not using these routes at the expected rate. A consideration for routes of this nature may be to improve frequency despite their present unpopularity. The lack of use may stem from potential riders choosing other means of transportation because timing the bus trip is an inconvenient stricture.

Looking at routes with exceptional rate-basis contributions, there are not clear commonalities. Route 75 (comparative map) provides the highest absolute contribution by a scant margin, but relative to its in-service hours it is significantly the leader. It connects two major transfer points, the University of Washington campus and the Northgate Transit Center, in an indirect, backwards-C shape. The east-west portions of its route have several connections to north-south routes, while the north-south portion serves a corridor that is not readily accessed by other transit. Route 65 (comparative map) is a fairly direct north-south route in northeast Seattle. Route 50 (comparative map) meanders through a largely east-west path in south Seattle with multiple connections to frequent light rail service. These three routes are similar in that they do not directly serve downtown Seattle and do not cross bridges over the Lake Washington Ship Canal, which are frequent chokepoints. However, the route with the next-highest rate-basis contribution is the Rapid Ride D line (comparative map), which shares none of the previous properties.

While the lack of commonalities between routes that contribute the most to Spontaneous Accessibility may be disappointing, it is an important result. There is no simple set of properties that make a transit line valuable. Instead, it is vital to analyze each route in terms of its contribution to the entire network. Spontaneous Accessibility contribution measurements are ideal for guiding this process, allowing both immediate and careful analysis of transit routes.

Friday, September 8, 2017

The Route Productivity Problem

Spontaneous Accessibility measurements concern themselves with properties of transit networks as a whole. This is most evident with Network Accessibility, but even Time Qualified Point Accessibility, though localized to a single center point and starting time, has this property. Though viewed through a narrow aperture, it measures the ability of the transit network as a whole to provide service. Though the blog has touched on the many advantages of Spontaneous Accessibility measurement, it is not without downsides. It can feel far removed from the techniques that planners can actually use to improve a transit network. The realm of planners is one of transit corridors, routes, and their respective frequencies and spans; these are the controls that can be manipulated in network design.

Spontaneous Accessibility measurements evaluate the outcomes from these manipulations, but on their own do not offer much guidance into how the controls can be manipulated to achieve a positive outcome. This is problematic because when planners make changes, they are rarely overhauling the entire transit network. While drawing out a new network from scratch and measuring its Network Accessibility could result in a vastly improved transit network, it is a costly endeavor that is incredibly disruptive to current transit users. For this reason, I consulted service planning documents from King County Metro in Western Washington and the Massachusetts Bay Transportation Authority (MBTA) of the Metro-Boston area, to demonstrate how Spontaneous Accessibility measurement could best improve and supplement tried and tested service planning processes.

Both documents establish procedures for evaluating the benefit that an individual transit route provides. King County Metro calls this route productivity in their 2016 System Evaluation document. Route productivity is based on two measurements, riders per platform hour and passenger miles per platform mile (where the "platform" qualifier indicates that the measurement includes time when the bus is out of service, such as driver breaks or deadheading). While route productivity is a secondary consideration to crowding and lateness when allocating additional service, for removing service it is the primary signal. Routes are divided into urban and suburban categories based on their characteristics. Then each route is measured on both measurements for peak, off-peak, and night timeframes. Routes that fall within the bottom 25% of these categories are candidates for service reductions when funding is imperiled.

The MBTA's Service Delivery Policy describes a Bus Route Cost-Benefit Ratio. This measurement is a weighted combination of the ridership of the route, the ratio of those on board who are transit dependent, and a Value to the Network measurement. The latter includes the catchment area: a count of people uniquely serviced by the route, the number of jobs near the path of the service, and the proportion of passengers who make use of the service to connect to additional service. Though a low score is not a trigger for making service cuts to a route, it may be used to make other modifications.

Both route productivity and Bus Route Cost-Benefit Ratio are fairly complex measurements. Ridership measurements, which inform all of route productivity and the vast majority of Bus Route Cost-Benefit Ratio, require that passenger boardings and deboardings are properly recorded. This can be difficult because equipment may be present on only a subset of buses, the recording may not work accurately, or, due to shortages, buses with malfunctioning sensors may still be used, polluting the data. Furthermore, ridership variation may have causes outside of the transit network itself. Weather, extended road closures, and special events may influence rider behavior enough to distort the six month data collection timeframe that King County Metro uses to measure route productivity. Measuring and utilizing catchment area is also complicated. While a route might appear to have a small catchment area because other transit service might exist in the proximity of a route's path, that service may or may not allow the same destinations to be reached as the route that is being evaluated.

Nevertheless, the ability to assign a value to a single route is clearly an important part of a practical transit planning process. While Spontaneous Accessibility is a network-level measurement, it is possible to apply its principles to the measurement of a single route. Each route contributes some amount of Spontaneous Accessibility to the whole network. A valuable route contributes Spontaneous Accessibility in a unique way, connecting origins and destinations at times that no other route does, whether directly or through the connections that it enables. To measure this, first, a Network Accessibility or Sampled Network Accessibility measurement is computed for the entire network. Then, using the same collection of Sectors if Sampled Network Utility was used, a single transit line is marked as ineligible and the measurement is made again. The proportion of change between the ratios, called the Sampled Network Accessibility Contribution (SNAC) or the Network Accessibility Contribution (NAC), is used to evaluate the impact of the route on the network's Spontaneous Accessibility. If the transit line was largely redundant, the network will hardly show an effect, as riders have alternate paths to the Sectors that the line served. Otherwise, the ratio may be substantially changed reflecting that many unanticipated trips have become more difficult.

Where NAR' and SNAR' indicate the ratios calculated with the proposed change in effect.


To demonstrate, SNACs modeling the elimination of several King County Metro routes that were considered unproductive by route productivity were calculated. A thirty minute isochrone and 2000 samples were used. Each route ranked in the bottom 25% in at least half of the timeframe and measurement type pairs for which it was eligible (some routes do not operate at night or off-peak, and thus do not have measurements from these periods) and did not have any measurement in the top 25%. As SNAC measures the Spontaneous Accessibility improvement of some change, routes that are more valuable have lower scores. The results indicate that though Metro's measurements view these routes as comparably unproductive, their contributions to the network's Spontaneous Accessibility vary widely, suggesting a variety of causes, and thus solutions, to their deficiencies.

Route Route Map SNAC Comp. Map (Common scale) Comp. Map (Normalized scale)
4 Link -0.00111 Link Link
24 Link -0.00455 Link Link
33 Link -0.00393 Link Link
37 Link -0.00045 Link Link
47 Link -0.00003 Link Link
99 Link -0.00011 Link Link

Routes 47 and 99 appear to be largely redundant with other service. For these routes, more frequent service is available on streets that are very close (Broadway for the 47 and 3rd Avenue for the 99), and thus for most trips, it is a better option to take this more frequent service and walk to destinations on the paths of these less frequent routes. They appear to be the strongest candidates for complete elimination. Route 37 provides value along the coastline of West Seattle, but the route's tail into the interior provides little benefit from a Spontaneous Accessibility standpoint. As such, costs can be reduced by truncating it. Route 4 provides most of its value on the path that it shares with route 3. It provides additional Spontaneous Accessibility value to the Sectors north of Mount Baker in the I-90 corridor. Perhaps this area would be better served by service to frequent transit on Rainier Avenue rather than a meandering path towards downtown. Routes 24 and 33 provide considerable value throughout Magnolia; reducing their service would make unanticipated trips to and from there considerably more difficult. However, route 24 is very circuitous and route 33 does not get to northern Magnolia in a particularly direct way. In this case, it may only be possible to preserve Spontaneous Accessibility and reduce hours by fundamentally restructuring service to Magnolia.

Conducting an analysis like this one takes mere days from conception, to execution, to visualization and evaluation. A more thorough study would consider a variety of walking speeds, to ensure the eliminated routes are not critical to maintaining Spontaneous Accessibility for riders with mobility issues. In addition, it would also be useful to know the SNAC of eliminating route per some cost of its operation. This would ensure that short routes are not disproportionately targeted. Also it would be best to study a variety of SNACs with different isochrone times. These variations would not extend the study time greatly, allowing much faster understanding of the value of routes than studying ridership for six months. It is also a more direct measurement. Low ridership is a symptom of many diseases afflicting transit networks; elimination is not always the proper cure. By measuring the properties of the network directly, it is more evident whether and how a route is providing value.

For both King County Metro and the MBTA, using Spontaneous Accessibility Contribution measurements could improve their route evaluation processes in a natural and non-disruptive way. Its extra insights allow any agency that must evaluate its routes to make more nuanced decisions without upending existing processes.

Thursday, August 24, 2017

Technical Brief: Rethinking Parking Requirement Exemptions with Spontaneous Accessibility

Rethinking Parking Requirement Exemptions with Spontaneous Accessibility proposes Spontaneous Accessibility as a mechanism for determining when developers of new residential or commercial sites in Seattle should be exempted from providing parking. Currently this decision is made by evaluating access to frequent transit using a distance and headway-based process. Replacing this process with Spontaneous Accessibility measurements incorporates additional precision and nuance, better determining whether new parking-exempted sites are truly served by transit that can meet the entirety of resident needs. Though focused on a single problem in Seattle, it provides a framework for using Network Accessibility and Point Accessibility to solve land use problems generally.

Wednesday, August 16, 2017

Technical Brief: Transit Planning with Spontaneous Accessibility

Transit Planning with Spontaneous Accessibility is a short document that explains how planners can use Spontaneous Accessibility measurements to improve their transit networks. It contrasts Spontaneous Accessibility with existing modeling techniques and explains how planners can use it to incrementally close more of the gap between transit networks and private vehicle ownership by creating networks that are more amenable to unexpected, unanticipated trips.

Monday, August 7, 2017

Two Months

Two months ago, Public Transit Analytics described Network Utility as a measurement that could quantify how useful a transit network is. However, computing this measurement in practice was difficult: calculating it for a reasonably detailed map of Seattle would take an infeasible amount of time. While Cumulative Point Utility was proposed as a method for simplifying the calculation, the parameters of using it practically were unclear. Unfortunately the desired clarity remained elusive. At the same time it became obvious that the utility measurements on the whole failed to communicate their purpose to transit planners. These two setbacks necessitated a challenging rethinking of these measurements, both in their terminology and calculation.

Until now, Public Transit Analytics proposed that how "useful" or the "utility" of a transit network was what its measurements quantified. Unfortunately these terms are both overly broad and fundamentally miscast in describing those measurements. "Utility" has a specific meaning in economics, which sometimes finds its way into transit planning literature. Meanwhile, there was an understandable resistance to using a term as general as "useful" to solely express the ability of individuals to reach destinations regardless of the time of day or the differing value of locations. Reviewing the literature of academic transit planning was critical to properly name these measurements, giving them precision and clarity.

Fundamentally, Public Transit Analytics's measurements quantify accessibility, which, broadly, is the ability of individuals to reach opportunities. Studies of accessibility are a perennial topic in peer-reviewed transit planning literature. Many of these studies use measurements that resemble what this blog described as Point Utility or Network Utility. However, these studies have often focused on a specific type of opportunity, such as access to jobs during the morning rush hour or how easily certain shopping centers can be reached by transit. In contrast, Public Transit Analytics's measurements have worked towards greater generality: focusing on the ability to start in arbitrary locations and reach arbitrary destinations, at arbitrary times of day. In considering this contrast, it's clear that both Public Transit Analytics and other researchers are measuring some way in which the transit network is useful. Other researchers have largely focused on transit trips that are preexisting or expected. On the other hand, Public Transit Analytics is measuring the ability to take unanticipated, unexpected trips. These trips may occur any time of day, with unpredictable origin and destination points. In other words, the measurements describe the ability of the network to support spontaneous transit trips, and therefore the measurements that once quantified utility now describe Spontaneous Accessibility. Building a transit network that excels at allowing these trips is difficult, given the limitations that transit service has in contrast to private vehicle ownership. By ensuring that new projects and restructures incrementally improve Spontaneous Accessibility, individuals can increasingly count on transit to meet all of their needs.

Furthermore, the literature review made it clear that accessibility-based measurements represent only a subset of the ways of quantifying the value of a transit network. Primarily, many agencies use a four step forecasting model to predict the ridership or total time saved of proposed modifications to transit networks. This blog formerly expressed some skepticism of such methods. After a careful examination of the literature, Spontaneous Accessibility measurements are more a complement than a replacement. When modifying a transit network, understanding its impact to existing riders and their anticipated trips is important. At the same time, improving Spontaneous Accessibility has value in attracting new transit trips, discouraging car ownership by making spontaneous trips on transit more achievable, and improving service for those who solely rely on transit.

This recasting of Spontaneous Accessibility would be for naught if it could not be calculated in a network-wide, all-day way feasibly. Unfortunately, the approach of using mutual information calculations to establish a threshold for using Cumulative Point Utility yielded inconsistent results. Consequently, Public Transit Analytics did not just rename Network Utility to Network Accessibility, but made its calculation faster. By rewriting its destination-finding algorithm to use dynamic programming and eliminating the consideration of Sectors that are entirely on water, the time to calculate Network Accessibility has been improved by multiple orders of magnitude. While now computationally feasible, it is still expensive. It's possible, though, to make a measurement of the current transit network using Network Accessibility, wherein every Sector center and minute of the day is used. For subsequent transit planning experiments, a sample of these starting points can be selected. The sample's closeness to the full Network Accessibility can be tested using a different information theoretic technique: Kullback-Leibler divergence. Once a sufficiently close sample is found, a Sampled Network Accessibility of the experiment can be compared to the original Network Accessibility.

The research that went into confronting these two issues yielded a very favorable outcome: Public Transit Analytics submitted a paper to the Transportation Research Board describing Spontaneous Accessibility and analyzing its change in Seattle over a year period. If accepted, it will be presented or published in January of 2018. The following map from the paper shows Spontaneous Accessibility in Seattle on January 25, 2016, before the opening of the Link light rail extension through Capitol Hill and the University of Washington. Each Sector is colored based on the proportion of origin location and time pairs that allow the Sector to be reached within 30 minutes. Averaging these proportions results in the Network Accessibility Ratio, which eschews the scaling factor that Network Utility used. In this case, the Network Accessibility Ratio is 0.06017. Currently, the map is only available in a non-interactive form, though improved interactive versions are in the works.

With the ability to compute Network Accessibility now possible, this blog will begin to primarily focus on using it to measure hypothetical transit network changes. In lieu of completing the Foundations of Evaluating Public Transit Networks series, a technical brief describing transit planning using Spontaneous Accessibility measurements will be published shortly.

Tuesday, May 30, 2017

Blessing in Disguise

Over the past week, Public Transit Analytics replaced a major component of the Score Generator software. One of the differentiating features of the Score Generator is the care that it gives to accurately determining what is reachable by walking in a public transit journey. When the virtual rider starts their journey or departs a transit vehicle, the stops that they can reach are not just those located in some radius of the point. Therefore, when Public Transit Analytics replaced the Score Generator's source of walking distance measurements, the decision to do so was made with utmost care. It is one with considerable implications, and some surprising benefits.

Before exploring these implications, it is useful to understand the process that the Score Generator uses to determine which destinations are in reach by walking. Recall that a Point Utility score is computed with a center point and a duration. When first run, the Score Generator builds two sets of points. The origin set contains the center point and every transit stop. The destination set contains every transit stop and points corresponding to the center of every Sector. The Score Generator calculates the straight-line distance between each origin and each destination. It then uses a walking speed estimate to convert these distances into times. Since these times are never longer than the actual walking time between the points, and no walking time can be greater than the duration, it retains only the measurements that are under that duration. These are called the candidate distance measurements.

Then, as the virtual rider journeys through the transit network, it checks how much time it has left to continue and considers all the candidate distance estimates for its current location that are less than or equal to the remaining duration. It takes these candidates and uses a software component called the Distance Client to get accurate walking directions to each destination. These directions include a total walking time, which provides the final filter on which destinations are reachable.

Prior to last week, the Distance Client relied on Google's Distance Matrix API to get walking times and distances. Google makes the Distance Matrix API available as a pay-per-use web service with no minimums and no upfront costs. For that reason, its presence made it possible to develop the Score Generator without needing considerable domain knowledge in mapping and wayfinding. Unfortunately, Google imposes a 100,000 request per day maximum for its standard pricing plan. In attempting to calculate a full Network Utility for a 10,000 Sector map of Seattle, it became clear that somewhere around four million distance measurements would be needed. Thus, acquiring the data would take around 40 days. Though premium service plans do exist, they are intended for usage patterns that involve a large number of continuous requests, not occasional periods of very heavy use.

Thus, current Utility maps from Public Transit Analytics use map data from OpenStreetMap with a locally-running instance of GraphHopper providing directions. This new solution maintains the most important factors of walking distance measurements: paths that account for the street layout and times that account for slowdowns and speedups from going up and down hills. However, to say the solutions yield identical maps would not be accurate. Compare the previous version of the Outbound Point Utility map from the Public Transit Analytics office (interactive version) with the current one (interactive version).
Overall, the current walking distance measurement source results in many more destinations being treated as reachable more often.  Based on several spot checks, variation appears to principally come from walking speed differences rather than routing differences. The open source nature of GraphHopper's navigation software gives some insight as to why. It appears that for most scenarios, it uses a walking speed of five kilometers per hour. This is a very typical speed used to model the preferred human walking speed. Google's speed selection algorithm is unknown, but appears to be slower on average.

That changing walking distance computation considerably alters Utility is an important observation. Both GraphHopper and Google intend to model what can be reached by some hypothetical average human being. An individual request to each service will probably result in only a minute or two of time variation. However, the aggregate impact when computing Point Utility is considerable. If so much variation exists between two systems trying to measure the same thing, even more variation must exist among the many riders of transit systems who, for a variety of reasons, may not behave anything like the average.

So far, the Public Transit Analytics blog has focused on how using the Score Generator makes transit networks more useful. For the network to also be just, it is necessary to ask for whom the network is being made more useful. If an individual's ability to move around the world is sufficiently different than the assumptions that walking distance calculations make, changes that make the network more useful for the average person may seriously degrade the network for that individual. Much like how using real schedule data instead of average transfer times results in a more genuine model of a transit network, a truly accurate model must also have the ability to capture a broad range of pedestrian abilities and preferences, not just some average.

Fortunately, using walking measurements based on open source solutions like OpenStreetMap and GraphHopper enables exactly that; the maps and software can be modified extensively. Transit planners working with Public Transit Analytics can opt for Utility maps that show their transit network from the perspectives of individual transit riders, accounting for factors ranging from mobility impairments, to age, to preferences. Though the need to change the walking distance measurement source was borne out of technical necessity, it has in fact been a blessing in disguise. By helping ensure that the unique needs of individuals are not lost amidst optimizing for averages, it has helped Public Transit Analytics further commit to its core tenet of justice.

Saturday, May 20, 2017

Foundations of Evaluating Public Transit Networks, Part 6: Similar, Rather than Different

Last week in the Foundations of Evaluating Public Transit Networks series, I highlighted the fact that shifting the center of a Point Utility computation a small amount can have a substantial impact on the reachability map and the corresponding score. This presented the problem of how to measure the utility of a whole network when individual points may tell very different stories about how useful the network is. This post describes one strategy for solving this problem by focusing on how Point Utility measurements from different centers are similar rather than how they are different, and using techniques from the discipline of information theory to define this similarity in a rigorous way.

To ease this discussion, this post makes use of the following terminology. Network Utility (NU) is the hypothetical measurement of how useful a transit network is using Public Transit Analytics's definition of useful. In theory, it would be calculated by running a series of full-day Point Utility computations centered at each Sector of the service area. As explained in the last post, this is a very difficult measurement to make, owing to the large number of Sectors from which Point Utility calculations must be run. A related concept is Cumulative Point Utility (CPU). Rather than aggregating the results from every Sector, CPU is the result of generating the Point Utilities at some sample of the Sectors' centers and combining these. CPU has the benefit of being flexible in the amount of computation required; there are no restrictions on how many or few samples make up a CPU calculation. There is, of course, the tradeoff that fewer samples will produce results further away from the true Network Utility.

Information theory comes in handy in establishing what "further away" means. Mutual information is an information theoretic technique that measures how much information one random variable indicates about another. It uses the joint and marginal probability distributions of two random variables. Thus, to measure how far away one Point Utility measurement is from another, it must be possible to model a Point Utility as a probability distribution. The diagram below indicates how this can be done.

Consider the simplified Point Utility maps above. Recall that in a Point Utility map, each Sector is assigned a shade of green depending on how often the Sector can be reached. Each shade of green corresponds to a number, one through nine, referred to as the "bin value". Treat each Sector as an observation of a random variable. The value of that observation is the bin value of the Sector. Sectors that cannot be reached are given a bin value of zero. Looking over a whole Point Utility map, one can count the number of Sectors with each reachability bin value. These sums can be divided by the total number of Sectors, creating a probability distribution for what the bin value of an arbitrary Sector would be on that map.

When considering two different Point Utility maps, it is then possible to construct a joint probability distribution. To do this, choose a Sector on the first map and find the same Sector on the second map. Keep a count of each pair of observations; for example Sector one has a bin value of 9 in the first map and a bin value of 5 in the second map, so the pair (X=9, Y=5) is recorded. Continue this process for each Sector, obtaining a total of each observation. Dividing these by the number of Sectors yields the joint probability distribution for the bin values of the two Point Utility maps.

With the joint distribution, and the marginal distributions that can be computed from it, it is possible to compute the mutual information of two Utility measurements of any type. This calculation can be used in two ways. If the Network Utility has been computed at great cost, the mutual information can be used to determine how accurately a Cumulative Point Utility approximates the Network Utility. Once a sufficiently accurate CPU has been found, changes to the transportation network can be measured using CPU rather than NU, saving computational resources and money.

Furthermore, even if the Network Utility is unknown, mutual information sheds light on whether the Cumulative Point Utility is approaching it. Consider building a series of Cumulative Point Utilities by selecting an initial Sector at random, adding new random Sectors, and computing a new CPU for after each new Sector is added. After each CPU is measured, the mutual information between it and the previous CPU is measured. Initially the mutual information will decrease: mutual information between any two Point Utilities is relatively high because both PUs indicate that the plurality of Sectors are unreachable and thus the maps are similar. As more PUs are combined into the CPU, fewer points are outright unreachable, and thus the maps will be less similar from the perspective of mutual information. As more PU measurements are added, it is expected that the rate of decrease will slow or reverse, as the data added from a PU is capable of being inferred from the previous CPU. In a more concrete sense, this means that one can learn something about what is reachable at a point by considering the points around it. After all, that point has similar transit stops within its walking range. Eventually, the random points that were selected comprise nearly all the information about the transit network, even though they are not an exhaustive collection of every location on the map.

Public Transit Analytics is actively working through some of the practical concerns of using Cumulative Point Utility. It is unclear how many samples would be sufficient and what properties of a transit network may result in alterations to the sufficiency criteria. Nonetheless, the approach of using mutual information appears to be a promising one. Its ultimate promise is a way of measuring an entire transit network in an unbiased way not seen in other models available to planners today.

Monday, May 8, 2017

Foundations of Evaluating Public Transit Networks, Part 5: Complex and Volatile, Again

Previously in the Foundations of Evaluating Public Transit Networks series I explained how Public Transit Analytics built Point Utility from Qualified Point Utility. Doing so necessitated examining the ways that Qualified Point Utility failed to account for how useful a rider would find a transit network. In that case, the "Qualified" nature of Qualified Point Utility, the fact that it is calculated at a single time, was scrutinized. The upcoming posts in the Foundations of Evaluating Public Transit Networks series follow the same pattern, but this time with the "Point" nature of Point Utility.

Just as looking at a transit network at a single time of day fails to consider that riders want to reach destinations throughout the day, a measurement fixed at a single point fails to capture the fact that riders exist throughout the transit network. Making transit network changes that optimize a single Point Utility may result in better transit for some riders. The Point Utility, though, says nothing about potential degradation to riders not near the selected point.

Thus, it is critical to determine how representative a single Point Utility measurement is of the overall network. To get a rough, intuitive sense of this, the Score Generator calculated the 30-minute Outbound Point Utility of the center of the Sector that contains the Public Transit Analytics office on January 25, 2016. Then, it calculated the same Point Utility but for the center of all of the adjacent Sectors. The results are depicted below, with an interactive version available as well. (The interactive version may take some time to fully load).

Not surprisingly, a variety of Point Utility scores were obtained by shifting the starting location. In this example, the most extreme shift of distance is approximately 650 meters (2,000 feet or one-third of a mile) and resulted in a score change of 14. A difference of one in a point utility score is usually non-trivial (in this 10,000-Sector map, every increment of Point Utility means that 14,400 more pairs of times and Sectors have become reachable). As such, it would be difficult to claim that the Point Utility Score at the center reflects the utility of the network on the whole; it may not even account for how useful the network is in the adjacent sectors.

Whereas Qualified Point Utility could be converted to Point Utility by merely considering the former at every minute of the day, it is more complicated to analogously consider the Point Utility at every Sector. In this map, there is an order of magnitude difference between the number of Sectors and the number of times of day. If a transit agency requires capturing a larger service area or using finer Sector granularity, the difference in order of magnitude could easily grow further. This could increase the time taken to generate a map, as well as its monetary cost, to unacceptable levels. In subsequent posts I will explore some techniques that may cut down this time and cost, and eventually surmount the problem of objectively measuring how useful a transit network is.

Friday, April 28, 2017

Foundations of Evaluating Public Transit Networks, Part 4: There and Back Again

A theme of the Foundations of Evaluating Public Transit Networks series has been iteratively producing better measurements by understanding the limitations of the current ones. Previously in the series, I concluded by stating that Point Utility, or any measurement that is focused at a single point, only partially describes how useful a transit network is. In this post, I will refine the measurement of Point Utility further by focusing on a single key problem. In its current form, Point Utility measures how often riders can reach destinations from a single origin point. Rarely, however, do riders want to go on a trip and never return. Therefore, even if a transit agency is only looking to measure how useful transit is at a given location, Point Utility will not do the job in its present form.

Fortunately, the Score Generator has a solution to this problem. Rather than answering the question of what destinations a rider can reach from a single starting point, it can treat the given point as a destination rather than an origin. From a technical perspective, the virtual rider starts their trip at the end time, calculates the time and distance of walking trips with each reachable point as the origin rather than the destination, looks at where buses have been rather than where they are going, and moves backward through time. Thus, the question becomes "from which locations can a rider start to reach the destination point within a time duration?".

The need to answer this question is most evident when a Qualified Point Utility map is desired. The example maps below compare the original Qualified Point Utility map (interactive version) from the Foundations of Evaluating Public Transit Networks, Part 1 post with a map at the same time and with the same duration, but showing origin points that can reach the Public Transit Analytics office (interactive version).
 

At a single time of day, transit service can be very asymmetric. Certain buses designed to get commuters into work may run only in a single direction at specific times of day. There is also the matter of timing. When looking at a single time, the distance one can go and the transfers one can make depend critically on the precise times at which buses are scheduled to be at stops.

It is logical to assume that when considering a Point Utility map, the all-day nature of the map will make the directional variation disappear. This is not entirely true, however. Somewhat different Point Utility scores are observed in the maps below: the Point Utility map from Foundations of Evaluating Public Transit Networks, Part 3* (interactive version) and a map showing the all-day reachability frequency of the Public Transit Analytics office from many destinations (interactive version).

Though the results are considerably less asymmetric, the two-point difference in Point Utility observed in the example is non-trivial. Several factors can explain this. One is as simple as geography: when walking, it is faster to walk downhill than uphill, so direction matters for locations in hills or valleys. The nature of transit routes can also introduce variations. Some buses, even ones that run in both directions all day, have directional variations in their routings, particularly near the ends of routes. Buses may make stops in a loop as they turn around. This can make for an easy transfer to another route in one direction, but a more difficult one in the other. While these differences do not seem as though they would have considerable impact, the differing Point Utility scores strongly indicate that transit agencies must consider both directions when doing analyses.

As a matter of terminology, when a Point Utility score refers to a point's reachable destinations it is referred to as Outbound Point Utility (oPU); when the score refers to the origins that can reach a point, it is called Inbound Point Utility (iPU). When the Point Utility is not prefaced or otherwise disambiguated, it refers to Outbound Point Utility by convention.

Because Inbound Point Utilities are computed and visualized almost identically to Outbound Point Utilities, it's possible to contrast two Inbound Point Utilities. The Outbound Point Utility example in the previous post* (interactive version) and the analogous Inbound Point Utility version (interactive version) are shown below.

The considerable difference seen in all the maps should underscore that relying solely on measurements that look at reachable destinations from a single point does not capture the full story of how useful the network is. Unfortunately, many of the transit planning tools that I have run across share this limitation. Considering the origin points from which a destination can be reached sheds light on a little bit more of the rider experience. In the coming weeks, I will explore Score Generator features that add to this illumination.

Is your transit agency limited to one-way analyses? Contact matt@publictransitanalytics.com to understand the full rider experience.

*These maps are actually regenerations of the original maps due to a Score Generator error that incorrectly placed some destinations beyond the bounds of the map in Sectors on the map. In the original maps, these manifest as reachable Sectors near Hunts Point that are in the water.

Wednesday, April 19, 2017

Then and Now: Comparative Maps

This week, I am taking a break from the Foundations of Evaluating Public Transit Networks series to explore a variation of Point Utility maps that should be of great assistance to both transit agencies and their customers. In last week's post, I proposed a hypothetical conversation between a transit planner and a rider. In that scenario, the transit planner can show a concerned rider the quality of transit service in their area by showing them a Point Utility map. Riders, however, are most often likely to become concerned when their network is undergoing change. Thus, a tool that can measure and illustrate change is a powerful one in a transit agency's arsenal.

Point Utility scores are designed to be comparative. It is possible for a transit planner to respond to a rider's concerns about a restructure or service cut by showing them Point Utility scores, centered at the rider's home or office, from before and after some network change. This, however, would likely fail to result in constructive dialog. A set of scores that demonstrates a massive improvement in the rider's transit situation may be sufficient on its own, but may still be too abstract to be compelling. In situations where the Point Utility score stays the same or declines, the score provides no diagnostic information to understand this decline. When compressing this much data into a score, some of the nuance is lost.

Of course, it is possible to present two Point Utility maps side by side, providing a depiction of the transit network before and after the change. This, however, becomes difficult to process visually. Keeping track of a single Sector when switching between maps can be challenging and colors can appear to be different based on the colors around them when they are in fact the same. For that reason, the Public Transit Analytics Score Generator can overlay one map on the other, yielding maps like the one below and its interactive version.

Specifically, this maps looks at the difference in 30 minute Point Utility at the Public Transit Analytics office using the previous example of January 30, 2017 as a trial, compared to a baseline of a Monday around the same time in 2016. In a Point Utility map, the frequency at which a Sector can be reached are divided into nine intervals, or bins. The comparative Point Utility map shows the difference between the two bin values at each Sector. Sectors more strongly orange can be accessed a greater number of times within the trial time span. Sectors more strongly colored blue can be accessed less frequently. Grey Sectors are ones where the bin value does not change. To get precise information on how much of a change occurred, hover the cursor over a Sector. Clicking on a Sector reveals the most common, or mode, path that serves as the fastest way to reach the sector for each of the baseline and trial times.

Just these pieces of information can be useful in diagnosing potential issues with a restructure, before or after it is implemented. In this example, it is somewhat surprising that there is not a significant change in Point Utility between 2016 and 2017. In that time, Puget Sound's Link Light Rail line had been extended, representing a large influx of frequent service in Seattle's Capitol Hill neighborhood and the eastern edge of the University of Washington. This freed up bus capacity to increase route frequency in north Seattle and prompted a substantial restructure of the bus lines serving the area to take advantage of the Link's fast connections. For the eastern edge of Wallingford, where Public Transit Analytics is located, the map shows that the results have been mixed.

Looking at the most common paths offers a first stab at explaining the degradation indicated by blue regions. An area of blue between Ravenna and Maple Leaf provides an interesting example (outlined in black below), as many new hours of service were invested in this area. Despite making considerable frequency improvements to the 372 bus, which runs on 25th Street in this vicinity, that bus does not provide a very direct transfer opportunity with the frequent east-west service near the Public Transit Analytics office, the 44 bus. Notably, this path is not the mode path for the trial; instead a path featuring a bus that only runs at commute times (not pictured below) is the most common one. In the past, the area was served largely by the all-day, though infrequent, 72 bus, which offered transfer opportunities more suited for east Wallingford. With its ability to highlight problematic areas, and hint at their causes, the map can indicate when reconsideration of certain parts of the restructure may be warranted.


While comparative Point Utility maps are still limited to showing how useful a transit system is at a single point, they represent perhaps the strongest tool available for having a constructive dialog when making changes to a transit network. As long as an agency's schedules reflect reality, Point Utility maps capture what a rider can actually do more accurately than the maps generated by any other tool that I have seen made available to transit planners. The increase in accuracy comes along with a comparative viewing mechanism unparalleled in other tools.

Contact matt@publictransitanalytics.com to discuss using comparative Point Utility maps in your transit agency's future projects.

Thursday, April 13, 2017

Foundations of Evaluating Public Transit Networks, Part 3: All Day Long

In the previous Foundations of Evaluating Public Transit Networks post, I went into detail on the limitations of Qualified Point Utility. I ran through an example that looked at the Qualified Point Utilities at six consecutive minutes, revealing that each of these times yielded very different scores and maps of reachable destinations. Instead of focusing on this observation as a weakness of Qualified Point Utility, this post explores how acknowledging this minute-to-minute volatility results in a better measurement.

Before deriving this measurement, it is worthwhile to recapitulate how Public Transit Analytics defines a useful transit network. Such a network allows people to reach their desired destinations at whichever times they wish to travel. While Qualified Point Utility helps to reveal what destinations a person can reach, its minute-to-minute variability makes it incomplete for  measuring utility. A better measurement would consider what is reachable in a way that incorporates the rider's desired travel times. People and their lives are unpredictable, though. Even with data that reflects rider behavior, it is important to consider that riders may be behaving in a certain way not because they desire to, but because the existing transportation systems limit them. Therefore, Public Transit Analytics chooses to measure how useful the network is in an aspirational way: measuring how close the network is to allowing a person to reach every Sector at all times of day.

Some assumptions must be made to make this tractable. Transit schedules tend not to vary considerably within days of the same type (weekdays, Saturdays, Sundays, and holidays). Thus, scores can be computed for single days that are chosen as representatives of each type. For the purposes of this derivation, January 30, 2017 is selected to represent all weekdays. With the representative day selected, a virtual rider starts their voyage at each minute of the day-long time span. For each of these voyages, the Score Generator computes which Sectors can be reached within a fixed duration—in the case of this example, 30 minutes. The number of reached sectors in each of the computations is summed. This sum is divided by the total number of reached sectors that would be achieved by a perfectly comprehensive transit network: the product of the number of measurement times (1440 for a full day) and the number of sectors on the map. Like Qualified Point Utility, this ratio is multiplied by 1000 and rounded to an integer for readability.


This measurement is referred to as simply Point Utility, as the time qualifier has been dropped (note the lack of a superscript time in the formula). Though the formula does simplify to the average of all the Qualified Point Utilities in a time span, writing it this way attempts to frame the measurement in a way that captures a rider's experience on the transit network. Riders are unlikely to think about how well their network scores in Qualified Point Utility at each minute of the day. By explaining the measurement as counting up reachable Sectors at each time of day, it is more clear that it measures something useful to riders.

Because Point Utility is derived from isochrone maps, it lends itself to visualization. Consider each time in which a Sector can be reached as adding a thin layer of green pigment over the Sector. Deeper shades of green thus indicate that the Sector is reachable at more times in the day-long time span. The areas with the deepest shade, as seen in the roughly circular area around the starting point, are typically those that can be reached by just walking. The map below uses the day of January 30, 2017 as its time span and measures how often one can reach Sectors in a 30 minute duration from the Public Transit Analytics office. On the interactive map, hovering over the Sector reveals the percentage of times of day when the Sector can be reached. Clicking on a Sector shows the paths to the Sector, and the percentage of the day that this path is the fastest way.


Transit planners can create these maps for individual riders with concerns about their transit network, centering the map on the rider's home or work. They can explain that areas with deep shades of green are ones that the rider can reach without preplanning, as ways to reach them exist throughout the day. From there, the rider can explain the ways in which their experiences match or do not match what the map indicates. Internally, planners can use the scores to evaluate whether a change that they are making has a generally beneficial or deleterious impact on a neighborhood or individual constituent. Because Point Utility scores are on the same scale as Qualified Point Utility scores, the utility of the network at a single time of day can be compared with the network as a whole. This can be useful when trying to quantify the difficulty faced by a person who needs to use transit at atypical times.

Though Point Utility represents a considerable improvement in measuring the overall utility of a transit network, it is limited by the fact that it is centered at a single point. As this series of posts continues, I will address that limitation, while also delving deeper into the uses of Point Utility.

Interested in using Point Utility measurements to improve the transit agency that you represent or use? Contact matt@publictransitanalytics.com to schedule a consultation.

Thursday, April 6, 2017

Foundations of Evaluating Public Transit Networks, Part 2: Complex and Volatile

In the previous post in the Foundations of Evaluating Public Transit Networks series, I ended with a brief discussion of why Qualified Point Utility on its own does not represent how useful a transit network is to its riders. One reason comes from the "Qualified" nature of the measurement. A Qualified Point Utility score does measure something, but only at a precise moment in time.

Looking at a transit network at a specific time of day does not provide an accurate view of the overall utility of the network. In some ways, this is an intuitive conclusion. People can use public transit networks at any time of day. Suppose, however, an agency chooses to limit its analysis to some majority of riders that uses transportation in a predictable, scheduled fashion. An agency dominated by day-shift commuters may limit its analysis to typical commute times. In this case, the range of starting times might be small enough for the agency to feel comfortable selecting a single starting time. The implied contention is that this single time is largely representative of the whole time range. This is observed in practice outside of Qualified Point Utility computations: King County Metro's comparative isochrone maps, examined in the previous post, have a starting time of 8:15.

To determine whether a single time can be representative, or put more technically, if a Qualified Point Utility at a single time is representative of the network's utility in a time span, I ran a brief experiment. I started by having the Score Generator generate the 30-minute Point Utility from the Public Transit Analytics office at 6:31 (). This yielded a score of 79 and is visualized below, with an interactive version available as well.


To determine how representative this score was for an individual who generally rides transit in the early morning, I then had the Score Generator run the same request, but for each of the subsequent five minutes after 6:31. The results are striking, particularly when visualized, as seen below and in the interactive version.

The range of scores, from a low of 49 at 6:34 to a high of 79 at 6:31, represents considerable variation in how useful the transit network is. As the map is a 100 by 100 sector grid, a score that is 30 points higher than another represents approximately 300 more sectors of the map that can be reached within the 30 minute time constraint. Furthermore, even when two consecutive times have the same score, as with 6:34 and 6:35, the area of the map that is reachable is considerably different.

The results of this experiment cast doubt on any method of evaluating a transit network that is limited to a single time, even if the transit agency believes that time to represent the common experience. Transit networks are complex and volatile; the interleaving of the schedules of many transit lines yields peaks and valleys in the number of destinations that can be reached on a minute-by-minute basis. While this assertion might appear to be a condemnation of Qualified Point Utility, it instead reveals the path going from Qualified Point Utility to a better measurement. In next week's post, I will detail how the Score Generator can do additional work to remove the time qualifier from Qualified Point Utility.

Is your transit agency evaluated in a way that fully accounts for its complexity and volatility? Contact matt@publictransitanalytics.com to arrange a consultation.

Thursday, March 30, 2017

Foundations of Evaluating Public Transit Networks, Part 1: From Maps to Scores

In the Foundations of Evaluating Public Transit Networks introduction post, I established the goal of measuring how useful a public transit network is: how well it allows many people to get to all of their desired destinations. Public Transit Analytics has developed a scoring system based on isochrone maps to accomplish this goal. This type of map has become an important, and increasingly standard, component of the transit planning process. If you are unfamiliar, public transit consultant Jarrett Walker describes them concisely and compellingly on his Human Transit blog. The transit planning software tool Remix, also uses isochrone maps to help transit planners see the impact of the service changes that they implement. My local transit agency, King County Metro, has produced a set of isochrone maps using Remix that highlight the impressive growth of their transit network expected between now and 2040.

With such a tool already in place for generating isochrone maps, it is logical to ask why Public Transit Analytics would implement an entirely new software system. I have never used Remix, but its wide adoption speaks to its quality. For King County Metro's long range planning, it provides a clear visual that the network is indisputably improving. However, looking at the maps that it is generating, there appear to be limitations that would hinder score production, especially for more surgical changes to a transit network. For that reason, Public Transit Analytics's Score Generator generates isochrone maps in what appears to be a somewhat different way.

Consider the isochrone maps from King County Metro or on the Remix blog post. The reachable area of the map is curvy and bulbous. Based on that, I would speculate that for every destination that a rider reaches in a transit vehicle, the map software draws a circle based on the amount of remaining time. This circle represents the area that the rider can reach on foot in the time remaining after they have exited the transit vehicle. This introduces a level of imprecision. Dead end streets and hills, for example, can drastically change this reachable area in real life.

Perhaps more critically, note the disclaimer on the bottom of King County Metro's maps. The maps are generated using "the average time spent waiting to transfer". This is another source of imprecision. A map that assumes an average transfer time can introduce errors. Such a map could overstate where riders can reach: if the rider arrives at the stop as the bus is pulling away, they will have to wait more than the average time. That might seem like a small error source, but these errors cascade. Each destination that the map thinks that the rider can reach opens up a set of connections that may in fact be impossible to reach. The reverse is true as well: the map can also understate where a rider can reach if there are circumstances that cause them to make a transfer with below average wait time. What is worse is that the difference in time between the average transfer and the true transfer time can be a significant amount of time relative to the total time.

The Score Generator's approach avoids these imprecisions. It divides the area that a transit agency serves into a grid of regions called Sectors. It also keeps track of a set of Transit Stops, as well as what Sector each of the Transit Stops is in.  The Score Generator models the course of a virtual rider that starts at some location, walks to other locations, and rides transit when at Transit Stops. When at a Transit Stop, copies of the virtual rider board every vehicle that arrives within the time constraint and exit at every stop. When a rider exits a vehicle, it marks that Transit Stop and the containing Sector as visited. It then then considers the rides it can take at that new stop, as well as each additional Transit Stop and Sector that can be reached by walking. It sends more copies of itself on each of these walks. Once at that new location, it marks as reachable each of these new locations as well, and potentially boards transit vehicles there, continuing the cycle until time is exhausted. Google's DistanceMatrix API is used to compute, with high accuracy, what can be reached by walking.

Of course, one could argue that such an approach is also imprecise, as it considers reaching any point within a Sector to indicate that the entire Sector was reached. This is moderated by the fact that the Score Generator allows for arbitrarily sized Sectors. Public Transit Analytics customers get to decide how small their Sectors need to be in order to produce a map of adequate precision. The tradeoffs are higher costs, both on the computational time taken and the need to acquire more distance measurements from the DistanceMatrix API.

The Score Generator also uses real schedules for every part of its calculation, including transfer times. This ensures that as long as the transit agency's schedules are accurate, the result will closely mirror what real riders experience. It will not under- or over-estimate what is reachable.

Once the Score Generator calculates what sectors can be reached within the time limit, it is easy to compute a score. This score is called Point Utility, reflecting the fact that it defines how useful the transit network is at a given locational point. Point Utility is Qualified by start time (in superscript) and a duration (in subscript). It is defined by the reached sectors divided by the total sectors, all multiplied by a scaling factor of 1000 and rounded to a three-digit integer to make the number more human-readable.

As an added benefit, because the scores are derived directly from maps, the maps themselves become a compelling visual for explaining the score within an agency or to its customers. As an example, here is a map of the  from the Public Transit Analytics office on a typical weekday. The map area is the bounding box around the city of Seattle, divided into a 100 by 100 grid of Sectors. An interactive version that shows the best route to the sector on hover and detailed information on click, is also available.

Of course, a Qualified Point Utility score on its own does not come close to representing how useful a public transit network is: real riders do not originate from a single location or do all their traveling at 10:00. Nevertheless, it is an important subcomponent that goes directly into the overall network utility calculation. In the next couple of weeks, I will be continuing this series of posts, building up the components that Public Transit Analytics uses to arrive at its overall public transit network score.

Do you represent a transit agency, municipality, or community group that would like analyses like this done for your local transit network? Contact matt@publictransitanalytics.com.

Sunday, March 19, 2017

Foundations of Evaluating Public Transit Networks, Introduction

When comparing two complex things of the same type, condensing the complex thing into a single comparative score can simplify decision making. This is a common strategy in a variety of disciplines. In sports, measurements like American football's Passer Rating and baseball's Wins Above Replacement (WAR) form a single score from many components of a player's performance. In the case of WAR, the combined season-long WARs of players on a team closely correlates with that team's number of wins. In this way, baseball players can be compared and ranked, even if they have very different sets of baseball skills. In real estate, Walk Score combines many elements of livability into a single score that homebuyers can use when comparing houses in different neighborhoods. Rotten Tomatoes uses a weighted aggregation of reviews to rank movies.

For transit planning, it would be helpful to have an analogous concept for evaluating how useful a public transit network is. Transit planners could use such a score in a variety of contexts. When considering multiple proposals to restructure transit service, an objective score can be used to select the better one. When a new transit line is planned, the score difference, between the transit network with the new line and without it, can be measured against the line's monetary cost to ensure that it is a good use of resources.

Of course, such a score is unlikely to be the final word in any public transit planning decision. Public transit agencies operate in the context of a government and community. The values of those entities may be extremely difficult to capture in a single score. Nevertheless, having scores available, and having tools that demonstrate how the scores were derived, can help guide conversations within an agency and among the community of riders. They can provide a compelling explanation of why certain decisions were made or why certain alternatives were not considered.

To create a score, a tempting choice may be to consider the number of riders as a score for how useful parts of the transit network are. Using ridership, however, makes it easy to draw erroneous conclusions. Low ridership can be cited as a reason to cancel a transit route, as some may attribute the lack of use to redundancy. However, the route might be fundamentally useful, but not often ridden because it does not run frequently enough for customers to rely on it. Additionally, doing any sort of speculative planning, such as adding new lines, requires projecting ridership, which is imprecise at best. On top of that, ridership is difficult to measure, requiring rider counters to work reliably and in a large enough sample to be representative.

Public Transit Analytics's core score does not use ridership. Instead, the score is motivated by one of the company's tenets: to help build transit networks that are more useful. A useful transportation improvement is one that allows more people to access more of the places that they desire to go. In this series of posts, I will discuss how Public Transit Analytics has derived its own process for measuring exactly that.