In previous articles, I reviewed the operation of 6 Bay and 94 Wellesley for the month of January 2016. This post updates that review with a different way of looking at headway statistics over the route and by time of day. The new chart format consolidates information previously shown only in separate chart sets.
In earlier analyses, I presented information for headways (the time interval between vehicles) at a point over a month in charts like this:
This set of charts includes several pages of detail showing individual vehicle headways, day-by-day, with statistics for the entire month at the end. This is useful for looking at behaviour at a point, but another way to summarize the data is to bring the stats for all timepoints on the route onto a single set of charts.
The new charts use the data shown on the weekday, Saturday and Sunday statistics pages from each timepoint set (such as the one linked above) and merge them on a single chart for each direction and type of day.
On each chart, the average headways are shown as solid lines while the standard deviation values are dotted and use a lighter version of the same colour as the corresponding averages.
The first page for 6 Bay shows weekday statistics from the south end of the route at Jarvis & Queens Quay to the north end at Bedford & Davenport. The line for Bedford (purple) breaks away from the other values because half of the service is scheduled to short turn at Yorkville during the peak periods. Generally speaking, the averages for each timepoint will stay close to each other except during transitional periods between service levels (the change does not necessarily complete within the same hour over the entire route) and in the case of major disruptions or diversions.
What the charts show, however, is the magnitude and evolution of the standard deviation in headways along the route. This is a value that measures the degree to which data values are close to or scattered around the average value. If the SD is low, then most of the individual values are close to the average, and therefore the headways are all close to the average value. If the SD is high, then headways are erratic. The average may be well-behaved and fit the schedule, but times between individual vehicles can vary considerably. Typically, about 2/3 of the data points will lie within one SD either way of the average. Therefore, if the average is 5 minutes, and the SD is 8 minutes, 2/3 of the data points lie between 2 and 8 minutes. The rest are beyond this range.
This has some relation to the TTC’s own goals for headway reliability. Until fairly recently, vehicles were considered to be “on time” if they were within 3 minutes of their scheduled time. On occasion, the TTC would report this value relative to scheduled headway, rather than to the timetable, to acknowledge that riders care more about reliability than the “on time performance” of individual vehicles. This measure has been replaced with a new target in which vehicles should leave terminals no more than 1 minute early and no more than 5 minutes late. This is ostensibly the same 6 minute window, but with three important differences:
- The measure is always to timetable values, not to headways. Service can be operating on a regular spacing, but be off schedule, and therefore rank poorly. However, “on time” performance is a TTC goal because it minimizes overtime payments.
- The measure is only at the terminal point on the assumption that if service begins its trip in good shape, this guarantees reliable service further down the line.
- Measurement at the terminal will expose excessive short turning because vehicles that do not reach the terminal cannot be counted as part of the “on time” metric.
This sounds good in theory, but the idea runs aground on two important factors.