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:

6 Bay Headways at Charles St. Southbound

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.

6_201601_MonthHeadways_TPSummary

94_201601_MonthHeadways_TPSummary

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.

Short Headways Mask Poor Service Reliability

A claim often made by the TTC is that services with very short headways will inherently run unevenly. It is impossible to maintain exact schedule-based headways at high frequency due to inevitable variations in stop dwell time and the effect of traffic signals which set a regular cycle on the spacing of vehicles crossing intersections. 510 Spadina, for example, is “blessed” with many closely-spaced traffic signals, and the only transit priority they provide is for turns at selected locations.

In theory, a wider scheduled headway should lead to less erratic service, although the TTC has never published any study (theoretical or practical) to establish if there is a “sweet spot” where the benefit of fewer vehicles/hour on reliability outweighs the inconvenience of longer scheduled waits.

The goal for on time performance is meaningless when the scheduled service operates on short headways because service can be bunched and yet still considered to be “on time”. For example, on a 3 minute headway, vehicles might be scheduled to leave at

1:00, 1:03, 1:06, 1:09, 1:12

but actually leave at

1:00, 1:08, 1:09, 1:10, 1:11

All of these vehicles are “on time” relative to the target, but instead of a well-spaced service, we have a gap followed by a parade. This leads inevitably to claims that service is achieving a reliability target while what riders see is gaps and bunching. Claims that the TTC has “improved” service should be taken with more than a few grains of salt because the target they are aiming for does not penalize the type of service commonly seen on busy routes.

Even worse, the vehicle in the wide gap will be the most crowded as passengers jam on the first to arrive to guard against being short-turned (if their bus or streetcar does turn back, at least there will be one in the following pack). Therefore, the average crowding condition seen by riders is worse than statistics that average passenger boardings over vehicle counts. Two buses, one full, the other empty, are “half full” on paper, but not to the average rider.

The six minute “on time” window allows headways to be six minutes wider than the advertised schedule while the route is still officially 100% on time.

The Inevitable Growth of Gaps Between Vehicles

When vehicles leave terminals on an uneven headway, and the gaps will widen along the route as vehicles on the short headway catch up with those on the long one. Unless additional vehicles join the service along the way (from a short-turn or branching point), the average headway will stay the same but the quality of the service experience by would-be riders will get worse with wider and wider gaps.

This can be overcome by arbitrarily holding vehicles to space out the service, and that tactic is enforced on the subway by signal-controlled dispatching at key points. On surface routes, however, holding vehicles requires hands-on supervision, and it can also frustrate both riders and motorists who cannot easily pass stopped vehicles. The problem is compounded when a route has a deliberately padded schedule whose intent is to ensure that vehicles do not have to be short-turned. Either vehicles dawdle along the route to kill time, or they must wait for several minutes now and then to avoid being too “early”.

The growth in wide gaps as vehicles move along a route shows up in gradual increases of the standard deviation of the headways. As more values are further from the average, the SD grows. This is evident in several cases for the summaries linked at the top of the article.

6 Bay Headway Patterns

The first page of the charts for 6 Bay show headways measured for northbound service on weekdays. Although the average values stay close together (except for the north end short turn as noted earlier), the SD values tell another story.

The dotted red line shows the SD for headways westbound at Jarvis Street (this screenline is used because vehicle behaviour closer to the loop at Dockside/Sherbourne is inconsistent). This value wanders around the three-minute mark for much of the day but jumps up in the evening showing that headways have become less reliable during that period.

Note also how the succeeding SD lines (working through colours) grow along the route. Service that was barely within a six-minute margin (and then only for the values within one SD of the average) becomes less reliable.

The situation is similar southbound with the lower values near the north end of the route and higher values toward the south end.

On weekends, the SD values generally run at 4 minutes or greater, even from the terminal points, showing that attention to “on time departure” is not very strong.

94 Wellesley Headway Patterns

The Wellesley bus has a different service level west of Yonge where only half of the vehicles run through to Ossington Station except during evenings.

As on 6 Bay, the average values tend to stay together and don’t bounce around too much, but the SD values show the pattern of widening headways working from east to west along the route. Even though Wellesley Station provides a chance for a “reset” of headways so that the through service can operate on a reliable spacing, in fact the SD values continue to rise from Bay through to Ossington Station with values over 5 minutes seen commonly. That high variation combined with the wider scheduled headway leads to very frustrating service where just missing a bus can have consequences far greater than implied by the advertised schedule.

Concluding Thoughts

The actual behaviour of service on these two routes is barely within a six minute window, and it is therefore impossible that it can achieve the TTC’s on time targets for a high proportion of the service. Moreover, as discussed at the outset, even that “target” allows erratic service to be counted as “on time” thereby masking what riders actually experience.

Even if vehicles left their terminals very close (say ±1 minute) to schedule, there would still be a requirement to reset spacing from time to time along the route, particularly when schedules give substantial “padding”. The six-minute “on time” window guarantees that vehicles will be unevenly spaced at the beginning of their trips with the inevitable result that even wider gaps and crowding will develop along the route.