Updated May 26, 2011:

The three sets of charts for each day and location previously published here have been replaced with a single set to simplify navigation.

Calculations of the average and standard deviation was previously based on headways that had been rounded to the nearest minute. This has been changed to use the unrounded values causing minor changes from the original version of the charts.

Data for December 29, 2006 was incomplete causing some headway information to be incorrect. This day has been dropped from the “basic statistics” charts.

Effective with the April schedules, the TTC changed the 7 Bathurst to formally be an articulated bus route on weekdays. Headways were changed to reflect the larger capacity of the vehicles, and the TTC trotted out a commonly-cited story that fewer, larger vehicles are easier to manage and can provide better service than more, smaller ones.

Did this actually happen? What does the implementation on Bathurst bode for other major bus routes, not to mention the streetcar system which will start moving to larger vehicles in fall 2014?

In these articles, I will look first at the headways actually operated on the route for March and April 2014 (the before/after pair), and later at the time required for vehicles to make their trips, congestion and layover times that affect the service.

As it happens, I also have data from December 2006 for this route, one of the first sets of data I attempted to analyze when I started on this effort back in 2007. How has the service changed between late 2006 and early 2014?

Note: I presume that readers have seen this type of article on my site before, and I will not go into the gory details of how the TTC vehicle tracking data are digested and presented. For those who want to know what’s “under the covers”, please refer to a separate article on the methodology.

What is the Scheduled Service?

Before we can talk about service as it is, we need to know what it is supposed to be according to the schedules. This is a starting point for comparing the reality of buses on the street to the creative fiction of the advertised service.

7_ScheduledService_2006_2014

Charts of the Headway Data

Charts are linked below for four locations in each of three time periods.

Northbound service is shown at Barton Street (just north of Bathurst Station) and north of Wilson.

Southbound service is shown at the bottom end of the on-street loop at Steeles Avenue, (specifically at Carpenter and Bathurst where the loop begins), and just north of Eglinton.

In both cases, the locations were chosen to show the service as it left the terminal and as it arrived midway along the route.

Service is shown for the months of March 2014 (before artics), April 2014 (after artics) and December 2006 (for historical comparison).

7_201403_NB_BartonAve_MonthHeadways 7_201403_NB_NofWilsonAve_MonthHeadways 7_201403_SB_NofEglintonAve_MonthHeadways 7_201403_SB_SofSteeles_MonthHeadways

7_201404_NB_BartonAve_MonthHeadways 7_201404_NB_NofWilsonAve_MonthHeadways 7_201404_SB_NofEglintonAve_MonthHeadways 7_201404_SB_SofSteeles_MonthHeadways

7_200612_NB_BartonAve_MonthHeadways 7_200612_NB_NofWilsonAve_MonthHeadways 7_200612_SB_NofEglintonAve_MonthHeadways 7_200612_SB_SofSteeles_MonthHeadways

These charts contain 13 (or 14 depending on the calendar) pages of charts:

The first 7 (or 8) show detailed headway information (described below).

The next 3 contain basic statistics: averages and standard deviations by hour for each type of day in the month (weekday, Saturday, Sunday).

The last 3 contain distribution charts for the data showing how closely (or nor) the values are clustered.

Basic Statistics

The basic statistics charts show information at the most consolidated level. For each type of day (weekday, Saturday, Sunday), the average headway and the standard deviation of the headway are plotted. The values included for each time period combine data for every day of the specific type through the month.

The average is the arithmetic mean of all observed headways within an hour for the type of day charted.

The standard deviation is a measure of the dispersion of values with about 2/3 of the data points falling in a span of ±1 standard deviation.

Where a month’s operation is “well behaved” with all of the days operating more or less the same way, then these values will be representative for every day. If there are many days with disrupted service (for example due to weather), the values will be affected because they are based on a mixture of “good” and “bad” days, but it will not be possible to determine when and how severe the problems were on a specific day.

The standard deviation values are also related to the problem of bunching. For example, if the SD is 4, then 2/3 of the headways lie in an 8-minute band around the average. During many periods, the SD is close to the average value, and this indicates that most vehicles are travelling in packs of at least two. This is particularly troubling when it appears shortly after vehicles leave their terminals where, in theory, some headway reliability could be more easily imposed.

Headway Distributions

These charts are, like the basic statistics charts above, based on data consolidated for all days of each type through the month and segmented by each hour of service. Within each hour’s data, the count of vehicles on a specific headway is plotted so that there is one vertical bar for each value from 0 to 30 minutes. The intent is not to show the individual values, but the shape of the data distribution.

If most headways lie in a narrow range, then the cluster for one hour will have a tall spike with much lower outlying values. If the headways are spread over a wider range, the cluster will be flatter. In the extreme case where headways are completely random, the cluster would have no peak at all.

Note that because there are fewer days and less frequent service included in the weekend data, the charts are more sparse and have lower peak values. However, the principle is identical.

Detailed Headway Charts

Each linked file contains 7 or 8 pages depending on the calendar:

The first 4 or 5 pages show data for weeks 1-4 (or 1-5) of the month.

One page shows all weekday data as a “cloud” of data points. The purpose is to illustrate both the general variation in values over the course of weekdays, and the very wide spread in actual values.

One page shows all Saturdays (Boxing day is included here).

One page shows all Sundays (Christmas and Good Friday are included here).

Each point represents the actual headway when a bus passed at the time in question. Trend lines between the points show the overall behaviour of the values through the day. The spread of points around the trend line shows the band within which the actual headways lie.

These charts show data for each day of the month independently, and allow identification of specific times where a major event such as a snow storm might have disrupted service (as opposed to monthly averages presented in the earlier charts).

Northbound at Barton Avenue

These charts show headways just after the service leaves Bathurst Station. The March trend lines show the shorter peak headways on each weekday except for the March 31 data. This was the day the new, artic-based schedules actually began to operate and so the headway trend for that day does not match the pattern from the preceding week.

One thing that is quite evident throughout March is the consistency of the trend lines from day to day, and on each type of weekend day. The only exception is that midday headways on March 12 are unusually long due to a heavy snowfall.

The other quite evident point is the width of the “cloud” of data points around the trend lines. The TTC’s target is ±3 minutes to the scheduled headway, but the data lie in a band almost 20 minutes wide. Very short headways correspond to vehicles running in packs, and this is troublesome to see so close to a terminal where it would be easy to manage regularly-spaced departures. This problem exists even on weekends, and some headways are twice the scheduled values.

In April 2014, there is no AM peak dip in headways because none is scheduled (see table above). Headways continue to have values well beyond the three-minute target range, although the problem becomes noticeably worse after about 3:00pm on weekdays with considerably more vehicles on very short (i.e. bunched) headways right through the PM peak into the evening. Weekend data are quite similar for March and April which operated on almost identical schedules.

Comparing the two months’ weekday operations, both have a lot of bunching, especially in the afternoon and evenings, and the primary difference is that April headways are longer. There is no indication that the larger, less frequent vehicles in April are managed any better for headway reliability than their shorter cousins were in March.

Data for December 2006 show values that are less spread out than in 2014, although headways well below and above the target are still evident.

Northbound North of Wilson

As with the service at Barton, the March 2014 headways at Wilson are spread out over a 20-minute wide band with many quite low values for all days of the week. The situation continues into April with the artic-based schedules. Indeed, in April there does not even appear to be a concentration of values near the target, but rather a fairly even range of values. This suggests that there is no attempt at all to manage the service or impose any headway discipline.

By contrast, the 2006 data generally lie within a narrower band, although there are still cases of very short headways and some in excess of two times the scheduled value.

Southbound South of Steeles

Service southbound from the northern terminal is even more irregular than northbound from Bathurst Station with the band of values extending into the 20-30 minute range. One reason for this is unscheduled short turns at points south of Steeles.

It is worth noting that service in 2006 was much better behaved except during the PM peaks and on Saturdays.

Southbound North of Eglinton

At Eglinton southbound, the data values are back to the 20-minute wide band we saw in the northbound charts. The contrast with the values at Steeles are due to the fact that northbound Short Turns are included and some of the very wide gaps were filled. However, this is little comfort to someone forced to wait two-to-three times the scheduled headway on the outer part of the route for a bus to arrive.

Service in April shows the same pattern we saw elsewhere with little evidence of clustering around the target headway on weekdays.

The 2006 data are much better behaved with a tighter range of values except on a few occusions, notably just before Christmas.

General Observations

The Bathurst Bus was notorious for irregular service before it was converted to articulated buses, and the pattern has not changed since the cutover. Headways range well beyond the TTC’s target for acceptable service, and passengers can just as easily be treated to a double headway as to a short headway thanks to bunching and the resultant uneven loading conditions.

There are noticeable differences between 2006 and 2014 data in that headway distributions (and standard deviation values) in 2014 are wider/larger than in 2006. This means that service experienced by riders will be more irregular today than in was 8 years ago.

Another point notable in all data is that the standard deviation does not often fall below 4 suggesting that there is a lower bound to the reliability of headways. Whether this is a question of the accepted practice for operations or some “transit fact of life” is worth investigation. However, a striking difference between 2006 and 2014 is that the standard deviations tend to stay at the same level most of the time in 2006, while they grow considerably in off-peak periods in 2014.

Any claim the TTC might have that the larger buses would provide more reliable service are demonstrably false. There may be a theory, somewhere, that might “prove” this assertion, but the service actually recorded on the street reveals a complete abdication of headway management, the alleged goal of TTC service.

In the next article, I will review the relationship between actual and scheduled running times, the amount of time TTC Service Planning allocates for buses to make their trips, as well as other factors that can affect service.