This article is a followup to two previous analyses of the 506 Carlton route’s behaviour:

Based on feedback from readers, I have experimented with alternative presentations of the data that better illustrate what is happening on the route. These versions will be added to the repertoire of charts I will use in future analyses, notably for the 505 Dundas route which is the next one in line for review.

Travel Times

In Part I, the speed of operation across the route was presented as a series of charts showing bus and streetcar speeds along the route. In the chart below, the eastern segment of Carlton is shown for the period from 8 to 9 am. Because the speed of buses and streetcars are often close to each other, the two lines on the chart obscure each other, and the pattern of the difference over the route is not immediately obvious.

The revised version of this chart is shown below. The changes are:

The thickness of the lines has been reduced so that there is a bit less of a problem with overlap.

The chart shows the entire route rather than only half so that the evolution of values over the route can be seen.

Trend lines have been added for the streetcar and bus values.

A second set of charts based on the same data show the difference values, and includes a trend line.

Another chart that was included in Part I was a comparison of end-to end travel times by time of day.

Note that this shows a fair amount of bus/streetcar overlap while the speed chart trend lines does not. There is an important difference between the two measurements.

The end-to-end times are just that – the arrival time at one end minus the departure time at the other.

The speed comparisons, by contrast, show the average speed for all vehicles observed at each point along the line. For the purpose of the analysis, the Carlton route is subdivided into 10m segments, and if a vehicle sits at one for a long time, that will contribute a lot of “zeroes” to the average speed calculation there, but only at that one point (i.e. a transit stop). This will pull down total travel time across the route, but will not have as severe an effect on the trend lines for the speed comparisons that are calculated separately for each point along the way.

The speed difference charts have a lot of downward spikes where the average bus speed is considerably lower than the average streetcar speed, and these generally correspond with transit stops suggesting that buses spend more time stopped serving passengers than the streetcars do. A very fine-grained review of the data will be needed to confirm this, but the pattern in the charts is quite regular and I believe this is a valid hypothesis. In other words, the buses manage to go faster than streetcars between stops, but spend more time at stops with the result that total travel times do not differ as much as the subjective “feel” that “buses are faster” might indicate. This situation varies by time of day and location as the relative position of trend lines on the speed charts shows.

Stepping through the westbound comparisons, one can see the space between the trend lines change over the course of the day and the location on the route. The lines lie closer together in the west end indicating that conditions there do not give the buses much advantage except very late at night. In the east end, particularly east of Coxwell, the buses are not delayed as much by other traffic. The eastbound data show a similar pattern, and there are even a few cases where the bus trend line drops slightly below the streetcar line.

(One important caveat about the behaviour of polynomial trend lines: If there is a substantial change near either end of the series, this will be interpreted as an inflection point in the curve and it could veer quite substantially away from the values further from the ends. This is part of the tradeoff for the smoother polynomial trend lines versus moving averages.)

Headway Reliability

In Part II, the headway reliability data were presented as a set of percentiles for data at individual points such as Yonge Street eastbound. However, the issue is not simply the dispersion of headways at one point, but how these values change as vehicles make their way from one end of the route to the other.

The new chart sets linked below group the data by time period for a specific percentile. In this example, the median headways (50th percentile) in the 8-9 am hour are shown at four locations:

Main & Danforth

Gerrard & Broadview

Carlton & Yonge

College & Dufferin

These values stay close together for all four locations as shown by the trend lines. These lines have the advantage of smoothing out the daily fluctuation, something that becomes even more important in later charts.

The 85th percentiles tell a different story from the medians. As service moves from east to west, the 85th percentile values grow showing that more riders will experience wider than scheduled headways. Note also that the daily swings in values are larger, and so there is greater variation in the day-to-day experience.

In the worst case, the maximum headways can be even worse and the trend line shows that these sit in a range well above the scheduled value especially for the western part of the route.

Finally, the 25th percentiles show that short headways and shorter not far west of Main Station, and by the time service reaches Broadview bunching is common. This is especially so for the bus service that has operated since mid-February. (Note that a polynomial trend line shows the change in values over a longer period and although the individual daily values drop at the February 18 schedule change, the trend line takes longer to fall to the lower level.)

If the trend lines are changed to 10-day moving averages, they show more of the fine-grained variation, but the message of the charts is roughly the same: bunching gets worse as one progresses across the route.

These charts show that headway reliability deteriorates inbound from terminals where, according to TTC’s stated goals, service should be very regular, but in practice, is already ragged and gets worse along the line. By the time vehicles reach Yonge Street, the service quality is considerably worse than the condition in which it left the terminal, let alone compared to the scheduled service. This problem continues on the outbound trip.

The situation is similar for buses and streetcars with the only notable difference being that buses, which start with more vehicles and shorter scheduled headways, in theory should provide shorter gaps even when the service is disorganized. But those gaps are still wide and the associated bunching remains at closer headways that with the streetcars.