King Street Update: November 2018 (Part II)

This is the second part of the November 2018 update of data from the King Street Pilot. Part I dealt with travel times and line capacity. For a detailed review of headway changes on 504 King and 514 Cherry, please refer to Part II of the October update.

With the consolidation of the King and Cherry routes, the scheduled service on each of two branches is roughly the same. When these were separate, service on the Dufferin and Cherry spurs was worse than on the main King route, and service to the outer ends of the 504 at Dundas West and Broadview Stations was better.

The revision has widened headways on the outer part of the route, but in a more troubling change, it has also widened the range of headways indicating that gapping and bunching now affect these areas to a greater degree. This is a fairly common effect on TTC routes when headways are widened. When headways are short, the gap between two cars running as a pair, or caused by a short turn, is not as noticeable to riders as the gap on a wider scheduled headway. Line management tactics, including a laissez-faire approach, that might work on short headways compound the effect of wider headways. Although one might expect some unevenness in service heading outbound to terminals after crossing the city, there are also problems with reliability inbound indicating that service is not well regulated at terminals.

As I have written many times, the TTC Service Standards allow a generous variation in “on time” performance at terminals which allows pairs of streetcars to be considered within the target. This allows management stats to look good while service to riders suffers.

(As a simple example, consider an eight minute headway where cars are to leave at 10:00 and 10:08. Within the standards, the first car can be up to five minutes late at 10:05 and the second one minute early at 10:07. This small gap would quickly collapse into a pair of cars travelling together. If the pattern repeats, the next pair of cars could be 16 minutes later, a much worse service than is scheduled or advertised, especially on the “ten minute network”.)

In the central part of the route, headways are short because two services overlap, and the spacing of streetcars is, to some degree, regulated by the combination of long cars, traffic signals and farside stop lengths. Only one car can serve a stop at a time leaving its follower on the nearside and likely held by the traffic signal. With shorter cars and nearside stops, it was common for pairs of cars to serve a stop at the same time and depart on the same signal cycle.

This is the last detailed review I will publish of the King Street pilot until March 2019 when the effects of route changes to take effect in mid-February will be visible. (All streetcar service will turn back at Dufferin for overhead and track reconstruction at Queen & Roncesvalles.) That update will include all data for December 2018 through February 2019 covering much of the winter period.

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King Street Update: November 2018 (Part I)

This article continues the series reviewing the effects of the King Street Pilot with data up to November 29, 2018. [November 30 will be included with the December update.]

November 2018 was the first full month of the consolidated 504/514 King/Cherry services with subroutes from Dundas West to Distillery (504A) and Broadview to Dufferin (504B). The new service design does not affect running times through the pilot area, but is does have an effect on headways depending which portion of the route one is travelling.

The transition to 100% low floor operation on 504 King is now complete and there was no change in the scheduled service capacity after the mid-October route consolidation. 503 Kingston Road trippers continued to operate with the smaller high-floor cars to the Charlotte Loop at Spadina through November. In January 2019, the 503 will revert to bus operation and will loop over the standard streetcar routing via Church-Wellington-York. This will slightly reduce the capacity for short trips within the pilot area during peak hours.

This article deals with travel times and line capacity. In Part II, I will turn to headways (the time between vehicles) and reliability.

Travel Times

The following charts show the travel times between Jarvis and Bathurst (the pilot project limits) in each direction for the pm peak hour, 5-6 pm, over the past three years. The 50th percentile (median, blue) and 85th (orange) are shown. As with all previous charts, there is a small reduction in travel time compared to the pre-pilot data, but there is also a marked reduction in the range of values showing a much more consistent travel time.

The values swing upward a bit in November, although they are still slightly better than a year ago when the pilot began. Some of this change is probably seasonal, but that will be verified with data from December and January. In the sets of charts showing the data for various times of day, this rise occurs mainly in the peak period.

The rise in November travel times does not show up in the westbound data for the preceding hour, 4-5 pm.

However, an increase is visible in the following hour, 6-7 pm.

The full sets of charts are linked below.

For a more thorough discussion of past events and trends in these charts, please refer to the October 2018 update.

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504 King vs 501 Queen Speed Comparisons (Part II)

This article continues the analysis of transit vehicle speeds on King and Queen Streets downtown over the past two years. The first installment of the article compared travel times between the vehicles on each street at specific times of the day and periods over the course of two years. Here, the same data are arranged to show the evolution of travel times on each street over time both before and after the implementation of the King Street Pilot.

King Street

Westbound

Here is a sample chart showing King Street westbound in the hour from 8 to 9 am.

Three periods in 2017 (January, September and early November) are plotted in “warm” colours (pink, red, orange), while periods in 2018 with the pilot in operation (January, July and October) are plotted in “cool” colours (green, blue and purple). This makes it easy to distinguish the groups of data that belong to the “before” and “after” periods.

As this is westbound data, the chart is read from left to right. A common pattern that shows up here is the different location of low speeds corresponding to stops once the pilot is active with “before” data dipping ahead of the intersection, and “after” data dipping following. The degree to which “after” data also includes a nearside dip indicates how traffic signals can compound the stop service time with farside stops. Note especially the green line which shows data from before the re-activation of Transit Signal Priority (TSP). At Jarvis, for example, there is a decided reduction in nearside delay comparing the blue (July 2018) and purple (October) lines with the green (January) one. There is also an improvement at York Street and at University Avenue.

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504 King vs 501 Queen Speed Comparisons (Updated)

Updated December 2, 2018 at 8:00 am: A sixth set of charts has been added covering the last two full weeks of September 2017. The intent is to show fall conditions before the pilot, but also before construction on King (at least some of which was to set up the pilot itself) slowed King cars in the early November 2017 data already published here.

With a year’s worth of the King Street Pilot now behind us, attention turns to two basic questions: should King Street remain as it is with a degree of priority for transit, cyclists and pedestrians; and should this scheme be extended to other major streets, notably Queen Street.

In previous articles I have reviewed the behaviour of the King and Queen routes:

This article provides a detailed look at average weekday speeds along the streets during six separate periods, and with hourly breakdowns from 6 am to 1 am.

  • January 16-27, 2017: Winter operations downtown deal with less traffic, especially on Queen Street. This is a “before” snapshot of the two streets.
  • September 18-29, 2017: Fall conditions after TIFF and before the beginning of construction at Queen & McCaul.
  • November 1-10, 2017: Just before the implementation of the pilot.
  • January 15-26, 2018: Winter operations with the pilot in place.
  • July 16-27, 2018: Summer conditions for the pilot. (2017 was a construction year on Queen and a direct comparison to 2018 is not available.)
  • October 15-26, 2018: Current fall conditions.

This gives a view of “normal” conditions, but does not capture all of the seasonal and special event variations, many of which are evident in the data in previous articles. The periods have been chosen to avoid skewing the numbers with special events such as TIFF, vacation periods and construction.

A Caveat About “Average Speed”

The values show in these charts are derived from TTC vehicle tracking data. This originates in GPS format, and after cleaning up the “rogue” points that are off route due to GPS errors, what is left is mapped onto a version of the route broken into 10m segments. The speed of a vehicle at each segment is determined by the “before” and “after” locations of adjacent GPS observations and the time difference (usually 20 seconds) between them.

These values give the average speed within each segment of all vehicles whose GPS data placed them there. This is not the same as the average speed over the entire pilot area on any given trip. What the numbers show is the locations where vehicles tend to be making good time between stops, the places where they are bogged down, and the places where they stop. Even at stops, the average is never zero because it includes observations where vehicles are just stopping or just starting up within a segment, not to mention variations in stopping location and cases where vehicles do not stop at all.

The Effect on Riders

Vehicle speeds on Queen are often comparable to those on King, but Queen is notorious for less frequent, unreliable and crowded service. Riders are very sensitive to waiting times at stops, and this is compounded if they cannot board the first vehicle to appear, let alone if they walk some distance without a streetcar ever passing them.

With the King Street Pilot there has been a reduction in the variability in travel times which has led to less irregular service. Scheduled service comes more often and the line’s capacity has been improved with new streetcars. Speed alone is not the only measure of a service improvement.

It is vital that debates about the effectiveness of changes to King are debated not just on speed but also on reliability and capacity for demand. The early focus on speed changes which were, in some cases, unimpressive, opened the field to critics who argued that there was a great upheaval for little benefit. It is the combination of more reliable travel time, increased speed, reliability and capacity that has affected the riding experience and drawn more people to use this route. Any move to expand either the scope on King or to another street must take all of these factors into account.

Reading the Charts

Each chart contains data for one hour’s operation in one direction. Here is a sample from the PM peak westbound in October 2018:

The blue line shows data for King while the green line shows Queen data. Trend lines are interpolated through the data for King (red) and Queen (yellow).

The limits of the chart are east to Parliament and west to Shaw, both beyond the Jarvis-Bathurst pilot, for a few reasons:

  • The wider scope shows conditions on the approaches to the pilot area.
  • The nature of the trend line calculation in Excel can cause misleading behaviour in the lines as Excel tries to project beyond the charts using values near the edges. Having a “buffer” area on either side of the pilot ensures that the trend lines do not include this problem through the Jarvis-Bathurst section.

Queen and King run parallel to each other with most north-south streets at the same location on both. This allows data from the two routes to be lined up on a single chart. A few notes about special cases:

  • Sherbourne Street is used as the reference point for aligning the data. The distance from Sherbourne to Bathurst is the same on each street.
    • Ontario Street is slightly offset on Queen relative to King.
    • Parliament Street is slightly further east of Sherbourne on King (measured as travel distance) than on Queen due to the shift in King’s direction just west of Parliament at Berkeley.
  • Victoria Street has a small jog at Adelaide. The line on the charts reflects its location on Queen which has a transit stop and traffic signal.
  • The stop and traffic signal at Queen and Augusta have no equivalent on King.
  • Niagara Street curves eastward between Queen and King, and so the crossing points are different on the two streets.

Westbound charts as above are read from left to right. Eastbound charts are in the same format and should be read from right to left.

Comments on the details of these charts are included later in the article.

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501 Queen and the Effect of the King Street Pilot (Updated)

Updated November 27, 2018: A major section has been added comparing travel times between Jarvis and Bathurst on Queen and King Streets.

With the King Street Pilot a year old, one area that also deserves a review is the effect it has had on transit service on Queen Street. The short answer is “very little” with the usual caveats about seasonal variations and unusual events that complicate direct before and after comparisons.

The charts presented here cover the period from March 2016 to October 2018, the same period as King Street charts in recent articles. Selected images are included in the post, and more extensive sets are linked in PDFs.

(Note that the level of detail in the three-year charts is such that they suffer when reduced in size to the scale of a blog post. Click on any of them to open a full size version in a new browser tab.)

Major Events on Queen Street

More so that on King Street, Queen has been affected by many construction activities over the three years, and of course it also has more special events disrupting service in the area parallel to the pilot on King. The major events affecting travel times between Jarvis and Bathurst Streets are highlighted in these charts.

  • April 2016: Reconstruction of King and Charlotte diverted service onto Queen adding to streetcar running times there primarily through delays where King cars turned off of Queen without assistance from traffic signals.
  • May to December 2016: Water main reconstruction on Queen west of Spadina triggered a long-running diversion of service via Spadina to King. The times shown are measured between King and Bathurst and Queen and Jarvis for this period where vehicles were diverted.
  • September 2016: Although TIFF closed part of King Street, the service was split rather than diverted. There is no effect on Queen running times beyond that already seen for the diversion of the 501 route.
  • May to August 2017: Construction continued for another summer on Queen including completion of work started in 2016 and replacement of the pedestrian bridge at Queen and Yonge. Buses operated on 501 Queen.
  • September 2017: Streetcars returned to Queen. Reconstruction of Dundas from Church to Yonge caused some traffic to shift south to Queen. King services diverted onto Queen during the opening weekend of TIFF.
  • October 2017: Reconstruction of Queen & McCaul caused Queen service to divert via King between Church and Spadina.
  • November 2017: King Street Pilot begins.
  • June 2018: Construction delays.
  • September 2018: TIFF diversions delay Queen service.

Chart Format

As with the King Street analysis, the charts here show the 85th percentile values for travel times in orange. This includes most trips across the area parallel to the pilot on King. The median value (50th percentile) is shown in blue. Half of the trips took longer and half shorter than this value. When these values track close together, most trips will lie in a fairly narrow band of values (see details for October 2018 later in this article). Where the lines pull apart, travel times seen by riders will have more variation in length.

Where the route was on diversion in 2016, the time shown is measured between Bathurst & King to Jarvis & Queen via Spadina.

For the diversion in 2017, the time is measured between Bathurst and Jarvis on Queen, but includes the diversion both ways via Spadina, King and Church.

Where a value drops to zero, this indicates that no car was observed between the two points usually due to a short-term diversion around a major blockage.

AM Peak 8 to 9 am

Westbound

The beginning of the pilot in November 2017 had no effect on AM peak travel times. The spike in late June 2018 was caused by construction delays according to TTC eAlerts.

Eastbound

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King Street Update: October 2018 (Part II)

This is the second part of the October 2018 update which began with a review of travel times and capacities on the combined 504 King and 514 Cherry routes. (514 Cherry was merged into the King service with a route redesign in early October and no longer exists as a separate route number.) This article looks at the evolution of scheduled and actual service levels on King from March 2016 to October 2018.

The purpose of this article is to show that many factors affect service reliability, and this varies both by location, date and time of day. In evaluation of the King Street Pilot it is important to distinguish between changes due strictly to the pilot and changes that occurred separate from it such as schedule updates.

There are a lot of charts in this article, with more in linked collections. As this is the anniversary of the King Street Pilot’s introduction, I am publishing a large amount of data here for reference by those who are interested in the details.

The King Street Pilot has had some effect on headways (the interval between vehicles). This has been more in the “shaving” of peak values which translates to more regular service even if the scheduled frequency changes little if at all. The TTC’s ability to add service has been constrained by its aging streetcar fleet that only recently has been sufficiently replaced by new cars that service on King is now, with few exceptions, fully provided by the larger Flexity low flow cars.

The table below [click to expand] shows the level of scheduled service over the past three years on the 504 King and 514 Cherry routes. The pdf linked below this table also includes information on the changes in scheduled travel times over the two routes.

504514_2016_2018_HeadwayHistory

Aside from the service reorganizations related to the 514 Cherry car, many of the changes from one schedule period to another relate to changes in the provision of trippers. These are vehicles that make one trip across the route intended to coincide with the peak of the peak periods. The level of tripper service is dictated partly by the season, but much more so by vehicle availability. With the merger of the two routes and the full conversion to Flexity operation, the trippers have vanished from the schedule.

The major changes over the period were:

  • June 2016:
    • 514 Cherry introduced.
    • Service levels on 504 King (and hence on the outer part of the shared route) were reduced except during the AM peak.
  • September 2016: 514 Cherry midday service improved. This change was reversed in May 2017 coinciding with the formal change of this route from CLRV to Flexity cars.
  • September 2017: Running times on 504 King were reduced to claw back an excess that had existed for a few years. Headways during all periods were improved slightly as a result.
  • November 2017: Pilot begins. Transit signal priority (TSP) is disabled at several intersections in the pilot zone where it had previously been active.
  • February 2018:
    • 514 Cherry service improved during the midday and early evening.
    • Roncesvalles Carhouse closes for major renovations causing the patterns of service build up/down to change as all cars now operate from east end carhouses.
  • May 2018: Running times on both 504 King and 514 Cherry were reduced to incorporate the benefit of the King Street Pilot. Headways were improved on both routes to varying degrees during most operating periods.
  • June 2018: Temporary consolidation of the routes for the construction season and the replacement of streetcar service on Broadview Avenue by a bus shuttle to Parliament Street.
  • July 2018: TSP is re-activated within the pilot zone.
  • September 2018: Temporary return to the traditional route structure.
  • October 2018: Permanent consolidation of the routes.

In the table of running times included in the pdf above, round trip scheduled values are shown in an “A+B” format where the first value is driving time and the second is recovery time. TTC has generally not provided a formal recovery time based on the length of trips, but rather simply used this as a way to pad out the total time to an even multiple of the headway. This can create situations where there is minimal or zero recovery time. With the new schedules in fall 2018, there has been a considerable increase in recovery times, and they can be longer than the scheduled headway. This has a few related effects:

  • There is a good chance that more than one car will be at a terminus at the same time. With the longer Flexity cars, this can produce congestion at Broadview and Dundas West Stations. The TTC attempts to offset this by scheduling the recovery time at Distillery and Dufferin Loops, although this is not always successful in avoiding on-street queuing of streetcars at the subway stations.
  • When schedules are “padded” either with excess driving time, or with recovery time, the concept of “on time departure”, already a flexible idea at the TTC where Service Standards allow a six minute window for “on time”, to be erratic because operators know they can make up time over a trip. Conversely, writing schedules too tightly leads to problems both with the variation in route conditions from day to day, not to mention the basic need for breaks from driving continuously.
  • Dufferin Loop has an operators’ washroom, but Distillery Loop does not (although a nearby theatre is used by some in a pinch, provided that it is open). This forces washroom breaks on the 504A service to be taken at Dundas West Station even though the recovery time is supposed to be taken at the Distillery terminus.

The balance of this article reviews changes in actual headways at various points along the route both for inbound and outbound services. The effects vary by location and time of day.

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King Street Update: October 2018 (Part I)

The King Street Pilot will celebrate its anniversary in mid-November after a year of some controversy but unquestionable success in the improvement of transit service downtown. The results for October 2018 continue the pattern shown through the pilot period of a substantially more reliable service on King Street. This reliability is the heart of the King Street project.

October 7 brought a permanent change in the route’s structure to merge the former 514 Cherry operation into 504 King with two separate branches overlapping from Sumach Street to Dufferin Street.

  • 504A operates from Dundas West Station to Distillery Loop on Cherry Street.
  • 504B operates from Broadview Station to Dufferin Loop.

The intent of this change is to give each branch a terminus where operators can have a rest break without blocking following service, something that the former 504 King from Dundas West to Broadview could not manage with the route’s conversion to the longer Flexity vehicles.

This change has also reduced the level of service between Dufferin Street and Dundas West Station, and from Sumach Street to Broadview Station, although this is partly offset by the increase of capacity with the new larger vehicles. However, service reliability on the outer parts of the route is an issue because any bunching or short turns produces a larger gap than would occur with the old service design.

Route 503 Kingston Road Tripper continues to operate to Charlotte Loop at Spadina rather than via Wellington to York Street due to construction on Wellington. This is expected to continue until mid-2019. Service on the 503 is provided by CLRVs and, with rare exceptions, these are the only old cars now seen on King Street.

In this article, the format of some charts has been adjusted to provide more information while maintaining continuity with previous articles in this series.

Part I of this review covers travel times and route capacity. In Part II, I will turn to headway reliability.

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Analysis of Service on 60 Steeles West Part II: Travel Times

In the first section of this article, I reviewed the headways on 60 Steeles West which, to be charitable, are not particularly reliable, especially west of Pioneer Village Station.

In this article, I turn to travel times along the route and how they vary by time of day. The chart formats here are similar to those in the first article, with one change: the charts breaking data into quartiles have been changed so that each quartile has its own colour making them stand out better.

As with the headway data, the behaviour of the route is broken by timepoints or screenlines along the route. Where the headway charts showed the intervals between buses passing a timepoint, the travel time charts show the time taken between these points, organized by time of day so that the rise and fall is clearly seen.

Here are the charts for westbound travel from Finch Station in April 2018. The first page shows the route between Finch and Pioneer Village Stations. It is no surprise that the biggest peak period effect falls in the afternoon for westbound travel.

The first section of the chart below shows the time taken at Pioneer Village Station by buses that are continuing through to the west. The segments from Jane to Weston Road, and from Weston Road to Islington also show the effect of PM peak congestion.

Worth noting is that some of the peaks are fairly broad with longer travel times showing up well before the “peak” hour in the early afternoon. This means that any move to provide better transit priority must address a wider period than an hour or two traditionally thought of as the “peak”.

This chart shows the last segment from Kipling to the east side of the loop west of Highway 427 via Signal Hill and Steinway. Note that Steinway is the eastern limit of the on-street loop, and times are measured just east of this location so that terminal layovers are not included in travel times. There is no evening service here.

The route’s behaviour eastbound in a few ways notably that there is less of a peak effect in the AM eastbound direction that in the PM. However, from Kipling to Islington there is a marked rise in travel times for both AM and PM peaks.

 

The full sets of charts are linked below.

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Analysis of Service on 60 Steeles West Part I: Headways

This article begins a series of reviews of major bus routes in suburban Toronto based on vehicle tracking data from October 2017 (before the subway extension to Vaughan opened) and April 2018. It includes charts showing the behaviour of headways (the times between buses) and travel times in a way that consolidates more information in an overview of how these values change by time (through the day) and along the route.

Many thanks to readers who contributed to the discussion of improvements in how these data are presented. For those interested in the underlying methodology of digesting the TTC data, please refer to this article.

Data for fall 2018 operations are not available because the TTC is in the process of shifting their vehicle tracking to a new system (“VISION”) and do not yet have a data extract tool to provide the kind of archival data I have been using for these analyses. Discussions about how this will be done, including the possibility of an Open Data Portal, are in progress. Buses which have converted to the new system do not appear in the data I receive from the old “CIS” system.

This article deals with headways, the time between vehicles. In Part II I will turn to travel times.

Headways and Service Reliability

A major issue for transit riders is the dependability of service. On most routes, the scheduled frequency is good enough that “on time” is a meaningless concept, but regular spacing between vehicles will guarantee that the typical wait is fairly short and predictable. If service is supposed to be 10 minutes or better, but just missing a bus could cost someone a 20 minute wait, for that rider the concept of a frequent service network rings hollow.

For its part, the TTC only measures service quality at the ends of routes, and then only against the schedule on the premise that if vehicles are on time, regular spacing will take care of itself. This simplistic view ignores the real world of transit operations and presents a rosy picture of service compared to actual experience.

For reference, here are the scheduled levels of service on 60 Steeles West during the months covered by this article [click to enlarge]. Both before and after the opening of Pioneer Village Station on the north side of the York University campus, the route operated with three branches:

  • a local service from Finch Station to York U/Pioneer Village
  • a local service from Finch Station to Highway 27
  • an express service from Finch Station to York U/Pioneer Village (peak periods only)

The level of service during peak periods on each of these is almost identical before and after the subway extension opened.

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King Street Update: September 2018 (Update 2)

Updated November 2, 2018: ERRATA: Capacity charts in the original version of this article omitted 514 Cherry cars from February to June 2018. This has been corrected.

Updated October 11, 2018: Charts have been added at the end of the article giving more detail about the effect of TIFF on operation of the King Street service.

September 2018 brought a major change on King Street with the presence of the Toronto film festival, TIFF, and diversion of service around the festival district. The service design was the same as in 2017, but last year the King Street Pilot and associated traffic restrictions downtown had not begun.

Other service changes in September included:

  • The return to the standard 504 King routing from Broadview Station following completion of track construction on Broadview.
  • Reinstatement of 514 Cherry following a split 504 operation during the construction period. (The split operation will become standard on Sunday, October 7.)
  • The 503 Kingston Road car resumed tripper operations to York Street, but this lasted only to mid-September when the route was extended again west to Spadina (Charlotte Loop) to accommodate construction on Wellington Street.

Peak Travel Times

PM peak travel times continued the pattern seen over the past year, but the TIFF period produced major disruptions because of service diversions. Note that in the chart below, travel times across the pilot area from Jarvis to Bathurst include the time spent on diversion all day on Thursday and Friday, September 6 and 7. Diversions also occurred at some times in the week of September 10-14, but these trips are not included below.

  • Westbound via north on York, west on Queen, south on Spadina
  • Eastbound via north on Spadina, east on Queen, south on Church

The effect of TIFF diversions was worse in 2018 than 2017 with the 85th percentile of travel times on Thursday September 6 hitting 54 minutes. The chart below expands the first three weeks of September and includes four percentile lines rather than the two used in the chart above. Note that the four lines stay close together indicating there was little spread between the best and worst case values.

  • Thursday/Friday September 6/7: The diversion via Queen more than doubled the travel time between the bounds of the pilot.
  • Monday September 10: No diversion or temporary service blockage at TIFF affected the period from 5-6 pm.
  • Tuesday September 11: Service was blocked at TIFF during the 5-6 pm hour:
    • some cars were held producing higher travel times at the 85th and 100th percentiles;
    • some cars diverted (not included below);
    • some cars ran through unimpeded producing a 25th percentile similar to “normal” days.
  • Wednesday September 12: Emergency sewer repairs west of Bathurst required a diversion via Queen for much of the day. No cars operated through King and Bathurst and so there were no trips on King between Jarvis and Bathurst to measure.
  • Thursday/Friday September 13/14: Travel times returned to close to values seen before and after the TIFF period.

Travel times eastbound were also affected by TIFF and the diversions, and the effect was comparable to westbound data.

I will return to the effects of TIFF on all day travel times later in this article.

Here are the full sets of charts:

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