Timetable Adjustments in the Wellington Region Using Real-Time Information
Aim:
To research methodology used to rectify timetable inaccuracies using Real-Time information and
recommend methodology for application in the Wellington region.
Summary of research:
RTI has the potential to provide an enormous amount of data that provides the potential to
significantly improve bus timetables by making them more achievable and improving their accuracy. This
report focuses on how to analyse RTI data to improve timetables.
“Traditional scheduling methods, created in an era of expensive manual data collection, are based on
mean observed running times, which are estimates from small sample sizes. Now, however, AVL
(Automatic Vehicle Location) data offers the possibility of using extreme values such as 85- and 95-
percentile running times as a basis for scheduling. Extreme values are important to passengers, who
care less about mean schedule deviation than about avoiding extreme deviations such as buses that are
early or very late. Extreme values are also important to planning, because a goal of cycle time selection
(sum of scheduled running time and scheduled layover) is to limit the probability that a bus finishes one
trip so late that its next trip starts late.” (1)
Because extreme values can only be estimated reliably from a large sample size, the RTI data available
to GWRC and operators offers new opportunities for analysis.
Research papers suggest advantages of focusing on extreme values in the context of refining
timetables. Two of the suggested advantages of focusing on extreme values are:
1) “
Recovery time is put into the schedule to limit the probability that a bus finishes one trip so
late that its next trip starts late. Therefore, logically, scheduled half-cycle times (scheduled
running time plus recovery time) should be based on an extreme value such as the 95th-
percentile running time….. Yet, some route-period combinations need more than this standard,
and others less, because they do not have the same running time variability. AVL data allows an
agency to actually measure 95th-percentile running times and use that to set recovery times.”
(1).
2) “
Passenger waiting time is an important measure of service quality. Studies show that
customers are more affected by their 95th-percentile waiting time – for a daily traveller, roughly
the largest amount they had to wait in the previous month – than their mean waiting time,
because 95th-percentile waiting time is what passengers have to budget in their travel plans to
be reasonably certain of arriving on time.”, indicating that a shift toward customer-oriented
measures goes hand in hand with the ability to measure extreme values (1).
Scheduling Philosophy:
There are a few different ways of scheduling the timetable effectively. The method chosen depends
upon the scheduling and operating philosophy of the transit agency and operators.
Trip Running Time – including Allowed time, Half-Cycle Time and Recovery Time
When looking at how to adjust the timetable, some schedulers choose to focus on running times for
the whole trip/journey. In doing so some schedulers choose to base schedules on mean running time
while others prefer to intentionally put in slack, as a fraction of mean running time, into the schedule
(for this approach to be successful it needs to be coupled with a practice of holding at timepoints). The
research suggests that a more “scientific, data-driven approach is to use a percentile value, or feasibility
criterion”. For example, a feasibility criterion of 85% means setting the allowed time to 85th-percentile
observed running time so that the schedule can be completed on time 85% of the time.
An alternative method is to use the ‘half-cycle time approach’. Half cycle time is the sum of running
time and recovery time. It is, in effect, the time from a bus’s departure at one terminal to its next
departure in the reverse direction. Because the purpose of recovery time is to limit the likelihood that
delays encountered in one trip will propagate to the next, half-cycle time is based logically on a high-
percentile value of running time.
Using the half-cycle approach combined with feasibility criterion is one option of creating more suitable
timetables. An example of such an approach is as follows: The chief engineer for operations analysis at
Brussels’ transit agency has recently been working with a scheduling software vendor to develop reports
to support statistically based schedules. Their approach uses three parameters, as explained in this
example: If the three parameters are 95%, 80%, and 5 min, then half-cycle time is set equal to 95th-
percentile running time, and allowed time is set equal to 5 min less than 80th-percentile running time.
That way, there will be an 80% chance that a trip finishes no more than 5 min late, and a 95% chance
that the next trip can start on time (1).
Herbert Levinson (Transportation Consultant and Professor Emeritus of Transportation) referred to in a
paper by Kimpel and Strathman (2) suggests that the scheduled run time should be set at the mean or
median run time in order to ensure that the majority of operators do not have to ‘kill’ time in order to
maintain schedule adherence. Levinson also contends that an optimal amount of recovery time for a
given bus trip is the 95th percentile run times minus the scheduled run time. A study for TriMet (Transit
Agency of Oregon) found that basing recovery times on 95th-percentile running times could lead to an
average reduction in recovery time of 7.3 minutes per trip and an estimated reduction in operating costs
of $7.1 million (2).
Segment Running Time
Scheduling running time on segments, or equivalently setting departure (or arrival) times at timepoints
relative to the trip start time, can either precede or follow scheduling route times.
Two suggestions for calculating running times at the segment level are discussed.
If the transit agency and operators are favourable to holding at timepoint then the ‘Passing Moments’
method, developed by The Delft University of Technology, may be considered. Applied at several Dutch
transit agencies, the Passing Moments method bases timepoint schedules on f-percentile completion
time from each timepoint to the end of the line, where completion time is running time from a point to
the end of the line, and f is the feasibility criterion (the transit agency in Eindhoven, for example, utilize
the 85th-percentile (3)). Segment running times are determined by working backwards from the end of
the line, without ever explicitly analyzing observed running time on timepoint-to-timepoint segments.
This approach was designed to overcome operators’ resistance to holding, which is the key to good
schedule adherence. If a schedule is written based on mean running time, operators know that, if they
hold at a timepoint, they will have a 50% chance of finishing the trip late and thereby getting a
shortened break; therefore, they are reluctant to hold. With 85th-percentile allowed times between
each timepoint and the end of the line, operators know that even if they hold, they have a high chance
of finishing on time. The Passing Moments method has two advantages compared to setting slack time
simply proportional to mean running time. First, it is sensitive to where on the route delays and running
time variability occurs. Second, it tends to put less slack in the early part of the route and more in the
later part of the route, which is a better way to distribute slack than simply applying it proportionately
throughout. It results in holding buses less in the early part of the route because they may need that
time later in the route.
If the transit agency and operators are not favourable to holding at timepoints then it may be better to
use a low feasibility criterion and (i.e. percentile value lower than the median) because running early is
more harmful to passengers than running late. TCRP Report 113 (1) states that “a statistically based
approach for segment-level scheduling might be to base departure time at a timepoint on 40th-
percentile observed cumulative running time (i.e., from the start of the line to a point). That way, there
will be only a 40% chance of a bus departing early, and those that depart early should not be very far
ahead of schedule”. TriMet uses the 40th percentile of running times to set the timetable schedule (3).
Homogenous Periods:
A challenge of analysing the running times using the preceding methods can be choosing the
boundaries of running time periods within which allowed time is constant or homogenous. A trade-off is
required between short periods within which scheduled running times match the data well versus
longer periods of constant allowed time but greater variability. TCRP Report 113 (1) provides a logical
method in resolving the trade-off: First determine, for each scheduled trip, an ideal allowed time and
then to make running time periods as long as possible subject to the restriction that no more than a
certain percentage of the scheduled trips in that period have an ideal running time that deviates by
more than given tolerance from the suggested running time for that period.
Scheduling Tools:
Some agencies, including King County Metro and Eindhoven, have software tools that suggest
scheduled running time, in combination with a parallel tool for establishing scheduling periods, i.e.
periods of homogeneous running time for which a common running time can be assigned. Users supply
a criterion such as “find as long a period as possible for which a common scheduled running time is
within 2 minutes of the 75-percentile observed running time for at least 90% of the scheduled trips in
that period.” (3).
At King County Metro, schedules are built beginning at the segment level, so running time analysis is
done at the segment level. In Eindhoven, schedules are first made at the route level, with running time
later allocated over segments, so analysis is first done at the route level, followed by another tool that
suggest segment running times.
Chapter 5 of the TCRP Report 113 (1) discusses a scheduling tool called TriTAPT, developed by the Delft
University of Technology. The TriTAPT program provides the ability to perform two integrated analyses:
the first divides the day into running time periods and establishes route running times for each period,
and the second allocates running time over a route’s segment.
This program is still available by contacting Peter Knoppers ([email address]).
Perhaps the program MiniTab, used by GWRC, has the capability of performing statistical and trade-off
analyses similar to what is described in Chapter 5 of TCRP Report 113 (1). Further research into
MiniTab’s capabilities may be required if the decision is to use the methods suggested.
Stop Level or Timepoint Level Detail?
While timepoint data is all that is needed for traditional scheduling, there is the issue of End-of-line
problems with timepoint data. Agencies with only timepoint records generally find data for the first and
last segments of the line to be unreliable because of unpredictable operator behaviour at the end of the
line (3). With stop data, operations near the end of the line are better tracked and far less information
about the final segment is lost. This could have some application in the Wellington area. Perhaps using
stops close to the end-of-line instead of end-of-line data could remove the effect of unpredictable
behaviour at the end-of-line (e.g. finishing a trip early because there are no passengers on board or
logging into the trip early).
References
1. Furth, P.G., Hemily, B.J., Muller, T.H.J., & Strathman, J.G. (2006). Using Archived AVL-APC Data to
Improve Transit Performance and Management (TCRP Report 113). Washington, DC:
Transportation Research Board.
2. Kimpel, T.J., & Strathman, J.G. (2004). Improving Scheduling Through Performance Monitoring
Using AVL/APC Data. Portland, OR, Centre for Urban Studies.
3. Furth, P.G., Hemily, B.J., Muller, T.H.J., & Strathman, J.G. (2003). Uses of Archived AVL-APC Data
to Improve Transit Performance and Management: Review and Potential (TCRP Web Document
H-28). Washington, DC: Transportation Research Board.
