Chapter 9. Putting an R for reliability into BRT
IntroductionTo achieve high satisfaction indicators, a public transport system needs to provide a
high level of service to its users. A high level of service not only requires that users
experience low waiting times, fast travel times, and a minimum comfort standard,
but also that this service is reliable; i.e. does not change significantly from day to day.
These expectations explain some of the success of heavy rail systems around the
world. However, heavy rail has a high infrastructure cost, ranging between US$ 70
to US$ 350 million per kilometer (Wright and Hook, 2010). This cost makes rail an
unviable alternative for corridors with passenger demand under 20,000 passengers
per direction per hour, and makes it very often too expensive for most developing
countries. These are precisely the countries where demand for public transport is
high.
To overcome these problems, BRT has risen as an alternative to rail potentially
offering the same level of service at a reduced cost. BRT bases most of its high level
of service on rapidness. The Rapid in BRT stands for both the speed of the buses and
the frequency. High frequencies create shorter trip times and higher capacity. This
reduces waiting times and improves comfort, two critical elements of the level of
service perceived by users. However, operating high frequency service on a
timetable is difficult. Even though segregated lanes helps isolate bus operations
from general traffic influence, BRTs worldwide still face severe bunching in which
buses tend to move in groups or bunched instead of keeping regular headways.
Even if buses are dispatched at regular headways, they will tend to bunch due to
inherent variability of passenger demand and therefore dwell times at bus stops,
and travel time between consecutive stops. This variability makes loaded and
delayed buses run even slower, while empty and ahead of time buses run even
faster. Therefore keeping regular headways is difficult since it becomes a textbook
example of an unstable equilibrium in which any perturbation will take the
operation away from the desired constant headways. Bus bunching has been widely
studied in the literature (Newell & Potts, 1964; Potts & Tamlin, 1964; Chapman &
Michel, 1978; Pilachowski, 2009).
This phenomenon substantially worsens the level of service generating problems
for the users, operators and the authority. Users wait longer and their waiting time
has more variability. Also, most users suffer crowded buses while only a few enjoy
empty ones. For users bunching hurts waiting time, service reliability and comfort,
creating an incentive for a mode shift away from transit. At the same time operators
experience high cycle time variability, since some buses run faster than others
increasing the number of buses and drivers needed to keep a smooth dispatching
operation. Finally, it puts pressure on the authority for more buses due to the
negative perceived frequency and comfort by users.
1
This reveals that in order to give an attractive level of service, rapidness is not
enough to provide rail-like level of service. BRT must also be reliable. Hence, the 2.0
version of this industry must come with an extra “R”: Bus Rapid and Reliable Transit
(BRRT).
Informal bus operations, existing in many developing cities, created their own
methods to address the issue of bunching. Since in these systems the bus drivers are
paid based on the number of passengers boarding their bus, getting too close to the
bus ahead reduces the demand captured and therefore their earnings. But
decelerating too much would risk being overtaken by the bus behind starting
competition between the drivers. This conflict in the streets is the reason why
traveling in bus under informal operations is usually considered a traumatic
experience and why these cities have a very high accident rate involving buses. But
this economic incentive for regularity created a solution.
In Santiago, Chile for decades bus operations were assisted by a group of people
called “sapos.” They stood on key street corners and provided information to bus
drivers regarding the headways of the buses ahead. The goal of the “sapos” was to
help drivers to strategically choose where to position their buses to avoid direct
competition with other drivers and keep their buses full. Since in this case the
financial benefits of regularity went to the drivers (and by default the riders) sapos
were financed by drivers, not by the bus owners. As Johnson et al (2005) shows that
sapos were quite effective in keeping headways more regular.
Under formalized bus operations the drivers no longer have the financial incentive
for regularity. But a formalized system with technological advancements, like GPS
on all of the buses, and a centralized dispatching offered other options for
addressing the problem.
The most common way to address reliability is to hold buses at certain critical stops
aiming at keeping similar headways ahead and behind every bus. However, Delgado
et al (2012) shows that if holding is implemented in a myopic way (as sapos always
did), it can end up over-holding buses and therefore damaging waiting and travel
times excessively. Many other control strategies have been proposed: station
skipping, boarding limits, overpassing-and-expressing, transit signal priority, etc.
In this chapter we present and discuss holding control strategies that use a complete
knowledge of the system based on our Holding Real-Time optimization model (HRT)
presented in Delgado et al (2012). First, we present a classification of control
strategies according to two different criteria. Second, we introduce and explain the
HRT control strategy, the data requirements and technology necessary for a
complete implementation. Third, two case studies are presented in order to
highlight the benefits of this strategy. The first case study is a simulation
2
experiment where we compare the proposed strategy against two benchmarks. In
the second case study, we present the results of a pilot program run in the
Transantiago system in Santiago, Chile. Finally, we summarize the main results by
evaluating the influence on the level of service to users and the cost to operators for
all three strategies and discuss the main challenges in the implementation of these
kinds of strategies in real operations.
Problem Statement: Classification of Control Strategies
In high frequency services, control strategies to avoid bus bunching have been
widely studied the last fifty years. These strategies can be classified according to
two main standards: i) the location where the control strategy is implemented and
ii) the level of real time information required to apply these strategies.
In the first group, Eberlein (1995) identified three sub-groups: at stations control
strategies, inter-station control strategies and other control mechanisms. Among at
stations control strategies, we find holding, station skipping, deadheading and short
turning. At station control strategies are the most widely used because they are easy
to understand and implement for the bus driver. In the case of inter-station control
strategies, overtaking, speed control and Transit Signal Priority (TSP) are the most
famous ones. Even though these strategies are more difficult to implement in
practice, because they need the direct intervention and judgment of the bus driver,
they are less annoying for passengers because the perception of time while the bus
is in motion is less than when it is stopped. Finally, in other control mechanism, we
find strategies as vehicle injection at specific points on the route to overcome
important disruptions in bus service operation.
Depending on the level of information, strategies can be classified as local or system
control. Local control strategies require reduced information than system strategies,
generally only the headway of the preceding bus. These strategies tend to overreact
in many situations due to the myopic view of the system, resulting for example in
unnecessary long holding times. Examples of local control regarding holding
strategies in the literature are the works of Barnett (1974), Turnquist & Blume
(1980) and Fu & Yang (2002).
The development and expansion of Intelligent Transportation Systems (ITS) have
enabled more advanced control strategies that overcome the limitations of local
control strategies. Dessouky, Hall, Nowroozi, & Mourikas (1999) specified the basic
technological components needed to implement these strategies, which are:
Automated Vehicle Location system (AVL), wireless communication system, Transit
Operations Software and Hardware and Automatic Passenger Counter (APC). Some
components like GPS can be found in many transit systems around the word,
including many in developing countries, such as Transantiago in Santiago, Chile;
Transmilenio in Bogotá, Colombia; Metropolitano in Lima, Perú; Transcarioca in Rio
3
de Janeiro; Guangzhou in China. Other components like APC, even though they have
been implemented in many systems in the form of RFID smart cards (i.e. Oyster in
London, Octopus in Hong Kong, Charlie Card in Boston, Bip in Santiago) the
information collected is still not always available in real time for transit operators.
(See Chapter 11 for a more in-depth discussion of the advancement of data
collection.)
Since 2000 control strategies using real time information that allow a complete
knowledge of the state of the system have been widely studied. Among at station
control strategies we find the holding control strategy presented in Ding & Chien
(2001), Eberlein, Wilson, & Bernstein (2001), Puong & Wilson (2008), Sun &
Hickman (2008), Bartholdi & Eisenstein (2012), Delgado et al. (2009, 2012). Real
time information have also allowed deployment of inter-station control strategies
such as Transit Signal Priority where the detection of the bus before the intersection
plays a relevant role to decide how to intervene in the traffic light cycle. (Dion &
Rakha, 2005; Lee, Greenwood, Bowie, Hung, & Shalaby, 2006; Li, Wu, Li, Bu, & Zhang,
2007; Liao & Davis, 2007).
Despite the greater technological availability, lack of incentives directly targeted to
reduce bus bunching and hence increase service regularity and reliability has
prevented bus operators and agencies from implementing more advanced control
strategies. Unlike under informal operations, none of the actors in a formal system
have a clear direct financial incentive and the increased number of actors
complicates implementation. (See Chapter 5 for a discussion on contract design.)
The next subsection provides a brief overview of the control strategy proposed by
Delgado et al. (2012).
Methodology: The HRT Control Strategy
In the HRT control strategy proposed by Delgado et al. (2009, 2012) control actions
are taken by a central control which has a complete knowledge of the state of
system. The state of the system is defined by the location of all buses in the corridor
and the passenger demand at all stops. This information when possible is obtained
by dynamic data from GPS that is updated every pre-defined time intervals. A
complete description of the information flow around the control software is
presented in the section describing the Transantiago pilot program. The central
control runs a deterministic rolling horizon mathematical programming model that
allows to control vehicles by minimizing total waiting times using as decision
variables the bus holding times at bus stops. The rolling horizon approach attempts
to predict the future evolution of the system by finding the optimal set of control
actions for all pairs of bus-stops considered in the planning horizon. This process is
4
repeated once and again every time interval refreshing the control actions with the
new information available.
The use of a rolling horizon approach is necessary to correctly capture the effects of
a present decision over the long-term costs. This is because control actions taken at
a certain instant have a direct influence in the future evolution of the system.
Moreover, given that the decisions applied to a specific bus affects all other buses in
operation, it is necessary to consider the control actions of all buses simultaneously
to correctly account for these interactions.
The bus line is modeled as a closed circuit, which implies that the last stop of the bus
route is also the beginning of the same line. Therefore, both outbound and inbound
directions of a line are considered as one major cyclic line. This is consistent with
the reality observed in bus systems, since in general the buses that arrive to the last
stop of the outbound leg are the same ones that later depart in the inbound leg of
the service. The planning horizon can be set to cover the whole circuit (as in
Delgado et al., 2012 ) or to cover a fraction of the total number of stops (Ortiz, 2012)
so as to decrease the model variables and make solving times compatible with a
real-time application.
The objective function of the optimization model tries to minimize the total waiting
times experienced by users in the planning horizon, which is composed of four
terms. (i) Wfirst : at-stop waiting time experienced by users as they wait for the first
bus to arrive; (ii) Win-veh :in-vehicle waiting time for passengers aboard a bus that is
being held; (iii) Wextra : extra-waiting time of passengers who could not board a bus
because it is at capacity and (iv) a penalty for passengers left behind when there is
available capacity due to boarding limits (decision variable presented in Delgado et
al., 2009 and 2012, which is not considered for practical reasons). All this terms are
normalized by the total passengers involved in the system and are weighted
according to the relative cost given by users, recognizing for example, that waiting
for an extra bus because the first one was full of passengers is probably more
annoying than waiting inside the bus while the bus is held at a stop.
The constraints of the model represent the evolution of the system (i.e. travel time
between stops, dwell times, passenger demand) in the planning horizon. The model
is also able to handle a heterogeneous fleet of vehicles with different capacities
without the need to use binary variables, making the solution compatible with realtime requirements.
5
The data necessary as an input for the optimization model can be divided in two
categories: static and dynamic data. Static data refer to information that will remain
constant as the system evolves in time; meanwhile dynamic data are expected to
vary across iterations of the optimization model.
The static information is the following:
 Number of bus stops on the line and the en-route distance between them.
 Average boarding and alighting times per passenger.
 Origin-Destination (OD) demand matrix: average number of trips that board.
at stop “i” and alight at stop “j” during the period of analysis.
The dynamic data are listed below:
 Number of buses operating in the line, their capacity and location within the
bus route (en-route distance from the last bus stop visited).
 Speed or travel time between consecutive bus stops.
 Passengers waiting at each bus stop.
 Passengers that have board each bus in every serviced bus stop.
Depending on the operator’s data collection and processing technologies, some of
the above dynamic data can be converted into static data and vice versa. For
example, if buses have Automatic Passenger Count (APC) devices, real-time
passenger arrival rates can be estimated (from the passengers that have board each
bus) and be considered as dynamic data. Otherwise, a fixed arrival rate (determined
from the OD matrix) can be multiplied by the (real-time) headway between
consecutive buses to estimate the number of passengers that arrived to the stop in
between both buses. The ideal scenario is to have as much dynamic data as possible
to model the system more accurately. (See Chapter 11 for a more in-depth
discussion of the advancement of data collection). Nevertheless, the model has
proven to perform well when dynamic data has been replaced by static data.
Using all these data as input, the optimization model is solved giving the optimal
holding time for each bus of the line in their respective next stops. All this holding
instructions are stored and sent to bus drivers, and are updated when the next
optimization event occurs.
Results/Case Study
6
Now we will present two different case studies. The first one is a simulation study
and the second one a real pilot program in the Transantiago system. The simulation
study is used as a means to compare the HRT control strategy presented and twobenchmark strategies:
 No control. That is the spontaneous evolution of the system, where buses are
dispatched from the terminal at a designed headway, without taking any control
action along the route, i.e. the only place where holding can take place is at stop 1.
 Threshold control. This is based on a myopic rule of headway regularization
between buses, where a bus is held if the headway with the previous bus is less
than the schedule headway or is dispatched immediately in the other case. We set
all the stops along the corridor as control points.
The simulation scenario allows a deeper understanding of the effect that different
control strategies have on both users and operators. While the pilot program shows
the potential of the tool and the challenges that need to be addressed in real world
applications.
Simulation scenario
In order to evaluate and compare the proposed model against the benchmark
strategies, we consider a high frequency service with designed headway between
buses of 2 minutes, where buses reach capacity at certain stops.
The transit corridor has 10 km of length, with 30 bus stops evenly spaced, where the
terminal is denoted by stops 1 and 31. Buses have a limited capacity of 100 passengers.
Travel times between stops for all buses follow a lognormal distribution with mean 0.77
min. and a coefficient of variation of 0.4. Boarding and alighting time per passenger are
set at 2.5 and 1.5 seconds respectively.
For the proposed holding strategy and the two benchmark strategies, we carried out 30
simulations runs, each of them representing 2 hours of bus operations. We consider a
warm up period of 15 minutes before any control strategy is applied to let the system to
freely evolve. This warm-up period is long enough for some bus bunching to appear. The
reason to adopt this warm up period is to distinguish the effect of the proposed control
strategies under stationary conditions and also under a more chaotic system.
We present four performance indicators to compare all three strategies:
 Average waiting times and standard deviations
 Bus trajectories
 Bus loads
 Cycle time distribution
Average waiting times and standard deviations
7
Average waiting times are calculated during the time period when the control strategies
take place (minutes 15-120). To isolate the impact of the control strategies we subtract
from the average waiting times, the minimum waiting time for the system, which
constitutes a fixed cost that cannot be avoided.
Table 1:
Objective Function Value and standard deviation for the three strategies
No
Threshold
HRT
control
control
Control
Wfirst
5349.06
1514.73
972.59
Std. Dev.
476.53
601.48
255.10
-71.68
-81.82
% reduction
Wextra
1535.20
2147.45
139.25
Std. Dev.
703.16
3180.44
147.14
39.88
-90.93
% reduction
Win-veh
388.40
8127.44
1582.36
Std. Dev.
63.31
1320.70
115.46
1992.53
307.40
% reduction
Tot
7272.66
11789.62
2694.20
Std. Dev.
877.59
4906.92
425.08
62.11
-62.95
% reduction
Table 1 presents the results yielded by the three control strategies. In this table the
average value for Wfirst, Win-veh,, Wextra and the total waiting time with their respective
standard deviations are reported. In each case the percentage change with respect to the
no-control case are added. The table shows that the proposed HRT strategy significantly
reduces waiting time due to bunching with saving around 63% when compared against no
control. The table also shows that the proposed strategy presents a much more stable
performance with standard deviations significantly lower than the no-control and
threshold control. Table 1 also indicate that even though the Threshold strategy generates
savings in waiting time for the first bus, these savings are counteracted by the enormous
holding times and extra waiting time, resulting in a worst performance than no control.
This situation, as was explained before, is due to the local view of the system that tends
to overreact in some cases as will be shown in the next subsection.
Bus trajectories
Figure 1 shows the bus trajectories for the three different control strategies for a typical
simulation run. While in the no control strategy (1a) buses bunch up, which leads to long
periods of time where no buses pass a stop, the application of the threshold control
strategy, as shown in 1b), avoids some of these bunching, allowing buses to maintain
more uniform headways. However, the myopic view of this strategy produces some long
holdings that propagate to the following buses at the same stop with significant cost for
passengers already in the buses and decreasing the total bus frequency. The trajectories of
8
the proposed control strategy shown in 1c) produce uniform headway pattern between
buses and also smaller headways than the threshold control that explain the waiting time
savings.
a) No control
b) Threshold Strategy
c) HRT Strategy
Figure 1: Trajectories of buses for the three strategies: a) no control; b) threshold
strategy; c) HRT Strategy
Bus loads
Figure 2 presents for the three different control strategies the associated loads of each
bus after it departs from stop 1 until it reaches stop 30. . The horizontal line
represents the bus capacity. The figure indicates that under no control loads between
buses at a given stop, present a great variability, with many buses running at capacity
9
while others ride empty (2a). This affects the level of service experienced by most users
since a very uncomfortable bus is suffered by many more users than a quite comfortable
one. The HRT strategy present the less variable and most uniform pattern in bus loads
(2c). In addition, the real-time holding strategy presents fewer buses running at capacity
and at fewer stops. This is very relevant since discomfort only happens at high load
factors so a more balanced load factor across buses yields a more comfortable experience
to users. These findings therefore suggest that the implementation of real-time holding
strategies can improve comfort compared to the other strategies, allowing buses to travel
less crowded and providing a more reliable experience.
a) No control
b) Threshold Strategy
c) HRT Strategy
Figure 2: Bus load at different stops, for different strategies: a)no control; b) threshold
strategy; c) HRT Strategy
10
Cycle time distribution
We next analyze the effect of the three strategies on the operator’s performance. Figure 3
shows the distribution of cycle times across all buses for the three different control
strategies. As it can be observed, under the no control strategy cycle time varies
substantially with some buses completing their cycle in 25 minutes while others spend
more than 40 minutes (3a). The use of local strategies reduces this variability but at a cost
of increasing the average cycle time for buses which directly affects the operational costs
(3b). In contrast, the HRT strategy presents the smallest average cycle time and the
lowest variability across the three strategies (3c). This data suggests that the proposed
strategy is also the most beneficial strategy from the operator’s point of view since the
low variability allows a smoother and more robust operation and planning at the
terminals. Furthermore, the reduction in cycle time also decreases the number of buses
needed to provide a given frequency. This is an important result since among operators
there is a belief that applying holding strategies always results in an increase in cycle
time.
11
b) No control
b) Threshold Strategy
c) HRT Strategy
Figure 3: Cycle Time Distribution, for three strategies: a) no control; b) threshold strategy
; c) HRT Strategy
In summary, the results presented above demonstrate that the proposed HRT
strategies not only reduce passenger waiting times, but also increase comfort and
reliability allowing buses to travel less crowded and at regular intervals. For
operators applying real time holding strategies is a possibility for offering a better
level of service for users at a reduced cost and is also beneficial for drivers since the
reduction in cycle time variability allows for a better shift planning process.
Transantiago pilot program
12
In order to validate our simulation results, we ran a pilot study on the route 210
service in Santiago from February to June 2014. The 210 service runs through the
city in a south-north direction (56 km long), has a high frequency (1 bus every 3-4
minutes during the morning peak period) and is one of the most demanded services
in the city (48,000 passengers transported on an average week day and 9,500 in the
morning peak period).
Service 210 suffers severe problems of regularity that are amplified along the route
because most of the time buses are not dispatched at regular intervals at the head of
the service. Figure 4 displays the coefficient of variation (COV) of headways, which
is defined as the ratio of the standard deviation to the mean, for the 210 service
measured at its initial point against the COV in a location in the middle of the service,
approximate 13 km from the head of the service. As can be seen, the COV is very
rarely lower than 0.5 (it should be zero if buses are dispatched regularly) and most
of the time is higher than 1 (which is worse than a Poisson process in which buses
are dispatched independent of one another without memory of the previous
departure). The figure also shows a clear correlation between the two
measurements indicating that if buses are dispatched regularly, then bus bunching
will be less severe in the route and therefore easier to correct.
Figure 4: Correlation between COV of headways at the first and second control point.
Figure 5 shows a diagram with the information flow around the control software.
First the vehicle location data and passenger load data (if available) are sent from
the bus to the operator, which sends the information to the server using a web
service communication channel. Then, the program processes all this information
and feeds the optimization model. The solving frequency of the optimization
problem can be set depending on the frequency of the GPS pulses. For instance, in
13
Transantiago we are generating control instructions every minute because the
system GPS pulses are refreshed every 30 seconds.
Figure 5- Schematic representation of information flow
As a way to incentivize transit operators to offer a high quality of service,
Transantiago introduce fines if operators do not achieve at least 90% of the
promised frequency or 80% of the desired regularity. The regularity fines are
calculated based on the ICR index, which computes the deviation of the actual
headway between two consecutive buses from the desired or designed one. This
calculation takes place in three points along the route: the beginning, a middle point
and at the end of the route.
The main results from the pilot program are that the regularity fines have reduced
in more than a 20% in June compared to March, month when the pilot program was
starting as shown in Figure 6. This result is of particular interest since these
improvements have been achieved improving the dispatches at the head of the
service and with only 15% of instructions accomplished by bus drivers along the
route. Involving bus drivers as a key element of the system is one of the main
challenges for a successful implementation. Training session, focus group and
surveys are been taking place to deeper understand their motivations and adapt the
console to their requirements.
14
Figure 6- Percentage of fine reduction in June compared to March 2014 for
line 210, at three different control points.
Discussion
As described in this chapter, high frequency bus services need real time control
strategies such as those described, to offer rail-like level of service to passengers.
The holding strategy presented here shows that bus headway regularity can be
achieved quite inexpensively. For users, headway regularity reduces waiting while
improving comfort and reliability, improving the level of service and thus reducing
the incentives for a mode shift away from transit. For operators, headway regularity
allows for a fleet and crew operation that can potentially stick to the schedule, while
not increasing cycle times. An important side effect found in our field study and our
simulations suggest that under some circumstances (competition with other
services or large fare evasion due to active capacity constraints), a regular service
can even capture more passengers, thus increasing its revenue.
The recent development of these tools suggests an auspicious future for urban buses
in developing countries that should be considered when urban development is
planned. Planners and authorities should see BRRT as a very cost-effective option to
provide high level of service public transport and stop the increasing market share
of private cars, with their associated externalities like congestion, accidents and
pollution.
However, several challenges must be addressed for successful implementation of
these real time control strategies. First, bus drivers’ behavior must be involved in
the designed system, since they are in charge of applying the control decisions. If not
properly incorporated, a small fraction of indifferent or boycotting drivers can be
15
enough to eliminate the promised benefits (Phillips et al, 2014). Thus, incentive
schemes for drivers should be designed and implemented. The control system relies
on technological components such as periodic GPS pulse, console platforms,
communication systems that must be implemented and properly maintained. Finally,
users should be educated about the control mechanisms used to reduce their
perception that they are being implemented against them.
A final concern regards who should be in charge of implementing these control
mechanisms. Hernández et al (2014) explain that when more than one operator
share a long enough section of the route they may use the control strategy to
position their buses strategically to capture more demand. This can harm the level
of service instead of improve it. If the transit authority is in charge of controlling the
buses, incentive mechanisms must be designed to ensure that operators and drivers
obey the instructions.
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