Australasian Transport Research Forum 2015 Proceedings
30 September - 2 October 2015, Sydney, Australia
Publication website: http://www.atrf.info/papers/index.aspx
Investigating multiplier effects created by combinations of
transit signal priority measures on arterials
Long Tien Truong1, Majid Sarvi1, and Graham Currie1
1Institute
of Transport Studies, Department of Civil Engineering, Monash University
Email for correspondence: long.truong@monash.edu
Abstract
Transit signal priority (TSP) has proven to be a cost-effective solution for public transport
vehicles at signalised intersections as it usually does not require substantial infrastructure
upgrades, while improving bus travel time and reliability. Numerous studies have focused on
the design and operation of TSP, while few have considered the optimum combination of
TSP at a corridor and a network level. However, it is unclear whether the combination of TSP
on an arterial or a network creates a multiplier effect on public transport benefits, i.e. benefits
from providing TSP at multiple intersections are higher than the sum of benefits from
providing TSP at each of those individual intersections. This paper investigates the effects of
combinations of TSP measures on signalised arterials to establish if a multiplier effect exists.
Results of a modelling test-bed reveal that combinations of TSP measures on signalised
arterials can create a multiplier effect on bus delay savings when signal offsets are optimised
to minimise bus delays. The existence of the multiplier effect suggests considerable impacts
of TSP on a network-wide scale.
1. Introduction
Transit signal priority (TSP) has proven to be a cost-effective solution for public transport
vehicles at signalised intersections as it usually does not require substantial infrastructure
upgrades while improving bus travel time and reliability. For instance empirical studies
indicate positive impacts of TSP on travel time savings (Furth and Muller, 2000; Kimpel et al.,
2005) and schedule adherence (Sakamoto et al., 2007). Moreover, improved travel times
and reliability might result in further benefits, including mode shifts towards public transport
and reductions in fleet requirements, operating costs, fuel consumption and exhaust
emissions (Lehtonen and Kulmala, 2002; TCRP, 2003; Currie and Sarvi, 2012).
TSP strategies can be identified as passive, active, and adaptive priority (Baker et al., 2004;
Smith et al., 2005). Passive priority usually involves offline signal timing optimisation in
favour of public transport vehicles. For instance, optimising traffic signal offsets can reduce
bus travel times substantially (Estrada et al., 2009). Active priority dynamically adjusts signal
timings to facilitate the movements of public transport vehicles following their detection. A
number of active priority strategies are used, including green extension, early green,
actuated transit phases, phase insertion, and phase rotation. The activations of these
strategies usually rely on the prediction of arrival times. Various arrival prediction models can
be found in previous studies, which use historical travel time data (Ekeila et al., 2009;
Wadjas and Furth, 2003), a combination of historical and real-time GPS data (Tan et al.,
2008), rule-based micro-simulation (Lee et al., 2005), and analytical methods using timespace or flow-time diagrams (Skabardonis and Geroliminis, 2008; Li et al., 2011). Adaptive
priority provides priority to public transport vehicles while optimising certain performance
criteria. For example, a mixed-integer nonlinear program is formulated in a traffic responsive
signal control system to minimise the total person delay (Christofa et al., 2013). In another
real-time TSP model, a stochastic mixed-integer nonlinear program is developed to minimise
bus delays and deviations of TSP signal timing from a background timing (Zeng et al., 2014).
In addition, TSP can be provided either unconditionally to all requested buses or conditionally
to requested buses that are behind schedule.
1
Numerous studies have focused on the design and operation of TSP, while a few have
considered the optimum combination of TSP at a corridor and a network level. For instance,
traffic micro-simulation is used to optimise signal timings and TSP settings on an urban
corridor and a suburban network (Stevanovic et al., 2008). In another study, a simulationbased planning framework is proposed to optimise locations for TSP implementation in a grid
network (Shourijeh et al., 2013). However, it is unclear whether the combination of TSP on
an arterial or a network creates a multiplier effect on benefits to public transport, i.e. benefits
from providing TSP at multiple intersections are higher than the sum of benefits from
providing TSP at each of those individual intersections. If a multiplier effect exists, it suggests
considerable impacts of TSP on a network-wide scale. Since the research literature has
highlighted the impact of signal coordination on the performance of priority measures on
arterials (Skabardonis, 2000; Truong et al., 2015a, b), it is essential to examine combination
effects in typical offset settings as well as optimised offsets that maximise benefits for public
transport.
This paper investigates effects of combinations of TSP on a signalised arterial to establish if
a multiplier effect exists. The rest of this paper is organised as follows. Section 2 presents a
modelling test-bed for examining combinations effects and models for bus and traffic delay
estimation and signal offset optimisation. In section 3, delay estimation and offset
optimisation models are then evaluated using traffic micro-simulation. Next, section 4
presents results of the test-bed, followed by a discussion of the multiplier effect. Conclusions
and direction for future research are presented in section 5.
2. Methodology
2.1 Test-bed
2.1.1 Case study
A hypothetical arterial is used as a case study for exploring effects of TSP combinations on
bus delays and traffic delays. The 5km hypothetical arterial is designed with typical suburban
arterial settings in Melbourne, Australia. Five fixed-time signalised intersections are equally
spaced on the arterial. The layout of the arterial is presented in Figure 1. Turning flows from
the arterial to side streets are set to equal to the turning flows from side streets to maintain
similar traffic demands on each link. A summary of test-bed characteristics is presented in
Table 1. For simplicity, the eastbound direction is selected for the analysis since the
westbound direction can be considered in a similar way. A bus line is eastbound with 15 bus
stops. Bus dwell times are assumed to be normally distributed with a mean of 15s and a
standard deviation of 10s. Stop skipping is considered when a random bus dwell time is nonpositive. To capture random variations in bus entrance times to the arterial, it is assumed that
deviations between actual and scheduled entrance times follow a normal distribution with a
zero mean and a 20s standard deviation. The assumptions of bus dwell times and entrance
times are made in agreement with previous studies (TCRP, 2003; Estrada et al., 2009).
Figure 1: Layout of the hypothetical arterial
#1
#2
#3
#4
#5
2
Table 1: Test-bed Characteristics
Feature
Traffic volume on 3-lane main arterial
Signal offsets
Traffic volumes on 2-lane side streets
Traffic composition
Desired speed distributions
Turning proportions
Traffic signals
Bus headway
Bus dwell times
Bus entrance time variation
Options
Three levels: 1600, 2000, 2400vph
Two levels: free-flow offset and optimised offset
0.2 traffic volume on the arterial
95% car and 5% heavy goods vehicle (HGV)
Car and HGV: 55-65kph. Bus: 60kph
Arterial: through (95%), left (3%), and right (2%)
Side streets: through (75%), left (15%), and right (10%)
Cycle = 120s, min green = 6s, yellow = 3s, all red = 2s. Split:
0.7 for the arterial and 0.3 for side streets
5min
Mean = 15s, standard deviation = 10s
Mean = 0s, standard deviation = 20s
2.1.2 TSP strategies
A typical TSP system is used in the test-bed (TCRP, 2010), which incorporates the following
strategies: (i) green extension that extends an ending green phase to allow an approaching
bus to pass through the intersection and (ii) early green that shortens the waiting time for a
bus arriving during the red phase. A maximum priority time of 10s is provided for each
strategy. To maintain signal coordination, the green phases for side streets will be reduced
by the amount of the activated priority time. The detection system for each intersection
includes a check-out detector placed at the stop line and a check-in detector placed after the
near-side bus stop and 100m from the stop line. When a bus is detected at the check-in
detector, a predetermined travel time with a slack time is used to predict its arrival interval at
the stop line and activate either early green or green extension. If green extension is
provided, the green phase is extended until either the detection of the bus at the check-out
detector or the maximum green extension time is reached.
2.1.3 Combination design
All possible combinations of TSP at five intersections (25=32 combinations including the base
case) along the arterial are considered. Each combination is then examined with three levels
of traffic volumes (1600, 2000, 2400vph) and two offset settings (free-flow offset and
optimised offset that minimises bus delay). Hence, there are 192 scenarios in total.
2.2 Delay estimation
The efficiency of delay estimation is important to the test-bed that involves optimising offset
for a large number of scenarios. In this paper, the LWR shockwave theory (Lighthill and
Whitham, 1955; Richards, 1956; Stephanopoulos et al., 1979; Skabardonis and Geroliminis,
2005; Liu et al., 2009; Ramezani and Geroliminis, 2014) and kinematic equations are used to
estimate traffic and bus delays. Monte-Carlo simulation is then applied to account for the
randomness in traffic arrivals, bus arrivals and dwell times. The following assumptions are
made.





There is a triangular fundamental diagram with parameters: free-flow speed 𝑣𝑓 ,
saturation rate 𝑆, jam density 𝑘𝑗 , and congested shockwave speed 𝑤 (see Figure 2).
The platoon dispersion effect is ignored.
There is no queue spillover from downstream links or turning bays (Hence vehicles
can always be discharged during green times).
A bus travels with a constant acceleration rate and a constant deceleration rate.
Bus stops do not affect traffic.
3
2.2.1 Shockwave analysis
Figure 2 describes the development and dissipation of shockwaves on an approach of a
signalised intersection as a result of signal phase changes during a signal cycle. When the
red interval starts, a queue forming shockwave (𝑣1 ) is generated and moves upstream of the
intersection if traffic queue has been fully discharged in the previous cycle. The speed of 𝑣1
can be different over time. For example, in Figure 2b 𝑣1 has a two-segment piecewise linear
form as a result of two arrival traffic states (𝑞𝑎 , 𝑘𝑎 ) and (𝑞𝑏 , 𝑘𝑏 ). When the green interval
starts, a queue discharging shockwave (𝑣2 ) is generated and moves upstream as vehicles
start to discharge at saturation flow rate. Since 𝑣2 has a higher speed than 𝑣1 , two
shockwaves will meet at a specific time when the queue length is maximum. As soon as the
two shockwaves intersect, a departure shockwave (𝑣3 ) is formed and moves towards the
stop line. In the beginning of the next red interval, if the queue is not fully discharged, a
residual queue forming shockwave (𝑣4 ) is generated moving upstream of the intersection
(see Figure 2c). As soon as 𝑣4 and 𝑣3 intersect, a new queue forming shockwave is formed
and a similar process is repeated in the following cycle. These shockwave speeds are
calculated using the following equations:
−𝑞𝑎
𝑗 −𝑘𝑎
𝑣1𝑎 = 𝑘
=𝑘
𝑆−0
𝑓 −𝑘𝑗
𝑣2 = 𝑆⁄𝑣
−𝑞𝑎
,
−𝑞
𝑗
𝑎 ⁄𝑣𝑓
= −𝑤,
𝑣1𝑏 = 𝑘
𝑣4 = 𝑘
−𝑞𝑏
−𝑞
𝑗
𝑏 ⁄𝑣𝑓
0−𝑆
⁄𝑣𝑓
−𝑆
𝑗
(1)
= −𝑤, 𝑣3 = 𝑣𝑓
(2)
Figure 2: Fundamental diagram and shockwaves on an approach of a signalised intersection
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑓𝑙𝑜𝑤
𝑆
𝑞𝑎
𝑡𝑖𝑚𝑒
𝑣1𝑎
𝑣𝑓
𝑞𝑏
𝑣2
𝑤
𝑣1𝑎
𝑣1𝑏
𝑘𝑏
𝑣3
𝑣1𝑏
𝑘𝑗 𝑑𝑒𝑛𝑠𝑖𝑡𝑦
𝑘𝑎 𝑘𝑚
(a) fundamental diagram
(b) no residual queue
Distance
𝑣2𝑖
𝑣1𝑖
𝑣4𝑖
𝑡𝑖𝑚𝑒
𝑣3𝑖
Queueing
Dwelling
𝑑𝑙
𝑑𝑣1
𝑑𝑠
Queueing
𝑙𝑏 𝑡 , 𝑣𝑏 𝑡
Bus trajectory
(c) residual queue
4
If the signal setting and arrival traffic rates are known, these shockwave speeds can be
deterministically calculated using the LWR shockwave theory. A shockwave profile model for
arterials, which tracks trajectories of shockwaves at every time step, can be found in a
previous study (Wu and Liu, 2011). It is noted that arrival flows to the back of the queue at a
specific time can be derived from the inflows at the link entrance since vehicles are assumed
to travel at the free-flow speed.
In this paper, shockwave speeds at each intersection of the signalised arterial is explicitly
estimated cycle by cycle to account for over-saturated situations where shockwaves
generated in a cycle may still exist in the following cycle. For each time step, distances from
the stop line to the front of each shockwave at the next time step can be calculated using
estimated shockwave speeds at the current time step. Since the back of the queue follows
trajectories of the queue forming and departure shockwaves (see Figure 2), the queue length
in the next time step can also be updated.
Flows discharged during green time, including saturation rate if the queue is being
discharged or arrival flow rate if the queue has been fully discharged, can be used to
calculate inflow rates to the downstream link. It is noted that turning flows from other
directions also contribute to inflow rates to the downstream link.
2.2.2 Bus movements
Once the shockwave speeds and queue length are estimated, it is possible to simulate
movements of a bus approaching the intersection. In a virtual vehicle probe model for
estimating travel times, a virtual probe is simulated with one of three decisions at each time
step, i.e. acceleration, deceleration, and no change in speed, depending on signal status and
distances to the stop line and the last queued vehicles in front of the virtual probe (Liu and
Ma, 2009). However, simulating bus movements is more complex considering decelerating
and accelerating movements before and after bus stops, particularly with the presence of
traffic queue. Figure 2 suggests that a bus at a specific time is in traffic queue if it is inside
the delay (shaded) regions bounded by trajectories of the stop line, queue forming and
residual queue forming shockwaves, and queue discharging shockwaves. For each time
step, a bus can make one of the following movements: accelerate or continue to travel at the
desired speed, decelerate, and stop, determined by its distances to obstacles, signal status,
current speed (𝑣𝑏 𝑡 ) and dwell time status. Distances to obstacles include the distances to
the next bus stop where passengers are waiting (𝑑𝑠 ), the front of the queue forming
shockwave (𝑑𝑣1 ), the front of residual queue forming shockwave (𝑑𝑣4 ), the next stop line (𝑑𝑙 )
(see Figure 2c). One-dimension kinematic equations are used to update the location and
speed of the bus at the next time step.
2.2.3 TSP control
If TSP is provided for an intersection, for each time step, the algorithm presented in Figure 3
is used to implement TSP control.
2.2.4 Monte-Carlo simulation
Traffic delays are then calculated using the flow rate and density of each region divided by
traffic shockwaves (Dion et al., 2004). Bus delay is calculated as the actual travel time minus
the free-flow travel time and the total dwell times, obtaining from their simulated trajectories.
A Monte-Carlo simulation method is then proposed to estimate traffic and bus delays
accounting for the randomness in traffic arrivals and bus entrance times and dwell times.
Traffic arrivals are assumed to follow a Poisson distribution. For each run, traffic arrivals
rates, bus entrance times, and dwell times are sampled from given distributions.
5
Figure 3: TSP control flowchart
Start
If a bus
checks in
Y
If TSP is not
activated
N
If a bus
checks out
Y
Estimate arrival time
Select TSP strategies
N
Y
If green
extension is
activated
N
N
If TSP is
selected
Y
Update signal
timings
N
Y
If extension
time is not
reached
Y
Stop green extension
Update signal timings
N
End
2.3 Offset optimisation
To investigate the maximum benefits in reducing bus delay from TSP combinations, an offset
optimization model that minimises bus delay can be formulated as follows.
𝑚𝑖𝑛
𝑠. 𝑡.
̂𝑏
𝐷
− 𝑐⁄2 ≤ 𝑜𝑖 ≤ 𝑐⁄2 , ∀𝑖 ∈ [1, 𝑁]
(3)
̂ 𝑏 is mean bus delay obtained from Monte-Carlo simulation, 𝑁 is number of
where: 𝐷
intersections on the arterial, 𝑐 is common cycle length, and 𝑜𝑖 is signal offset for intersection i
on the arterial.
Given the complexity of the objective function, e.g. using Monte-Carlo simulation method, a
Genetic Algorithm (GA) is proposed to solve the problem. In addition, GA has been found to
be useful in optimising signal control on mixed traffic arterials (Duerr, 2000). It is noted that
as both traffic and bus delay can be estimated, an offset optimisation model considering for
both bus and traffic delays can be developed in a similar way.
3. Validation
Based on characteristics of the test-bed, parameters for the fundamental diagram are set to:
capacity = 1800 vph per lane, free-flow speed = 60kph, jam density=140vpk per lane. Bus
acceleration and deceleration rates are 1.2m/s2 and 1.2m/s2 respectively. These values are
consistent with values reported in the literature (Estrada et al., 2009; Skabardonis and
Geroliminis, 2005). Other parameters are selected as: simulation time = 1h, time step =1s,
and the number of Monte-Carlo simulation runs = 100.
The delay estimation model is coded in C++ and the offset optimisation problems are solved
by using the Genetics Algorithm (GA) toolbox in Matlab (MathWorks, 2014). The crossover
rate and mutation rate are set to 0.8 and 0.01 respectively. The population size and
generation size of the GA are set to 100 and 50 respectively. Examples of GA results and
bus trajectories in a TSP case are presented in Figure 4. A fast convergence trend of the GA
is evident. The computation time for optimising offsets of one scenario is about 6 min on a
personal computer with Intel Core i7-3770 CPU (3.4GHz).
The test-bed is coded in VISSIM (PTV, 2014) for evaluation. TSP control is modelled using
Vehicle Actuated Programming (VAP). It is tedious to evaluate all combination cases. Hence,
six combinations are selected for evaluation, including the base case and combinations with
one to five intersections with TSP. Each combination is evaluated with the three traffic
volume levels and the two offset settings. There are 36 evaluation scenarios (about 19% of
6
all scenarios). Measures of performance include bus delay, arterial traffic delay, and mean
side street traffic delays. A sequential approach is applied to calculate the minimum number
of runs for each scenario to achieve a 95% confidence level for all measures of performance
with percentage errors of 2% (Truong et al., 2015c, d). The root mean square error (RMSE)
and the mean absolute percentage error (MAPE) are used to compare results of VISSIM and
the proposed models.
Figure 4: Examples of GA results and simulated bus trajectories
a) Examples of GA results
b) Sample bus trajectory
A summary of validation results is presented in Table 2. Overall, results suggest there is a
good fit between the proposed delay estimation model and VISSIM, particularly in terms of
bus delays. Figure 5 shows delays obtained from the proposed model and VISSIM in more
detail. It is clear that bus delays in optimised offsets are significantly smaller than those in
free-flow offsets, suggesting the effectiveness of the proposed offset optimisation model.
Table 2: Summary of validation results
Measures of performance
RMSE (s)
MAPE (%)
Bus delay
5.06
1.43
Traffic delay on the arterial
6.53
10.96
Mean traffic delay on side streets
0.68
1.19
4. Results and discussion
4.1. Percentage change in delays
Figure 6 presents percentage change in delays of different combinations when compared to
base bases in the free-flow offset setting. It can be seen that as the number of intersections
with TSP increases, bus delays decrease whereas side street traffic delays increase. The
reductions in bus delays are significantly higher than the increases in side street traffic
delays. When traffic volumes increase, the increase in side street traffic delays is larger.
However, the impact of traffic volumes on the reduction in bus delays seems negligible. It is
also noted that changes in arterial traffic delays are mixed, i.e. disbenefits with low traffic
volumes and benefits with 2400vph. At an intersection, TSP can reduce both bus and traffic
delays on the main approach as green time is extended. However, changes in green time
affect coordination between intersections. The reason for the benefits with 2400vph may be
that in this case greater arterial traffic delays savings obtained from TSP in near saturated
conditions exceed the negative impact of TSP on traffic coordination in free-flow offsets.
7
300
250
250
200
200
Delay(s)
300
150
150
100
50
50
0
0
1600vph
2000vph
Proposed model
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
100
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Delay(s)
Figure 5: Results of the proposed model and VISSIM
2400vph
1600vph
VISSIM
Proposed model
300
250
250
200
200
Delay(s)
300
150
50
50
0
0
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
100
Proposed model
2400vph
1600vph
VISSIM
300
250
250
200
200
Delay(s)
300
50
50
0
0
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
100
Proposed model
2400vph
1600vph
VISSIM
e) Side street traffic delays in free-flow offsets
VISSIM
150
100
2000vph
2400vph
d) Arterial traffic delays in optimised offsets
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Delay(s)
c) Arterial traffic delays in free-flow offsets
1600vph
2000vph
Proposed model
150
VISSIM
150
100
2000vph
2400vph
b) Bus delays in optimised offsets
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Base
TSP1
TSP12
TSP123
TSP1234
TSP12345
Delay(s)
a) Bus delays in free-flow offsets
1600vph
2000vph
2000vph
Proposed model
2400vph
VISSIM
f) Side street traffic delays in optimised offsets
Note: TSPij indicates TSP is provided at intersections i, j.
8
Figure 6: Percentage change in delays in free-flow offsets
8%-10%
Percentage
change in
delays
8%-10%
Percentage
change in
delays
6%-8%
4%-6%
2%-4%
6%-8%
4%-6%
2%-4%
0%-2%
0%-2%
-2%-0%
-2%-0%
-4%--2%
10%
8%
6%
4%
2%
0%
-2%
-4%
-6%
-8%
-10%
-12%
-14%
-16%
-18%
-20%
-6%--4%
-8%--6%
-10%--8%
-12%--10%
-14%--12%
-16%--14%
-18%--16%
-20%--18%
2400
1
-6%--4%
-8%--6%
-10%--8%
-12%--10%
-14%--12%
-16%--14%
-18%--16%
-20%--18%
2400
1
2000
2
-4%--2%
10%
8%
6%
4%
2%
0%
-2%
-4%
-6%
-8%
-10%
-12%
-14%
-16%
-18%
-20%
2000
2
3
3
1600
4
1600
4
5
5
Volume
(vph)
Number of intersections with TSP
Number of intersections with TSP
a) Percentage changes in bus delays
Volume
(vph)
b) Percentage changes in arterial traffic delays
8%-10%
Percentage
change in
delays
6%-8%
4%-6%
2%-4%
0%-2%
-2%-0%
-4%--2%
10%
8%
6%
4%
2%
0%
-2%
-4%
-6%
-8%
-10%
-12%
-14%
-16%
-18%
-20%
-6%--4%
-8%--6%
-10%--8%
-12%--10%
-14%--12%
-16%--14%
-18%--16%
-20%--18%
2400
1
2000
2
3
1600
4
5
Number of intersections with TSP
Volume
(vph)
c) Mean percentage changes in side street traffic delays
Figure 7 presents percentage change in delays compared to base bases when offsets are
optimised to minimise bus delays. Similar to observation with free-flow offsets, results
indicate bus delays decrease and side street traffic delays increase with increasing numbers
of intersections with TSP. The reductions in bus delays are higher than the increases in side
street traffic delays, particularly in low traffic volumes. In addition, when traffic volumes
9
increase, the increase in side street traffic delays is larger. It can be seen that the reduction
in bus delays is not affected by traffic volumes. Since optimised offsets for each scenarios
tend to be different, changes in arterial traffic delays are mixed.
Figure 7: Percentage change in delays in optimised offsets
8%-10%
Percentage
change in
delays
8%-10%
Percentage
change in
delays
6%-8%
4%-6%
2%-4%
6%-8%
4%-6%
2%-4%
0%-2%
0%-2%
-2%-0%
-2%-0%
-4%--2%
10%
8%
6%
4%
2%
0%
-2%
-4%
-6%
-8%
-10%
-12%
-14%
-16%
-18%
-20%
-6%--4%
-8%--6%
-10%--8%
-12%--10%
-14%--12%
-16%--14%
-18%--16%
-20%--18%
2400
1
-6%--4%
-8%--6%
-10%--8%
-12%--10%
-14%--12%
-16%--14%
-18%--16%
-20%--18%
2400
1
2000
2
-4%--2%
10%
8%
6%
4%
2%
0%
-2%
-4%
-6%
-8%
-10%
-12%
-14%
-16%
-18%
-20%
2000
2
3
3
1600
4
1600
4
5
5
Volume
(vph)
Number of intersections with TSP
Number of intersections with TSP
a) Percentage changes in bus delays
Volume
(vph)
b) Percentage changes in arterial traffic delays
8%-10%
Percentage
change in
delays
6%-8%
4%-6%
2%-4%
0%-2%
-2%-0%
-4%--2%
10%
8%
6%
4%
2%
0%
-2%
-4%
-6%
-8%
-10%
-12%
-14%
-16%
-18%
-20%
-6%--4%
-8%--6%
-10%--8%
-12%--10%
-14%--12%
-16%--14%
-18%--16%
-20%--18%
2400
1
2000
2
3
1600
4
5
Number of intersections with TSP
Volume
(vph)
c) Mean percentage changes in side street traffic delays
10
4.2. The multiplier effect
The effects of TSP combinations and traffic volume on percentage changes in bus and mean
side street traffic delays is analysed by a stepwise multiple linear regression analysis. The
percentage change in bus delays (PCB) and percentage change in side street traffic delays
(PCT) are considered as dependent variables. Traffic volume in 1000vph (𝑉), the number of
intersections with TSP (𝑁𝑇𝑆𝑃 ), and its non-linear forms such as 𝑁𝑇𝑆𝑃 1.25, 𝑁𝑇𝑆𝑃 2 are
independent variables. It is noted that bus delay savings can be defined as the reduction in
bus delays or the negative of PCB. A summary of best-fit regression models is presented in
Table 3.
Table 3: Regression models for PCB and PCT
Regression
coefficients
Intercept
𝑁𝑇𝑆𝑃
Free-flow offset
Model 2
Model 3
Model 4
PCB
PCT
PCB
PCT
-0.18
-3.18**
-0.47
-0.44**
-0.33*
𝑁𝑇𝑆𝑃 1.25
𝑁𝑇𝑆𝑃 . 𝑉
Adjusted
Optimised offset
Model 1
-0.77**
0.70**
R2
0.95
0.63
0.32**
0.91
0.62
Note: all models are significant at p<0.01. ** = significant at p<0.01. * = significant at p<0.05
Results suggest that there are linear impacts of the interaction between traffic volume and
the number of intersections with TSP on the changes in side street traffic delays (Model 2
and 4). For example, side street traffic delays increase with increasing traffic volumes or
increasing number of intersections with TSP. Similarly, the relationship between the number
of intersections with TSP and bus delay savings is linear in free-flow offsets (Model 1). It is
also found that traffic volumes do not statistically affect bus delay savings.
Model 3 shows a non-linear relationship between the number of intersections with TSP and
bus delay savings in optimised offsets (adjusted R2 = 0.91). In other words, there is a multiplier
effect of TSP combinations on bus delay savings. The existence of the multiplier effect is
further illustrated in Figure 8. The dash lines represent a theoretical constant return to scale
effect of the number of intersections with TSP on bus delay savings, calculated based on
mean bus delay savings from combinations where TSP is provided at one intersection. It is
clear that the curves of actual bus delay savings are above the theoretical constant return to
scale curves, indicating that a multiplier effect is occurring.
7%
6%
Percentage bus
delay saving
Constant return to
scale effect
5%
4%
3%
2%
1%
8%
8%
7%
7%
Percentage bus delay saving
Percentage bus delay saving
8%
Percentage bus delay saving
Figure 8: The multiplier on bus delay savings when offsets are optimised
6%
5%
4%
3%
2%
1%
0%
a) 1600vph
5%
4%
3%
2%
1%
0%
1
2
3
4
5
No of intersections with TSP
6%
0%
1
2
3
4
5
No of intersections with TSP
b) 2000vph
1
2
3
4
5
No of intersections with TSP
c) 2400vph
11
5. Conclusion
This paper has investigated the effects of combinations of TSP measures on arterials to
establish if a multiplier effect exists. A hypothetical arterial with typical suburban arterial
settings in Melbourne, Australia was used as a case study. All possible spatial combinations
of TSP at five intersections of the arterial were considered with three levels of traffic demand
and two signal offset settings, i.e. free-flow offsets and optimised offsets that minimise bus
delays. Due to the large number of scenarios involving an offset optimisation problem, a
simplified delay estimation model using shockwave theory, kinematic equations, and MonteCarlo simulation was applied in this paper. The offset optimisation problem was solved by
GA. The effectiveness and computational efficiency of the delay estimation model and the
offset optimisation model was suggested by evaluation using traffic micro-simulation.
Results indicated that when signal offsets are optimised to minimise bus delays,
combinations of TSP measures create a multiplier effect on bus delay savings. In free-flow
offsets, the effect of TSP combinations on bus delay savings is linear. Traffic volumes do not
statistically affect bus delay savings. The effect of TSP combinations on arterial traffic delays
is mixed and negligible compared to the effects on bus and side street traffic delays. In
addition, linear effects of TSP combinations and traffic volumes on the increases in side
street traffic delays are evident. It is also found that bus delay savings are significantly higher
than the increase in side street delays, particularly in low traffic volumes. Overall, the
existence of the multiplier effect suggests considerable impacts of the implementation of TSP
measures on a network-wide scale.
It is worth noting that the multiplier effect is demonstrated in the typical configurations of the
hypothetical arterial. In addition, bus headway variation should be considered in the
investigation of combination effects. Future research should explore this effect using both
theoretical and empirical analyses.
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