A Novel VSL Control Strategy with Traffic State Prediction
Based Collision Probability Assessments
By
Jie Fang
Fuzhou University, Fuzhou, Fujian, China
and
Department of Civil and Environmental Engineering
University of Alberta, 3-019 NREF, Edmonton, Alberta, Canada T6G 2W2
Tel: 1-780-492 5114, Fax: 1-780-492- 0249
Email: [email protected]
Md. Hadiuzzaman
Graduate Research Assistant, Department of Civil and Environmental Engineering
University of Alberta, 6-106 NREF, Edmonton, Alberta, Canada T6G 2W2
Tel: 1-780-492 0658, Fax: 1-780-492 0249
Email: [email protected]
Md Ahsanul Karim
Graduate Research Assistant, Department of Civil and Environmental Engineering
University of Alberta, 6-106 NREF, Edmonton, Alberta, Canada T6G 2W2
Tel: 1-780-492 0658, Fax: 1-780-492 0249
Email: [email protected]
Ying Luo
Graduate Research Assistant, Department of Civil and Environmental Engineering
University of Alberta, 4-080 NREF, Edmonton, Alberta, Canada T6G 2W2
Tel: 1-780-9640130, Fax: 1-780-492 0249
Email: [email protected]
Tony Z. Qiu*
Assistant Professor, Department of Civil and Environmental Engineering
University of Alberta, 3-005 NREF, Edmonton, Alberta, Canada T6G 2W2
Tel: 1-780-492 1906, Fax: 1-780-492 0249
Email: [email protected]
Word count: 5986 words + 5 (4 figures + 1 table) * 250 words = 7236 words
*Corresponding author
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ABSTRACT
With the ever-increasing number of vehicles on roadways, traffic safety has become one
of the most serious challenges facing transportation engineers. To mitigate traffic safety
concerns, a variety of active traffic control measures, such as Variable Speed Limit
(VSL), have been intensively investigated and consequently deployed. VSL is usually
adopted to advise a lower speed limit more appropriate to a congested traffic condition,
and to take advantage of the homogenous traffic flow effect. However, in earlier studies,
due to the absence of traffic state prediction, the impact of the applied VSL control was
not quantitatively analyzed. In this study, a Model Predictive Control (MPC) framework
was adopted to predict and assess future traffic states. Taking into consideration the
impact of VSL control, a macroscopic traffic flow model was also adopted. The collision
probabilities of the predicted traffic states were assessed by a precursor-based collision
prediction model to determine the optimized control signal. By this design, the proposed
algorithm controller provides a robust method for determining the VSL control plan to
optimize safety performance over a traffic network. To evaluate the proposed control
algorithm, a field-data-based simulation study was conducted to reproduce a major ring
road in Edmonton, Alberta, Canada. The proposed algorithm was used to implement VSL
control on the studied 11-kilometer freeway stretch. The proposed algorithm control
scenario was then compared with the uncontrolled scenario. The evaluation proved that
the proposed VSL control algorithm can effectively reduce the collisions probability of a
congested traffic network with no significant compromises to mobility.
Keywords: Active Traffic Demand Management; Variable Speed Limit; Traffic Safety.
TRB 2014 Annual Meeting
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INTRODUCTION
Transportation engineers have been working for decades to resolve traffic-related
problems; however, with the explosively growing number of automobiles on roadways,
traffic congestion causes loss of productivity and mobility. Furthermore, as a result of
increased traffic incidents, the amount of property damage and loss is ever growing.
Recently, a variety of active traffic control measures, such as Variable Speed Limit
(VSL), ramp metering, manageable lanes, etc., have been investigated and deployed.
VSL control provides drivers with a more appropriate operating speed (lower than the
posted static speed limit) in response to dynamic road conditions. Normally, the posted
speed limit on highways suggests the standard operating speed for road users in ideal
conditions. However, during adverse traffic conditions, such as excessive demand or
reduced roadway capacity (construction), the posted speed limit may no longer be the
optimal operating speed [1]. Through field implementations and simulations, earlier
studies report that by enhancing the speed homogeneity effects, VSL improves traffic
flow in terms of safety [1, 2, 3], and potentially mobility [4, 5]. A statistical crash
probability model is usually used to assess the safety benefits of a VSL control. AbdelAty developed a crash probability model [6] to formulate incident likelihood by
examining traffic state measurements of the previous 15 minutes. This real-time crash
probability model was later adopted in [4] and [7] to evaluate the performance of a VSL
control. Hellinga and his colleagues designed a control algorithm [8] to implement VSL
using decision trees. Based on the analysis of a crash probability model, he concluded
that VSL reduces crash probability.
However, in most of the above mentioned literature [4, 8], the crash probability model
was adopted only as the Measure of Effectiveness (MOE) that evaluates system
performance after VSL implementation. Therefore, in these studies, the VSL control
algorithm neglected to consider the crash risk in future time periods (the previous
algorithms do not quantitatively evaluate the VSL impact to choose the control plan that
leads to minimized safety risks). To overcome this problem, this study proposes a VSL
control algorithm with traffic state predictions based on a safety assessment feature. The
designed control strategy aims at optimizing the network safety performance according to
prevailing and predicted traffic conditions. The VSL impact on traffic flow was taken
into consideration during prediction, then a real-time crash probability model was
adopted to determine the most appropriate control plan with the most desirable network
safety performance.
The remainder of this paper is organized into sections: section 1 is a brief literature
review of existing VSL control strategies and crash probability evaluation efforts; section
2 presents the proposed VSL control algorithm with the crash probability prediction
model; section 3 presents a field-data-based VISSIM simulation study to reproduce realworld traffic conditions and implement the proposed control algorithm. The VSL
controlled network performance is compared with the baseline condition (uncontrolled
case) to evaluate the efficiency of the proposed control algorithm. Lastly, section 4
presents conclusions and future work.
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LITERATURE REVIEW
In Europe, a field VSL control study was implemented as early as the 1990s. Van den
Hoogen and Smulders implemented VSL in the Netherlands [9]. In Finland, Rämä
investigated driver behaviors on a highway [3] under weather-controlled VSL. These
studies focused on implementing the VSL control as a measure to improve the speed
homogenization effect and to mitigate the speed differences among individual vehicles
for safety benefits. Later, field implementations continued in North America. In
Washington [11], 25 VSL signs were installed on both directions of I-90. The VSL
advised to reduce traveling speed through construction zones. In Missouri, a VSL system
was deployed along the I-270/I-255 corridor in St. Louis [10]. The report concludes that,
although no significant mobility benefit was found, the number of crashes was noticeably
reduced.
Some studies used a crash probability model to quantitatively examine the safety benefits
of VSL control. A major approach to establishing these crash probability models is to
take traffic state variables (speed, volume, etc.) prior to a collision as the model’s input
variables. Such models are referred to as precursor-based collision prediction models, as
the variables are observed prior to collisions. To formulate the incident probability, a loglinear crash probability model [12] was developed by Lee et al.. By analyzing loop
detector data, Lee et al. identified the coefficient of variation in flow speed and density as
the two most significant collision precursors. In another study, Lee et al. found that the
speed difference between upstream and downstream traffic also has a significant impact
on traffic safety [13]. In yet another paper Lee et al. suggested adopting a real-time crash
probability model as the evaluation tool to examine the proposed VSL control strategy’s
efficiency [14]. The designed control strategy lowered the speed limit, while the adopted
model found that the crash probability is higher than the pre-defined threshold. Similarly,
this study also identified as the critical indicators the traffic state variables 5-10 minutes
prior to the incident. Another study conducted by Lee et al. proposed a VSL control
strategy to change the speed limit based on the evaluation results from the adopted crash
probability model [15]. Based on the evaluation of a simulation study, the authors
reported a potential collision reduction of 5-17%.
A statistical crash probability model [6] was first developed by Abdel-Aty. The traffic
state variables, taken 30 min prior to an incident, were divided into six 5-min periods and
evaluated by their relationship with incident probability. The authors reported that traffic
state variables within 15 min before incident occurrence are the most statistically
significant variables related to the crash. This real-time crash probability model was later
adopted in [1] and [4] as the MOE that evaluates the performance of using VSL to
mitigate the risk of rear-end incidents. Hellinga designed an algorithm to implement VSL
control using decision trees [8]. Based on the evaluation of a crash probability model,
Hellinga concluded that VSL reduces crash probability.
As shown in the reviewed literature, much work has been done to involve a real-time
crash probability model in VSL control applications. However, in the existing literature,
the crash probability model was adopted only to assess crash likelihood considering
current traffic conditions. The reviewed control strategies do not quantitatively analyze
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neither the impact of the selected VSL control inputs on traffic dynamics nor the
correlated traffic safety performance. Moreover, most of these VSL control algorithms
determine the control input (VSL value to be advised) based on predefined thresholds (on
traffic state variables or measured crash probability). Given that the traffic flow dynamic
is a complicated stimulate and response system, it is arbitrary to assume that simply
lowering the speed limit is the optimal solution, regardless of its impact to traffic
dynamics. Therefore, there is a clear need for a prediction-based active traffic control
algorithm that considers both the current traffic conditions and the VSL-controlled future
traffic states. In this study, the authors propose to adopt the Model Predictive Control
(MPC) framework and conduct a prediction-based safety-oriented VSL control strategy
with a crash probability prediction model. There are three advantages to this design:
1) The designed control strategy processes a macroscopic traffic flow model to predict
future traffic states. Traffic state measurements are predicted considering both the
current state and the tentative VSL control inputs.
2) Several constraints are added to the control strategy to ensure the designed strategy is
feasible in reality and to avoid an abrupt change of the advised speed limit.
3) The designed control algorithm aims at optimizing the network safety performance
according to both the prevailing and predicted traffic state measurements, which
reflects the impact of the tentative VSL control inputs. A real-time crash probability
model is adopted in the control algorithm to evaluate the safety performance of each
feasible control plan. The optimal control plan that leads to the most desirable
network safety performance (lowest overall crash probability) is chosen.
The approach of prediction-based active traffic control has received attention from
researchers in recent years. However, most of the earlier studies focused on optimizing
the controlled network’s mobility performance, rather than the safety performance. Hegyi
et al. proposed a macroscopic traffic flow model based VSL control strategy aimed at
postponing potential traffic breakdowns [16]. The study implemented the VSL control in
the MPC framework, which has a rolling horizon system to include the predictionevaluation-optimization procedures in each time step. The control strategy aimed at
optimizing the traffic network’s mobility benefits by evaluating the Total Travel Time
(TTT) and Total Travel Distance (TTD). It was reported that the implemented control
restrained the traffic flow from exceeding the critical density and suppressed the
shockwave. The same framework was adopted in Long et al.’s work [17] to examine the
contributions of a VSL control in terms of network mobility performance improvements.
Hegyi et al. tested the VSL control with MPC framework through a simulation study
conducted in PARAMICS [18]. The study concluded that the MPC-based VSL control
approach was able to reduce the overall network TTT by over 30%.
In summary, earlier prediction-based active traffic control studies concentrated on
optimizing the network mobility performance. It is not yet clear if prediction-based active
traffic controls approach can be used to optimize the network safety performance. To this
end, in the proposed study, the authors adopted the MPC control framework and
conducted a safety-oriented prediction-based VSL control algorithm. The designed VSL
control algorithm determines the optimized control input according to corresponding
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network safety performance measured by a crash probability model. The safety
performance was evaluated, while taking into consider both the prevailing traffic
condition and the predicted traffic condition affected by the control inputs. This could
overcome the disadvantage that most previous safety-oriented studies did not
quantitatively analyze the significant impact of the VSL control on traffic flow dynamics.
Through a field-data-based simulation study, the efficiency of the proposed control
algorithm was evaluated by comparing the controlled network performance with the
uncontrolled baseline case.
METHODOLOGY
Proposed VSL Control Framework
Notations
k: Time index;
Np: Prediction Horizon;
x(k): Traffic state variable vector (flow, speed, occupancy) at time step k;
u(k): Candidate control plan at time step k;
x(k+1|u(k)): Model predicted traffic state variables at time step k+1, given the control
input (advised VSL value), u(k) is implemented;
P(x(k+1|u(k))): Model predicted incident probability at time step k+1, given the
control input, u(k) is implemented;
u*(k): Optimized control input for time step k.
In the proposed framework, the entire network runs on a rolling horizon system. The
current time step is denoted as k, and the consecutive time step is denoted as k+1, k+2…,
respectively.
Apply VSL control
k-10
...
k-2
k-1
k
k+1 k+2
...
k+Np
Traditional safety assessment algorithm
Proposed control algorithm
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Figure 1: Rolling Horizon System and Control Algorithm
As illustrated in Figure 1, previous studies [18], took the traffic variables prior to the
current time step k to assess traffic safety risks. Typically, the traffic state variables of
previous time steps (e.g. k-1, k-2…k-10) are brought into the safety assessment model to
measure safety risk, then used to determine whether a lower speed limit should be
advised. However, one main drawback of this approach is that the impact of the VSL
control (advised VSL value) is not quantitatively evaluated. Therefore, the proposed
control algorithm includes traffic state prediction to evaluate the impact of the applied
VSL control. At the current time step (k), for every candidate control input (VSL value),
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the future traffic state variables (time step k+1, k+2… k+Np) were predicted. Along with
the traffic state variables in the previous time steps, the predicted traffic state variables
were evaluated by the collision probability model (see Figure 2). The control input that
leads to an optimal safety performance will be adopted and applied in the traffic network.
The control procedures of the proposed algorithm are demonstrated in Figure 2:
Figure 2: Framework of Proposed Control Algorithm
As shown in Figure 2, the designed algorithm controller takes the traffic state variables
on the current time step x(k) as the input to determine the optimized control input u*(k).
The controller of the designed algorithm includes three major components: the traffic
state prediction model, the collision probability prediction model and the optimization
module. The traffic state prediction model takes into consideration both the current traffic
state x(k) and the candidate control plan u(k) when predicting the traffic state for the
consecutive time step, denoted as x(k+1|u(k)), x(k+2|u(k)),…x(k+Np|u(k). Along with the
traffic state measurement in previous time steps, the predicted traffic state variables were
assessed by the collision probability prediction model. Based on the safety performance
measured by the model, the optimization module selected the optimized control input
u*(k) with the optimal safety performance. After applying the selected control input u*(k)
to the traffic network, the updated traffic state variables were sent to the controller again
for optimizing the control signal for the next time step. The proposed control algorithm
quantitatively optimized the VSL control input and eliminated the uncertainty brought
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about by the impact of the applied control. In the next section, the details of the controller
design are described.
In the proposed control algorithm, a macroscopic traffic flow model was adopted to
predict traffic states. The macroscopic traffic flow model divides a freeway into discrete
links to analyze their spatial-temporal aggregated characteristics. Here m represents the
index of the links, while k represents the index of the continuous time steps. Lu et al.’s
model [19] was adopted in the proposed control algorithm. The model takes the current
traffic state variables x(k) and control plan vector u(k) as the inputs to predict future
traffic conditions. Lu et al.’s model is a simplified version of the METANET model: the
fundamental diagram assumption in the original model is replaced by advising the control
variable in the VSL (um(k)) directly. The model is composed of the following equations:
T
 qm −1 ( k ) − qm (k ) + qon − qoff 
ρm ( k + 1) =
ρm ( k ) +
Lmλ m 
[1]
vm ( k +=
1) vm ( k ) +
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T
τ
(u ( k ) − v ( k ))
m
m
T
µT  ρ m +1 ( k ) − ρ m ( k ) 
vm ( k ) ( vm −1 ( k ) − vm ( k ) ) −
+


Lm
τ Lm  ρ m ( k ) + κ 
m;
[2]
Where vm(k), qm(k) and ρm(k) are the current link speed, flow rate and density of link
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T is the length of the time step, Lm and λm are the length and number of lanes in link m;
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qon and qoff are the flow rate at the on-/off-ramp;
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um(k) is the advised VSL value at link m;
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τ,v and κ are the model parameters;
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Equation (1) is the flow conservation equation, which is similar to both Lu et al.’s
model and the original METANET. Equation (2) is the speed prediction model, which
incorporates the VSL control. The future link speed is predicted based on the advised
VSL value and the traffic states of the adjacent links. To modify the current link speed,
the link speed is predicted using three different terms: 1) the relaxation term; 2) the
convection term; and 3) the anticipation term. The relaxation term reflects the impact of
the applied VSL control to the link speed. The convection term expresses the speed
convection effect: the downstream link will take the link speed from the upstream link
with delays. The anticipation term reflects the phenomenon that the link speed is affected
by drivers’ anticipation of travel speed according to the downstream traffic density.
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Collision Probability Prediction Model
The predicted traffic state variables, along with the previous traffic state variables were
evaluated by the safety assessment model. A precursor-based collision prediction model,
following the methodology presented in the author’s earlier work [5] is adopted. The
similar case-control logistic regression technique was adopted to model traffic incidents.
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In the model, the case referred to a collision, while the control referred to a no-collision
event. The dependent variables of the model were designed as a binary variable (collision
versus no collision). The traffic characteristics (speed, occupancy and flow) prior to a
collision event, and a corresponding no-collision event, were considered as the
explanatory variables of the model.
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The traffic state variables 30 min prior to the incident were selected and divided into six
5-min time slices. These traffic state variables were indexed as time slice 1-6. Index 1 is
the 5-min slice right before collision occurrence. Two years of collision data, which
includes 46 collisions at the experimental site, were used to conduct the model. After
calibration, the probability of x as a collision was computed using the following equation:
exp (Constant −b1SV2 +b2 LogAO1 +b3 LogSS2 )
P( x) =
[3]
1 + exp (Constant −b1SV2 +b2 LogAO1 +b3 LogSS2 )
Where SV2 is the standard deviation of volume in the last 5-10 min, AO1 is the average
occupancy in the last 0-5 min prior, and SS2 is the standard deviation of speed 5-10 min
prior to the incident. The calibrated value of the constant, b1, b2 and b3 are -1.207, 3.149,
4.028 and -3.694, respectfully. For more detailed descriptions of the model, please refer
to the original paper [5].
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VSL Control Optimization
As shown in Figure 2, the optimization module in the proposed algorithm controller uses
the evaluation results from the collision probability prediction model to determine the
optimized VSL control input. The optimization aims at minimizing the overall safety risk
in the examined prediction horizon Np (10 min in this study). The optimization process is
a problem of minimizing the objective function J:
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J ( x) =
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As shown in Equation (4), the objective function measures the summation of incident
probability over all the m analyzed links, as well as the entire prediction horizon (from
time step k+1 to Np-1). The collision probabilities were evaluated at every link and at all
time steps within the prediction horizon (Pm, j (x)) and separately for each feasible control
input. The average overall collision probability was then used to determine the optimal
VSL control input.
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N p −1 M
∑
∑P
j=1 i=1
m, j
( x)
[4]
In consideration of safety and limitations of field operations, several constraints must be
applied to the optimization problem:
[5]
um ( k ) ∈ ( 30, 40...80km / h )
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um ( k ) − um −1 ( k ) ≤ 20km / h
[6]
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um ( k ) − um ( k − 1) ≤ 10km / h
[7]
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Among the listed constraints, Equation (5) narrows the selections of the candidate VSL
values to be between 30-80 kilometers/hour (km/h). The upper boundary was set to 80
km/h to match the static speed limit of the studied area. The lower boundary was set to 30
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km/h, because drivers rarely follow a speed limit less than 30 km/h. Furthermore, to
improve the clarity of a VSL control message, the advised speed limits were only
selected from multiples of 10 km/h. Constraint 2 in Equation (6) was established to
prevent an abrupt speed limit change between two successive links. The difference of
speed limits between two adjacent links was limited at less than 20 km/h. Constraint 3 in
Equation (7) was established to prevent an abrupt speed limit change between two
consecutive time steps at the same link. The difference of speed limits between two
successive time steps was limited to less than 10 km/h.
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EXPERIMENTAL DESIGN
Lastly, to optimize the control plan, several optimization techniques could be considered.
For applying the designed control algorithm over a large network with multiple VSL
locations, a standard non-linear optimization method could be adopted, such as genetic
algorithm, sequential quadratic programming, and so forth. However, in this study, there
were only four VSLs deployed. Furthermore, the selection of the candidate VSL control
signal was limited by the applied constraints. Thus, it is unnecessary to adopt a
sophisticated optimization method in the controller. Alternatively, the control algorithm
simply traverses all the candidate control inputs to determine the optimal control input
and the time consumed for optimization is still acceptable for online application (less
than 1 min).
To evaluate the effectiveness of the proposed control algorithm, a field-data-based
simulation study was conducted. For implementing the proposed control algorithm, an
11-kilometre (km) freeway stretch was selected from the Whitemud Drive, a major,
congestion-prone highway that serves as the inner ring road of Edmonton, Alberta,
Canada (Figure 3).
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Figure 3: Site of Application Study: Whitemud Drive.
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The westbound direction of this freeway stretch, which consists of three lanes for most of
the segments, was reproduced in microscopic traffic simulation software, VISSIM. The
AADT (Annual Average Daily Traffic) of the selected highway is higher than 40,000
vehicles, which causes the road segment to suffer from daily recurrent traffic congestion
during peak hours. The operating speed could be lower than 50 km/h for more than 70%
of the workday peak hours. On this stretch, the traffic is monitored by over 30 loop
detectors, which report the traffic state measurements at 60-second intervals. A complete
morning peak hour demand profile (from 6:00-9:00 AM) was input into VISSIM to
reproduce the real-world traffic demand. In VISSIM, virtual loop detectors were placed at
the middle of each link, as well as where the actual loop detectors are located on
Whitemud Drive. To accurately reproduce the congested real-world traffic condition and
driver behaviors, the simulation parameters, such as driving behavior parameters and link
characteristics, were adjusted so that the data collected by the virtual loop detectors
closely matched the actual loop detector data.
After careful calibration, the simulation site was considered the baseline test bed; on the
baseline test bed, the proposed VSL control algorithm was implemented to evaluate its
impact on traffic flow. Based on the analysis and results of the loop detector data, two
bottlenecks were identified in the studied area, and marked in Figure 3. In this study, the
VSL with the proposed control algorithm was implemented at four locations: before and
after each of the two recognized bottlenecks. The VISSIM model was coded through the
COM interface to facilitate the proposed active VSL control algorithm.
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RESULTS ANALYSIS
To evaluate the proposed control algorithm, the traffic network performance without VSL
control was considered the baseline condition. The VSL controlled traffic network
performance was then compared with the baseline condition, in terms of both safety and
mobility. To quantitatively evaluate the performance of the proposed control algorithm,
three MOEs were selected: Total Travel Time (TTT), Total Travel Distance (TTD) and
Collision Probability (CP). The first half hour of the study period was considered the
warm-up period of the simulation; therefore, it was excluded from the comparisons.
The TTT measures the total travel time of all vehicles on the studied network during the
experiment, which was formulated by Equation (8):
TTS =T ∗ Lm ∗ λm ∑ ρ m ( k )
[8]
m
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Where Lm and 𝜆𝑚 are the length and lane number of link m;
T is the length of the time step;
𝜌𝑚 (𝑘) and 𝑞𝑚 (𝑘) are the link density and flow rate in 𝑥 ∗ (𝑘)|𝑢(𝑘).
Equation (8) measures the TTT over all the m links throughout the entire study period. A
smaller TTT indicates that the vehicles were able to go through the studied network in
less time. The result was aggregated at 1 min intervals. The TTD measures the total travel
distance of all the vehicles within the network, formulated as Equation (9) below:
TTD =T ∗ Lm ∗ λm ∑ qm ( k )
[9]
m
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Similar to TTT, TTD examines the effectiveness of VSL on the network-wide traffic flow.
TTD measures the traffic flow efficiency based on the discharge flow rate. A larger TTD
indicates better network mobility performance with more efficient traffic flow.
While the first two MOEs were selected to measure network-wide mobility performance,
CP was selected to measure the network-wide safety performance. Using the above
mentioned model (Equation (3)), CP can be measured for each link at each time step. The
average overall CP was recorded for comparison.
To demonstrate the overall VSL system performance, global MOE comparisons for the
study period are summarized in Table 1:
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Table 1: Comparisons of Overall Network Performance
Bottleneck
Crash
Probability*
(%)
Overall
Crash
Probability
(%)
TTT
(vehicle*hr)
TTD
(km)
Uncontrolled
36.2
17.8
3281.4
187814.3
Proposed VSL Control
23.4
14.2
3089.0
189598.4
Relative Change
Compared to
-35.4%
-19.8%
-5.9%
Uncontrolled Case
*Crash Probability at two identified bottlenecks were measured
+0.9%
As demonstrated in Table 1, the proposed VSL control algorithm has significantly
lowered CP. For the two identified bottleneck locations where the network has the
highest safety risks, CP was significantly reduced from 36-23%, which is a 35% relative
reduction. This was achieved by quantitatively analyzing the impact of the VSL control
on traffic flow dynamics. UAnother interesting fact is that under the proposed control,
improving network safety performance does not lead to compromises in mobility
performance. The comparisons of TTT show that the proposed control algorithm
decreased TTT by approximately 6%. According to Equation (8), the control algorithm
managed to restrain the traffic flow density as an effect of lowering the CP. This also
contributes to mobility improvements, as the experienced delay was reduced (indicated
by the reduced TTT). There was a slight increase observed in the TTD calculation (0.9%).
The reason for this is that in the adopted CP model, the increased flow rate does not
necessarily go against better safety performance. Thus, while optimizing the traffic
network, the flow throughput is not tightly restricted by the control algorithm unless
when preventing the over-critical density. Therefore, when the flow density and demand
decreased after the peak hour, a higher discharge volume was encouraged by the
algorithm to enable a more efficient traffic flow, which is beneficial to both safety and
mobility. The detailed trend of comparison results is illustrated in Figure 4 below:
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Figure 4 (a)
Figure 4 (b)
Figure 4: Comparison Results for a) Total Travel Time; and b) Network Overall
Collision Probability
Figure 4a demonstrates the measured amount of TTT for both scenarios, aggregated at 1min levels. Figure 4b demonstrates the evaluation result of collision probability for both
scenarios. In Figure 4a, the blue line shows the changes in network traffic conditions. It
can be observed that in the uncontrolled scenario, the traffic became increasingly
congested after 7:30 AM (the measured TTT increase). The measured TTT reached its
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peak at approximately 8:30 AM, and then started to decline as the demand decreased. In
the scenario with the proposed VSL control, the traffic flow characteristic pattern (red
line) was significantly changed. In the controlled scenario, since the traffic was not
congested, the proposed control algorithm was not activated before 7:00 AM. Thus, the
two measured TTT profiles are on top of each other. At approximately 7:20 AM,
benefitting from the designed traffic state prediction feature, the proposed control
algorithm was able to anticipate the forthcoming congestions and thereby, activate the
control.
To sustain a more stable traffic flow and to prevent any abrupt flow speed changes
(safety risks) due to the traffic breakdown, the speed limits were lowered at the VSL
locations placed ahead of the identified bottlenecks. The proposed control algorithm
engaged this control action to take advantage of the speed homogeneity effect: by
lowering the speed limit, the differences of the travel speed between individual vehicles
were mitigated to enhance network safety performance. As a consequence of the lowered
travel speed, it is observed in Figure 4b that the increase of collision probability between
7:30-8:00 AM in the controlled scenario (red line) is smoother than the uncontrolled
condition (blue line). As a compromise, in Figure 4a it is observed that the TTT in the red
line went higher than the uncontrolled scenario after 7:30 AM. Furthermore, in the
controlled scenario, the network reaches its capacity earlier than the uncontrolled
scenario. This causes both the measured TTT and the collision probability to appear
higher in the VSL controlled scenario during its peak hour (around 8:00 AM).
However, benefitting from the speed homogeneity effects enhanced in the VSL control
scenario, the peak demand was also discharged earlier than the uncontrolled scenario.
Figure 4a and 4b both show that, in the VSL control scenario, the traffic flow recovered
from the congestion earlier than the uncontrolled scenario, at just after 8:30 AM. The
reasoning behind this is that, in the adopted safety assessment model, the increased traffic
volume does not go against better safety performance. Therefore, the control algorithm
encourages more discharge flow by gradually raising the speed limit once the demand on
the network decreases. Secondly, the homogeneous traffic flow enabled by the applied
VSL control increases the throughput of the network (proved by the increased TTD
observed in Table 1) to allow the peak demand to discharge faster.
In summary, the analysis of the evaluation results prove that the application of the
proposed VSL control algorithm can not only effectively reduce the collision probability
on a congested traffic network, but also improve traffic safety performance without
significant compromises in mobility.
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CONCLUSIONS AND FUTURE WORK
In this paper, the authors proposed an algorithm that optimizes the VSL control signal
through quantitatively predicting and assessing the network safety performance. The
proposed control algorithm design processed a traffic state prediction feature and a
precursor-based collision prediction model. Before implementation, the candidate VSL
control input was analyzed against the current traffic condition to predict future traffic
states. Based on the predicted control results, the associated safety performance (collision
probability) was measured. The VSL control plan that leads to the least network-wide
collision probability was selected for implementation. Different from earlier studies, the
proposed control algorithm: 1) introduces traffic state prediction into safety-oriented
active traffic control applications. 2) Avoid the uncertainty brought about by the impact
of the implemented control.
To evaluate the efficiency of the proposed control algorithm, a field-data-based
simulation study was conducted. The proposed algorithm was implemented to perform
VSL control over an 11-km congested highway stretch. The control algorithm
successfully predicted the forthcoming traffic breakdown and lowered the speed limit to
restrain CP. The speed limit was gradually raised during the congestion recovery phase to
encourage a more efficient and safer traffic flow. The proposed VSL control algorithm
effectively reduces CP on a congested traffic network, while no significant mobility
compromises were observed.
In terms of traffic safety, the proposed algorithm helps to reduce the number of
congestion-related collisions by predicting traffic states and providing a dynamic and safe
VSL control. If the proposed algorithm and control is adopted by traffic-safety authorities,
then CP may decrease, rendering a safer road for all users. In future studies, the authors
plan to evaluate the proposed VSL control algorithm in real-world implementations. The
Whitemud drive corridor evaluated in this paper has been equipped with appropriate VSL
signs and the dynamic control system. The authors look forward to reporting the field
experiment results.
ACKNOWLEDGEMENT
The authors would like to thank Ken Karunaratne, Iris Ye, Wai Cheung, Adrian Loh,
Daniel Kabaroff, Craig Walbaum, Stevanus Tjandra, Yongsheng Chen, Gerry Shimko
and other staffs from City of Edmonton for their help and support to this study. This
research work was supported by the Natural Sciences and Engineering Research Council
(NSERC) of Canada, Alberta Traffic Safety Fund and City of Edmonton. The contents of
this paper reflect the views of the authors who are responsible for the facts and the
accuracy of the data presented herein. The contents do not necessarily reflect the official
views or policies of the City of Edmonton. This paper does not constitute a standard,
specification, or regulation.
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Paper revised from original submittal.
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