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Citation: Yao, J.; Qian, Y.; Feng, Z.;
Zhang, J.; Zhang, H.; Chen, T.; Meng,
S. Hidden Markov Model-Based
Dynamic Hard Shoulders Running
Strategy in Hybrid Network
Environments. Appl. Sci. 2024,14,
3145. https://doi.org/10.3390/
app14083145
Academic Editor: Juan P. Torreglosa
Received: 23 February 2024
Revised: 31 March 2024
Accepted: 2 April 2024
Published: 9 April 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
applied
sciences
Article
Hidden Markov Model-Based Dynamic Hard Shoulders
Running Strategy in Hybrid Network Environments
Jinqiang Yao 1, Yu Qian 2, Zhanyu Feng 2, Jian Zhang 2, * , Hongbin Zhang 2, Tianyi Chen 1and Shaoyin Meng 1
1ITS Branch, ZheJiang Communications Investment Group Co., Ltd., Hangzhou 310002, China;
sensorchina@aliyun.com (J.Y.); z.spike@hotmail.com (T.C.); 13173989967@163.com (S.M.)
2Jiangsu Key Laboratory of Urban ITS, Department of Intelligent Transportation and Spatial Informatics,
School of Transportation, Southeast University, Nanjing 211189, China; yu_chien@foxmail.com (Y.Q.);
zhanyufeng@seu.edu.cn (Z.F.); zhb1918@163.com (H.Z.)
*Correspondence: jianzhang@seu.edu.cn; Tel.: +86-18061855688
Abstract: With the development of vehicle-road network technologies, the future traffic flow will
appear in the form of hybrid network traffic flow for a long time. Due to the change in traffic
characteristics, the current hard shoulder running strategy based on traditional traffic characteristics
cannot effectively serve the hybrid network traffic flow scenario, and will even lead to the further
deterioration of traffic congestion. In order to propose a hard shoulder running strategy suitable for
a hybrid network environment, a traffic breakdown prediction method based on a hidden Markov
model was established. Secondly, the characteristics of traffic breakdown in a hybrid network
environment were analyzed. Finally, based on the traffic breakdown characteristics in a hybrid
network environment, a dynamic hard shoulder running method based on the hidden Markov model
was proposed. The effectiveness of HMMD-HSR was verified by simulation and comparison with
HMM-HSR, LMD-HSR, and N-HSR. The simulation results show that the HMMD-HSR proposed in
this paper can improve operation efficiency and reduce travel time in a congested expressway.
Keywords: hybrid network environments; breakdown probability; discrete time hidden Markov
chain; active traffic management; hard shoulder running
1. Introduction
1.1. Background
Due to the rapid development of vehicular networking technology, regular human-
driven traffic flow is gradually evolving into a mixed traffic flow where human-driven
vehicles (HVs) and connected-automated vehicles (CAVs) coexist. Previous studies have re-
ported that the deployment of CAVs is a long-term process, with heterogeneous traffic flow
as a required stage [
1
,
2
]. The fast-growing trend of intelligent transportation systems (ITS)
including active traffic management (ATM) [
3
] brings new opportunities and challenges to
traffic management. ATM generally takes freeways and expressways as research objects,
employing various management and control strategies to tackle regular and occasional
congestion issues based on the present and expected traffic circumstances [
4
]. As one
of the ATM systems, hard shoulder running (HSR) [
5
] has received considerable critical
attention since it utilizes existing physical infrastructure and significantly reduces the cost
of reconstruction [6].
Initially, the hard shoulder was primarily intended for safety [
7
]. It provides a safe
temporary parking spot for malfunctioning vehicles on a freeway with high volumes and
speeds, ensuring driving safety while not interfering with normal traffic. According to
recent research, temporarily opening hard shoulders as additional lanes can successfully
ease congestion [
8
–
12
]. Existing studies of HSR strategies usually focus on traditional
road scenarios [
13
–
17
]. For example, Ma et al. [
12
] proposed dynamic hard shoulder
running (D-HSR) and applied different D-HSR strategies to study accident management
Appl. Sci. 2024,14, 3145. https://doi.org/10.3390/app14083145 https://www.mdpi.com/journal/applsci
Appl. Sci. 2024,14, 3145 2 of 18
using micro-simulation. He suggested that only the shoulder 0.5 miles upstream and
downstream of the accident location needed to be opened, and that the D-HSR strategy was
more appropriate for property damage only (PDO) events. A hybrid hard shoulder running
operation system (H-HSROS) proposed by Hussein et al. [
18
] enables transit departments to
operate HSR safely and efficiently. Li et al. [
6
] employed the cellular transmission model to
conduct linear programming modeling of the hard shoulder running, ramp metering, and
speed coordination control measures and took the minimum total delay as the optimization
goal. The researcher modified the optimization goal to include a safety factor based on
the frequency of shoulder changes, allowing the objective function to represent trade-offs
between efficiency and safety. Arora et al. [
19
] applied model predictive control (MPC) to
introduce a new dynamic control strategy based on variable speed limit (VSL) and hard
shoulder running (HSR), and discovered that the combined effect of various intelligent
transportation system (ITS) strategies was far greater than the effect of a single strategy
through experiments. Zhou et al. [
20
] proposed a VSL and HSR joint control strategy based
on reinforcement Q-Learning, which established a connection between traffic flow data
and the ATM control strategy during the self-learning process. Despite several studies on
HSR, with the rapid rise of CAV market penetration, few researchers have investigated
HSR in a hybrid network environment. Most of the earlier research focused on other ATM
strategies in a hybrid network environment [21–27].
Numerous studies have demonstrated that the addition of CAVs will modify the
headway and speed of traffic flow, resulting in changes in road capacity [
28
–
30
]. Therefore,
current HSR research in traditional traffic scenarios cannot meet these requirements. To
develop a hard shoulder opening approach that is more suitable for a hybrid network
environment, this paper analyzed the features of traffic speed breakdown in the hybrid
network environment and proposed a dynamic hard shoulder opening strategy based on
a hidden Markov model (HMM). The remaining sections of this article are organized as
follows. Section 2describes the freeway scenario and hybrid traffic flow while Section 3
introduces a traffic breakdown prediction model and a hard shoulder dynamic opening
strategy. Section 4analyzes the traffic breakdown characteristics of the hybrid network
scenario and verifies the effectiveness of dynamic hard shoulder running based on HMM
(HMMD-HSR) by comparing it to hard shoulder running based on HMM (HMM-HSR),
dynamic hard shoulder running based on logistic model (LMD-HSR), and no hard shoulder
running (N-HSR). Finally, Section 5summarizes the research results. The main contribution
of this paper is as follows:
(1)
Modeling a mixed traffic flow expressway scenario and proposing a traffic breakdown
prediction method based on a hidden Markov model;
(2)
Analyzing the characteristics of traffic breakdown in a hybrid network environment
by comparing them with the logistic model-based prediction method;
(3)
Proposing a dynamic hard shoulder running method (HMMD-HSR) based on the
traffic breakdown characteristics and verifying its effectiveness through a combined
simulation of SUMO (1.9.2) and MATLAB (R2019b).
1.2. Literature Review
The existing research on the HSR strategy have focused on identifying the key indica-
tors that determine the opening and closing of the hard shoulder. The following categories
of indicators are commonly considered:
(1)
Traffic flow: Urban highway congestion is primarily caused by the traffic flow exceed-
ing road capacity during peak hours. Therefore, many scholars consider traffic flow to
be the key index for implementing the HSR strategy, which temporarily expands the
road capacity by opening the hard shoulder. Carlson et al. [
31
] found that opening the
hard shoulder when traffic exceeded a certain threshold helped alleviate congestion
caused by heavy traffic flow. Cohen [
32
] also explored the effect of the dynamic open-
ing of the hard shoulder on road bottlenecks, using traffic flow as a starting point. The
hard shoulder increases the traffic capacity of bottleneck sections.
Appl. Sci. 2024,14, 3145 3 of 18
(2)
Safety: Extensive studies have been conducted on the safety impact of opening the
hard shoulder [
5
,
33
–
36
], and the primary purpose of the hard shoulder is to serve as an
emergency lane for vehicles that have broken down. If the goal is to maximize highway
capacity, the hard shoulder will be in use throughout the simulation. However, it is
important to consider the needs of accidents and not overuse the hard shoulder. In
that case, Li et al. [
6
] introduced a safety weight to incorporate safety factors into the
design of the hard shoulder open strategy. Other researchers believe that HSR can be
used as a supplementary measure to VSL. The hard shoulder is only opened when
VSL is unable to handle excessive traffic [
19
,
20
] in order to balance the negative impact
on safety indicators.
(3)
Speed: Some researchers have explored the possibility of the open threshold of the hard
shoulder from the angle of speed change characteristics. Ma et al. [
37
] introduced the
concept of traffic breakdown as a threshold for hard shoulder opening. Chen et al. [
38
]
argued that breakdown occurs when traffic flow switches from free to congested, which
is frequently accompanied by continuous oscillation, resulting in large-scale congestion.
Consequently, it becomes necessary to identify traffic breakdowns and manage them
in advance. The definition of traffic breakdown has not been uniformly quantified.
Many researchers have different definitions of breakdown based on the changing
characteristics of road sections from free to congested, establishing a speed drop
threshold or a density rise threshold [
39
,
40
]. Ma et al. [
37
] defined the critical vehicle
speed and provided a method for calculating the drop threshold. However, most traffic
breakdown studies have only focused on traditional human-driving scenarios, and it
appears that few studies have examined mixed traffic flow scenarios.
As different users place different emphasis on safety indicators and traffic, there are
many possible weighting relationships between safety indicators and traffic, which will
also have a great impact on the hard shoulder opening policy. Considering that the speed
characteristics of the road section can reflect the change in traffic flow and the possibility
of accidents, this paper mainly considered the speed factor when designing the dynamic
HSR strategy.
2. Hybrid Network Expressway Scene Modeling
2.1. Dynamic Expressway Hard Shoulders Opening
The expressway hard shoulder refers to the pavement area with a certain strength
adjacent to the carriageway. Various countries place differing emphasis on the shoulder-
setting. In typical countries such as the United Kingdom and the Netherlands, both the
right and left hard shoulders can be utilized for HSR. According to the Federal Highway
Administration (FHWA), expressway use is increasing at a rate of roughly 2% per year, and
this trend is expected to continue. The survey also highlighted that traffic congestion has
not only increased, but has also become more unstable over the past 20 years [
41
]. Relevant
research has shown that in congested road sections during peak hours, temporarily allowing
traffic to run on hard shoulders and implementing coordinated speed control can increase
the traffic capacity by 15% to 30% without the need for road expansion [
42
–
44
], thereby
alleviating regular traffic congestion problems.
According to the relevant standards, the hard shoulder will only be opened when it
is safe and with no obstructions. Drivers must obey the signs and speed limits to ensure
their own safety as well as that of other road users, and the hard shoulder is applied as an
extra lane only when it is declared open. If there is no effective signal on the hard shoulder,
drivers should not use it as it is illegal and unsafe, and whether an accident occurs on
the original road or the open hard shoulder, all hard shoulders should be closed to avoid
affecting emergency vehicles. Due to the increasing popularity of CAVs, the composition of
expressway traffic flow is expected to change in the future [
45
]. As shown in Figure 1, while
considering setting up a hard shoulder opening strategy, it is also vital to fully consider the
characteristics of connected vehicles and non-connected vehicles.
Appl. Sci. 2024,14, 3145 4 of 18
Appl. Sci. 2024, 14, x FOR PEER REVIEW 4 of 19
of expressway traffic flow is expected to change in the future [45]. As shown in Figure 1,
while considering seing up a hard shoulder opening strategy, it is also vital to fully con-
sider the characteristics of connected vehicles and non-connected vehicles.
Figure 1. An expressway with hard shoulder opening applies.
2.2. Hybrid Network Traffic Flow Modeling
HVs are often not very capable of obtaining road instructions. This has been reflected
in many studies on the acquisition rate of expressway road instruction [41,46]. While con-
nected autonomous vehicles are frequently equipped with on-board units (OBUs) that can
be integrated into any car or used as a vehicle simulator in the absence of actual traffic,
allowing real-time information exchange between the vehicle and the infrastructure [47]
and ensuring full access to road indication. Therefore, in the subsequent work, we as-
sumed that CAVs can obtain all road information indicated by variable message signs
(VMSs). Considering that hard shoulder opening messages are often displayed on VMSs,
which are similar to expressway routing instructions, the information acquisition rate of
human-driving vehicles on expressway hard shoulders conforms to the Logit utility
model.
𝑃𝑐
(
𝑤
,
𝑤
)
=
(
)
(
)
, (1
)
𝑃𝑐 is the probability that HV accepts VMS information. This is affected by two fac-
tors: 𝑤1 is the driver’s driving experience, and 𝑤2 is the driver’s personality. 𝑎, 𝑏, and 𝑐 are
the fiing parameters, respectively.
In a mixed traffic flow randomly composed of CAVs and HVs, we defined 𝜌 (0≤
𝜌 ≤ 1) as the penetration rate of CAVs. When the front vehicle of the CAV has a vehicle-
to-vehicle communication function, these CAVs will adopt collaborative adaptive cruise
control (CACC) mode, known as CACC vehicles [48–50]; otherwise, they will follow with
adaptive cruise control (ACC), known as ACC vehicles, as shown in Figure 2 [51,52]. Cur-
rently, the most common forms of car-following are:
Figure 2. Changes in the CAV follower model.
Figure 1. An expressway with hard shoulder opening applies.
2.2. Hybrid Network Traffic Flow Modeling
HVs are often not very capable of obtaining road instructions. This has been reflected
in many studies on the acquisition rate of expressway road instruction [
41
,
46
]. While
connected autonomous vehicles are frequently equipped with on-board units (OBUs) that
can be integrated into any car or used as a vehicle simulator in the absence of actual traffic,
allowing real-time information exchange between the vehicle and the infrastructure [
47
]
and ensuring full access to road indication. Therefore, in the subsequent work, we assumed
that CAVs can obtain all road information indicated by variable message signs (VMSs).
Considering that hard shoulder opening messages are often displayed on VMSs, which
are similar to expressway routing instructions, the information acquisition rate of human-
driving vehicles on expressway hard shoulders conforms to the Logit utility model.
Pc(w1,w2)=exp(a+bw1+cw2)
1+ex p(a+bw1+cw2), (1)
Pc
is the probability that HV accepts VMS information. This is affected by two factors:
w
1
is the driver’s driving experience, and w
2
is the driver’s personality. a,b, and care the
fitting parameters, respectively.
In a mixed traffic flow randomly composed of CAVs and HVs, we defined
ρCAV
(0
≤ρCAV ≤
1) as the penetration rate of CAVs. When the front vehicle of the CAV has a
vehicle-to-vehicle communication function, these CAVs will adopt collaborative adaptive
cruise control (CACC) mode, known as CACC vehicles [
48
–
50
]; otherwise, they will follow
with adaptive cruise control (ACC), known as ACC vehicles, as shown in Figure 2[
51
,
52
].
Currently, the most common forms of car-following are:
Appl. Sci. 2024, 14, x FOR PEER REVIEW 4 of 19
of expressway traffic flow is expected to change in the future [45]. As shown in Figure 1,
while considering seing up a hard shoulder opening strategy, it is also vital to fully con-
sider the characteristics of connected vehicles and non-connected vehicles.
Figure 1. An expressway with hard shoulder opening applies.
2.2. Hybrid Network Traffic Flow Modeling
HVs are often not very capable of obtaining road instructions. This has been reflected
in many studies on the acquisition rate of expressway road instruction [41,46]. While con-
nected autonomous vehicles are frequently equipped with on-board units (OBUs) that can
be integrated into any car or used as a vehicle simulator in the absence of actual traffic,
allowing real-time information exchange between the vehicle and the infrastructure [47]
and ensuring full access to road indication. Therefore, in the subsequent work, we as-
sumed that CAVs can obtain all road information indicated by variable message signs
(VMSs). Considering that hard shoulder opening messages are often displayed on VMSs,
which are similar to expressway routing instructions, the information acquisition rate of
human-driving vehicles on expressway hard shoulders conforms to the Logit utility
model.
𝑃𝑐
(
𝑤
,
𝑤
)
=
(
)
(
)
, (1
)
𝑃𝑐 is the probability that HV accepts VMS information. This is affected by two fac-
tors: 𝑤1 is the driver’s driving experience, and 𝑤2 is the driver’s personality. 𝑎, 𝑏, and 𝑐 are
the fiing parameters, respectively.
In a mixed traffic flow randomly composed of CAVs and HVs, we defined 𝜌 (0≤
𝜌 ≤ 1) as the penetration rate of CAVs. When the front vehicle of the CAV has a vehicle-
to-vehicle communication function, these CAVs will adopt collaborative adaptive cruise
control (CACC) mode, known as CACC vehicles [48–50]; otherwise, they will follow with
adaptive cruise control (ACC), known as ACC vehicles, as shown in Figure 2 [51,52]. Cur-
rently, the most common forms of car-following are:
Figure 2. Changes in the CAV follower model.
Figure 2. Changes in the CAV follower model.
Appl. Sci. 2024,14, 3145 5 of 18
(1) HDV follows HDV.
When the vehicles are both human-driven cars, and the driving behavior or speed of
the front vehicle suddenly changes, the rear car needs a certain amount of reaction time
to make a judgment and then adjust its driving behavior. Since the proportion of HDV is
1−ρ, the theoretical proportion of this following mode is P1.
P1=(1−ρC AV)(1−ρC AV)(2)
(2) HDV follows CAV.
P
2
is when the front automobile is connected and automated and the car behind
is human-driven. When the status of the front vehicle changes, the vehicle behind still
requires some reaction time to adjust. Therefore, it is the same as the first following mode
with a proportion of P2.
P2=ρC AV(1−ρC AV )(3)
(3) CAV follows HDV.
When the front car is human-driven and the car behind is connected and automated,
the car behind is outfitted with relevant sensing equipment (such as cameras, etc.). There-
fore, when the lead car abruptly accelerates or decelerates, the on-board sensors of the
following car precisely capture the behavior in front and make quick decisions. Compared
with Formulas (1) and (2), the expected headway is shorter. The proportion of this following
mode is P3.
P3=(1−ρC AV)ρC AV (4)
(4) CAV follows CAV.
When the vehicles are both connected and automated, they can share real-time road
information and driving behaviors, achieving “vehicle-to-vehicle communication”. For
instance, if the front vehicle decides to speed up and slow down, the following vehicle
can receive that at the same moment, allowing the corresponding decision to be made
promptly. In this car-following mode, the front and rear vehicles can be treated as a whole,
and the expected headway is the shortest. According to the analysis, the proportion of this
car-following mode is P4.
P4=ρC AV2(5)
3. Dynamic Hard Shoulder Running Strategy Based on Hidden Markov Model
Considering the difference between the ability of the CAV and the HV to obtain traffic
information in mixed traffic flow, it was assumed that the VMSs were evenly distributed
on the road sections. The main basis for HSR in this paper is the traffic breakdown, as
shown in Figure 3, which occurs when the average speed in a road section suddenly
drops and does not recover for a long period of time. As mentioned in Section 2.2, there
are variations in car-following models for mixed traffic flows with CAVs, and existing
research has indicated that the traffic capacity differs across different penetration rates.
Consequently, there are also differences in the phenomena of traffic breakdown at varying
penetration rates. The unchanged traffic breakdown prediction method (with a penetration
rate of 0) cannot accurately predict traffic breakdown in mixed traffic flows with CAVs.
Therefore, hereinafter, we will propose a traffic breakdown prediction method in mixed
traffic flows with CAVs as well as investigate the impact of different penetration rates on
traffic breakdown in mixed traffic flows with CAVs, ultimately constructing HSR strategies
in such situations. It is worth noting that the scenario in this paper is an ideal scenario that
does not consider weather and other factors, and only discusses the impact of the traffic
characteristics of CAVs and HVs.
Appl. Sci. 2024,14, 3145 6 of 18
Appl. Sci. 2024, 14, x FOR PEER REVIEW 6 of 19
Figure 3. Traffic breakdown diagram.
3.1. Traffic Breakdown Probability Calculation
In order to detect traffic breakdown incidents, the specific manifestation of traffic
breakdown must first be defined. The breakdown state can be defined as an abrupt drop
in vehicle speed that fails to recover above a critical speed over a period of time. To ad-
dress the differences in the characteristics of traffic flow on different lanes, the paper
adopted the cross-sectional speed detection method to define the breakdown state of a
roadway in a hierarchical manner. A road’s breakdown situation must be clear and defi-
nite before defining its breakdown state. Define the breakdown as a state in which the
vehicle speed is less than the critical speed 𝑉 (km/h) and does not recover above 𝑉 for
𝑇(min), where 𝑉 is the critical speed. The limit of 𝑇 is to prevent misjudging transient
deceleration as a traffic breakdown.
The physical meaning of 𝑉 is that a breakdown is considered to have occurred when
the speed is less than that value. Intuitively, if the speed is close to 𝑉, a rapid and wide-
spread deceleration is likely to occur, leading to a breakdown in the traffic flow. Therefore,
the confirmation of 𝑉 is to find a speed point at which a significant fluctuation occurs
when the vehicle speed reaches this value.
Therefore, 𝑉 can be determined through the following three steps:
(1) Calculate the average speed 𝑉 for a continuous period of time 𝑡 (min);
(2) Calculate the standard deviation 𝜎 of the speed in 𝑡;
(3) Repeat the previous two steps to calculate the standard deviation 𝜎 of all average
speeds 𝑉, respectively. The critical speed 𝑉 is the 𝑉 corresponding to the
greatest value of 𝜎. The formulas for each parameter are as follows:
𝑉
(
𝑡
)
=
∑
𝑞
𝑣
∑
𝑞
(6)
𝜎
=
∑
𝑝
(
𝑣
−
𝑣
)
(7)
𝑝
=
∑
(8)
where 𝑞 is the flow rate at moment 𝑡; 𝑣 is the average speed on the road at moment 𝑡;
𝑉(𝑡) is the weighted average speed during period 𝑡 (min) starting at moment 𝑡, and
the weights are the traffic flow at the corresponding moments; 𝜎 is the weighted standard
deviation of the speeds during period 𝑡 starting at moment 𝑡, and the weights are 𝑝.
Figure 3. Traffic breakdown diagram.
3.1. Traffic Breakdown Probability Calculation
In order to detect traffic breakdown incidents, the specific manifestation of traffic
breakdown must first be defined. The breakdown state can be defined as an abrupt drop in
vehicle speed that fails to recover above a critical speed over a period of time. To address
the differences in the characteristics of traffic flow on different lanes, the paper adopted
the cross-sectional speed detection method to define the breakdown state of a roadway
in a hierarchical manner. A road’s breakdown situation must be clear and definite before
defining its breakdown state. Define the breakdown as a state in which the vehicle speed
is less than the critical speed
Vc
(km/h) and does not recover above
Vc
for
Tc
(min), where
Vc
is the critical speed. The limit of
Tc
is to prevent misjudging transient deceleration as a
traffic breakdown.
The physical meaning of
Vc
is that a breakdown is considered to have occurred
when the speed is less than that value. Intuitively, if the speed is close to
Vc
, a rapid
and widespread deceleration is likely to occur, leading to a breakdown in the traffic flow.
Therefore, the confirmation of
Vc
is to find a speed point at which a significant fluctuation
occurs when the vehicle speed reaches this value.
Therefore, Vccan be determined through the following three steps:
(1) Calculate the average speed Vmean for a continuous period of time tc(min);
(2) Calculate the standard deviation σof the speed in tc;
(3)
Repeat the previous two steps to calculate the standard deviation
σ
of all average
speeds
Vme an
, respectively. The critical speed
Vc
is the
Vme an
corresponding to the
greatest value of σ. The formulas for each parameter are as follows:
Vme an(t)=∑t+tc−1
i=tqivi
∑t+tc−1
i=tqi
(6)
σ=q∑t+tc−1
i=tpi(vi−vt)2(7)
pt=qt
∑t+tc−1
i=tqi
(8)
where
qt
is the flow rate at moment
t
;
vt
is the average speed on the road at moment
t
;
Vme an(t)
is the weighted average speed during period
tc
(min) starting at moment
t
,
and the weights are the traffic flow at the corresponding moments;
σ
is the weighted
standard deviation of the speeds during period
tc
starting at moment
t
, and the weights
are pt.
Appl. Sci. 2024,14, 3145 7 of 18
According to the setting method of
Vc
and the definition of single-lane breakdown,
single-lane breakdown incidents can be detected from the raw data, which can be carried
out through the changes in the speed of each lane in the studied road section.
3.2. Traffic Breakdown Predict Model under Hybrid Network
The traffic breakdown state cannot be directly detected by the detector, however, it is
closely related to traffic flow parameters such as density and speed. Furthermore, the CAV
penetration rate
ρCAV
is also regarded as a factor, given the characteristics of mixed traffic
flows with CAVs. Considering the memorylessness of both traffic breakdown and traffic
flow parameters, this paper modeled the evolution process of traffic breakdown using the
hidden Markov model (HMM).
HMM extends the concepts of the Markov process and the Markov model, the com-
plexity of which lies in the fact that the signals that occur in state transitions in the model
cannot be directly detected, and those that cannot be directly detected are referred to as
hidden states. Changes in hidden states can lead to changes in display states, which can
be detected directly. HMM can be used to solve three categories of problems: evaluation
problems, decoding problems, and learning problems. The traffic breakdown state is re-
garded as a hidden state in this research, whereas the detectable upstream vehicle density
and CAV penetration rate are display states, thus establishing HMM.
HMM can be constructed with the following six parameters:
Number of hidden state types
N
. All hidden states constitute the set
S=
{s1,s2,s3,· · · ,st,· · · ,sN}
, where
st
represents the hidden state of moment t, and the hidden
state type is defined as the breakdown type, which can be denoted as S={0, 1};
Number of display state types
O
. All display states constitute the set
O=
{o1,o2,o3,· · · ,ot,· · · ,om}
. The display state is expressed by the upstream vehicle den-
sity and the CAV penetration rate, with the upstream vehicle density ranging from 0 to the
historical maximum values, and the CAV penetration rate ranging from 0 to 1.
The initial hidden state distribution vector
π
,
πi=P(i1=si)
,
i=
1, 2,
· · ·
,
N
, where
πiis the probability that the hidden state is siwhen t=1;
Hidden state transition probability matrix
A
,
A=aij N×N
, where
aij
is the prob-
ability of a hidden state transitioning from
si
at moment
t
to
sj
at moment
t+
1, that is,
aij =Pit+1=sj∨it=si,i=1, 2, · · · ,N;j=1, 2, · · · ,N;
Observation probability matrix
B
,
B=bj(k)N×M
, where
bj(k)
is the probability of
generating the observation okunder the condition that the hidden state is sjat moment t.
Two-state corresponding probability matrix
BN×M=nbjko
describes the correspon-
dence between the display state and the hidden state, where
bjk =POkat t|St=sj
,
1⩽j⩽N, 1 ⩽k⩽M,t=1, 2, 3, · · · .
Learning the existing traffic data parameters is required after the establishment of the
HMM. A segment with three lanes is chosen in the HMM developed in this paper. The
hidden state type is defined as the breakdown type, and the number of hidden states
N=
2.
Different display state division granularities might be chosen based on the precision of the
prediction demand. The lower the division granularity, the higher the prediction accuracy,
but it will also result in a significant increase in computer storage and computation. The
learning methods for three parameters in HMM—the initial hidden state distribution
vector
π
, the hidden state transition probability matrix
A
, and the two-state corresponding
probability matrix B—are as follows:
(1) Learning of hidden state transition probability matrix A:
This method is similar to that described in Section 2, in which the traffic breakdown
types can be identified from raw data. That is, with the sampling interval set to
tc
minutes,
the raw data can be used to compute the one-step transition probability matrix of the
breakdown states. The one-step transition probability here refers to the probability of
transitioning from the current state to the state after
tc
minutes. Assuming that there are
fij
Appl. Sci. 2024,14, 3145 8 of 18
moments where the breakdown state transitions from state ito state jacross all samples, we
can estimate the hidden state transition probability matrix Abased on these frequencies.
aij =PSt=sj∨St−1=si=fi j
∑k=N
k=1fik
(9)
(2) Learning of two-state corresponding probability matrix B:
Similar to the estimation of the hidden state transition probability matrix
A
, the
frequency is estimated by recording the number of occurrences of each display state
(upstream density and penetration rate) under each hidden state (traffic breakdown type).
The two-state corresponding probability matrix
B
is a large and sparse matrix with a size
of N×MN−1.
(3) Learning of initial hidden state distribution:
This model assumes prior knowledge of the hidden state at the initial moment and
does not require parameter learning. If the breakdown state at the initial moment is denoted
as k, then only the kth bit of the initial hidden state distribution vector is set to 1, while all
other bits are set to 0.
3.3. Viterbi Algorithm Prediction
The proposed freeway HSR strategy in mixed traffic flows with CAVs in this research
was mainly based on the traffic breakdown prediction based on the hidden Markov model
in Section 3.2. The road detector detects the traffic density
K
of a road segment as well as
the corresponding CAV penetration rate
ρCAV
and the average vehicle speed
Vme an
per
tc
minutes. Therefore, the breakdown state variables
S(t)
,
K(t)
,
ρCAV (t)
and
Vme an(t)
can be
obtained at the current moment t.
In order to predict the road traffic state in the next
tc
minutes, the display state
sequence with a length of
tc
is obtained by first estimating
K(t+tc)
,
ρCAV (t+tc)
after
tc
minutes based on the road segment density and CAV penetration rate transition matrix
and the current traffic observations. Since the breakdown state of the past
tc
minutes is
known, the breakdown state before
tc
minutes is defined as the initial value of the hidden
state, which corresponds to the initial hidden state distribution vector
π
. Then, the Viterbi
algorithm is used to predict the traffic breakdown state after
tc
minutes based on the display
state sequence and the initial hidden state distribution vector
π
as well as the hidden state
transition probability matrix
A
and the two-state corresponding probability matrix
B
. The
prediction process is as shown in Figure 4.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 8 of 19
are 𝑓 moments where the breakdown state transitions from state i to state j across all
samples, we can estimate the hidden state transition probability matrix 𝐴 based on these
frequencies.
𝑎
=
𝑃
{
𝑆
=
𝑠
∨
𝑆
=
𝑠
}
=
∑
(9
)
(2) Learning of two-state corresponding probability matrix 𝐵:
Similar to the estimation of the hidden state transition probability matrix 𝐴, the fre-
quency is estimated by recording the number of occurrences of each display state (up-
stream density and penetration rate) under each hidden state (traffic breakdown type).
The two-state corresponding probability matrix 𝐵 is a large and sparse matrix with a size
of 𝑁×𝑀.
(3) Learning of initial hidden state distribution:
This model assumes prior knowledge of the hidden state at the initial moment and
does not require parameter learning. If the breakdown state at the initial moment is de-
noted as 𝑘, then only the 𝑘th bit of the initial hidden state distribution vector is set to 1,
while all other bits are set to 0.
3.3. Viterbi Algorithm Prediction
The proposed freeway HSR strategy in mixed traffic flows with CAVs in this research
was mainly based on the traffic breakdown prediction based on the hidden Markov model
in Section 3.2. The road detector detects the traffic density 𝐾 of a road segment as well as
the corresponding CAV penetration rate 𝜌 and the average vehicle speed 𝑉 per
𝑡 minutes. Therefore, the breakdown state variables 𝑆(𝑡) , 𝐾(𝑡) , 𝜌(𝑡) and 𝑉(𝑡)
can be obtained at the current moment 𝑡.
In order to predict the road traffic state in the next 𝑡 minutes, the display state se-
quence with a length of 𝑡 is obtained by first estimating 𝐾(𝑡+𝑡), 𝜌(𝑡 +𝑡) after 𝑡
minutes based on the road segment density and CAV penetration rate transition matrix
and the current traffic observations. Since the breakdown state of the past 𝑡 minutes is
known, the breakdown state before 𝑡 minutes is defined as the initial value of the hidden
state, which corresponds to the initial hidden state distribution vector 𝜋. Then, the Viterbi
algorithm is used to predict the traffic breakdown state after 𝑡 minutes based on the dis-
play state sequence and the initial hidden state distribution vector 𝜋 as well as the hidden
state transition probability matrix 𝐴 and the two-state corresponding probability matrix
𝐵. The prediction process is as shown in Figure 4.
Figure 4. Viterbi algorithm process.
Figure 4. Viterbi algorithm process.
Appl. Sci. 2024,14, 3145 9 of 18
Since the final result of the Viterbi algorithm is the probability of an event occurring, in
order to specify the traffic state and provide a basis for HSR, the maximum event probability
obtained for each operation is defined as
δ(i,t)
, that is, the breakdown state of the road
section at moment tis most likely to be i.
3.4. Control Process
The HSR strategy proposed in this paper is shown in Figure 5. After obtaining the
traffic state
i
of the road section in future
tc
minutes, the Freeway Control Center, as shown
in Figure 1, opens the roadside hard shoulder in advance to mitigate any impending future
traffic breakdown. In addition, since the hard shoulder is primarily used as an emergency
lane for vehicles with emergency needs, the strategy proposed in this paper will determine
whether the hard shoulder needs to be closed after opening for
Ts
to avoid affecting the
normal use of the hard shoulder. After opening the hard shoulder for Ts, the future traffic
state is predicted based on the observed traffic data, and if the road remains in a breakdown
state in the next
tc
minutes, keep opening the hard shoulder; otherwise, close the hard
shoulder. The specific control steps are as follows:
Appl. Sci. 2024, 14, x FOR PEER REVIEW 9 of 19
Since the final result of the Viterbi algorithm is the probability of an event occurring,
in order to specify the traffic state and provide a basis for HSR, the maximum event prob-
ability obtained for each operation is defined as 𝛿(𝑖,𝑡), that is, the breakdown state of the
road section at moment 𝑡 is most likely to be 𝑖.
3.4. Control Process
The HSR strategy proposed in this paper is shown in Figure 5. After obtaining the
traffic state 𝑖 of the road section in future 𝑡 minutes, the Freeway Control Center, as
shown in Figure 1, opens the roadside hard shoulder in advance to mitigate any impend-
ing future traffic breakdown. In addition, since the hard shoulder is primarily used as an
emergency lane for vehicles with emergency needs, the strategy proposed in this paper
will determine whether the hard shoulder needs to be closed after opening for 𝑇 to avoid
affecting the normal use of the hard shoulder. After opening the hard shoulder for 𝑇, the
future traffic state is predicted based on the observed traffic data, and if the road remains
in a breakdown state in the next 𝑡 minutes, keep opening the hard shoulder; otherwise,
close the hard shoulder. The specific control steps are as follows:
Step 1: Obtain 𝐾(𝑡−𝑡), 𝜌(𝑡− 𝑡) as well as 𝜋(𝑡−𝑡) 𝑡 minutes ago and 𝐾(𝑡),
𝜌(𝑡) at the current moment;
Step 2: Predict the traffic state for the next 𝑡 minutes with the Viterbi algorithm and
if a traffic breakdown occurs, open the hard shoulder; otherwise go to Step 3;
Step 3: At this time, if the hard shoulder has been opened and the opening time is
longer than 𝑇, or if the hard shoulder has not been opened yet, skip to Step 4. Otherwise,
continue to open the hard shoulder
Step 4: Close the hard shoulder and start the next loop.
Figure 5. HSR scheme.
4. Numerical Results and Discussion
4.1. Scene Introduction
4.1.1. Scene Characterization
In this section, we analyze the effectiveness of the traffic breakdown prediction model
and the hard shoulder opening strategy in the context of the hybrid network traffic flow
described above. The experiment was carried out through the secondary development of
SUMO and MATLAB, and the studied scenario is shown in Figure 6. The experimental
Figure 5. HSR scheme.
Step 1: Obtain
K(t−tc)
,
ρCAV (t−tc)
as well as
π(t−tc)tc
minutes ago and
K(t)
,
ρCAV (t)at the current moment;
Step 2: Predict the traffic state for the next
tc
minutes with the Viterbi algorithm and if
a traffic breakdown occurs, open the hard shoulder; otherwise go to Step 3;
Step 3: At this time, if the hard shoulder has been opened and the opening time is
longer than
Ts
, or if the hard shoulder has not been opened yet, skip to Step 4. Otherwise,
continue to open the hard shoulder
Step 4: Close the hard shoulder and start the next loop.
4. Numerical Results and Discussion
4.1. Scene Introduction
4.1.1. Scene Characterization
In this section, we analyze the effectiveness of the traffic breakdown prediction model
and the hard shoulder opening strategy in the context of the hybrid network traffic flow
described above. The experiment was carried out through the secondary development of
SUMO and MATLAB, and the studied scenario is shown in Figure 6. The experimental
scenario was selected from the basic section of the motorway, length = 5500 m, the number
of lanes in the section was 3, and the speed limit value of the section was 110 km/h.
The length of the hard shoulder was 400 m, and the speed limit value was 80 km/h
Appl. Sci. 2024,14, 3145 10 of 18
(ref. [
13
] showed that the speed of vehicles on the hard shoulder tends to be lower than
80 km when the hard shoulder is open). The basic characteristics of the traffic flow in the
simulation scenario at different penetration rates are shown in Figure 7. The basic plots of
density versus traffic flow of the road section at different penetration rates are presented
in Figure 7a,b, from which it can be seen that the capacity of the road section gradually
increases with the increase in the CAV penetration rate. The speed versus roadway density
and speed versus roadway flow for different penetration rates are shown in Figure 7c,d.
From Figure 7c,d, as the CAV penetration rate increases, the road section density and flow
rate increase at the same speed.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 10 of 19
scenario was selected from the basic section of the motorway, length = 5500 m, the number
of lanes in the section was 3, and the speed limit value of the section was 110 km/h. The
length of the hard shoulder was 400 m, and the speed limit value was 80 km/h (ref. [13]
showed that the speed of vehicles on the hard shoulder tends to be lower than 80 km when
the hard shoulder is open). The basic characteristics of the traffic flow in the simulation
scenario at different penetration rates are shown in Figure 7. The basic plots of density
versus traffic flow of the road section at different penetration rates are presented in Figure
7a,b, from which it can be seen that the capacity of the road section gradually increases
with the increase in the CAV penetration rate. The speed versus roadway density and
speed versus roadway flow for different penetration rates are shown in Figure 7c,d. From
Figure 7c,d, as the CAV penetration rate increases, the road section density and flow rate
increase at the same speed.
The hard shoulder switch is
changed through the traci interface
Three-lane expressway
Figure 6. Simulation scene construction.
Figure 7. Basic characteristics of motorway traffic flow: (a) Density flow relationship at each 𝜌; (b)
Density-flow diagram; (c) Density-velocity diagram; (d) Velocity-flow diagram.
Figure 6. Simulation scene construction.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 10 of 19
scenario was selected from the basic section of the motorway, length = 5500 m, the number
of lanes in the section was 3, and the speed limit value of the section was 110 km/h. The
length of the hard shoulder was 400 m, and the speed limit value was 80 km/h (ref. [13]
showed that the speed of vehicles on the hard shoulder tends to be lower than 80 km when
the hard shoulder is open). The basic characteristics of the traffic flow in the simulation
scenario at different penetration rates are shown in Figure 7. The basic plots of density
versus traffic flow of the road section at different penetration rates are presented in Figure
7a,b, from which it can be seen that the capacity of the road