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Impact of Connected and Automated Vehicles on Capacity of
single lane road based on macroscopic fundamental diagram
Amirhosein Karbasi
Master Student, Tarbiat Modares University
Amirhosein.karbasi98@gmail.com
Behzad Bamdad Mehrabani
Ph.D. Candidate, Université catholique de Louvain
behzad.bamdad@uclouvain.be
Mahmoud Saffarzadeh
Full Professor, Tarbiat Modares University
saffar_m@modares.ac.ir
Abstract
Shortly, Automated Vehicles (AV) will be used in urban streets in many
countries. On the other hand, many countries are faced with congested
problems and are looking for some way to solve congestion problems.
Therefore, it is necessary to find the impact of these vehicles on
different aspects of transportation planning. In recent years many
researchers have been encouraged to investigate the impact of
Connected and Automated Vehicles (CAV) on the capacity of
transportation networks. In this paper, we have a specific goal, and the
goal is to show how CAVs can influence roads' capacity. In this
research, we choose the SUMO simulator to reach our goal. Besides, we
use Krauss car-following model to specify the following vehicle
behavior and also choose the speed-density relationship and
macroscopic fundamental diagram (MFD) to determine the density and
capacity of our network. In the last part, we show the result of a
simulation-based on data collected from the SUMO simulator. Based on
results, CAVs have great potential to improve transportation networks'
situation from a capacity perspective.
Keywords: Connected and automated vehicles, Fundamental diagram,
SUMO, Capacity.
Introduction
Nowadays CAVs have become a solution to reduce congestion and a lot of researchers work on the
impact of this kind of vehicle on the capacity of roads (Xiao et al. 2018). One of the import aspects of
automated vehicles is a different level of automation. There is a classification about the automation
level that specifies a definition for every automation level. This definition is published by the Society
of Automotive Engineers (SAE) (Parkhurst 2016). Table 1 shows the definition of different levels of
automation and the meaning of automation in this article is level 5 of automation.
The other aspect of CAVs is connectivity. Connected vehicles are able to connect to other vehicles (is
known Vehicle to Vehicle communication (V2V)) or they can connect to specific infrastructure (is
known Vehicle to Infrastructure communication (V2I)) (Atkins Ltd. 2016).
The concept of this study is related to importance of emerging vehicle automation and connection
aspect of this vehicle. In this study we tried to show the impact of CAVs on the capacity of a single
road.
Table 1. definition of different level of automation defined in SAE J3016 definition(Parkhurst 2016)
Level of Automation
Definition
Level 0
No automation
The full-time performance by the human driver of all aspects of the dynamic driving
task, even when enhanced by warning or intervention systems
Level 1
Driver Assistance
The driving mode-specific execution by a driver assistance system of either steering or
acceleration/deceleration using information about the driving environment and with
the expectation that the human driver performs all remaining aspects of the dynamic
driving task.
Level 2
Partial Automation
The driving mode-specific execution by one or more driver assistance systems of both
steering and acceleration/deceleration using information about the driving
environment and with the expectation that the human driver performs all remaining
aspects of the dynamic driving task.
Level 3
Conditional Automation
The driving mode-specific performance by an automated driving system of all aspects
of the dynamic driving task with the expectation that the human drivers respond
appropriately to a request to intervene.
Level 4
High Automation
The driving mode-specific performance by an automated driving system of all aspects
of the dynamic driving task, even if a human driver does not respond appropriately to
a request to intervene.
Level 5
Full Automation
The full-time performance by an automated driving system of all aspects of the
dynamic driving task under all roadway and environmental conditions that can be
managed by a human driver.
Literature Review
There are some studies about the impact of vehicle automation on the capacity of transportation
networks. Lu et al. (2019), exanimated impact of automated vehicles on the capacity of 36
intersections and a part of the urban road using speed density formula and macroscopic fundamental
diagram and they concluded that AVs can improve the capacity of intersections. In another study
Hartmann et al. (2017) investigated the impact of autonomous vehicles on the German freeways using
microsimulation. Also, Atkins Ltd. (2016), determined the impact of CAVs using microsimulation for
different types of urban networks include intersection, freeway, roundabout, and complex networks.
Olia et al. (2017) used Fritzsche car-following model to find the impact of automated vehicles and
cooperative automated vehicles on the capacity of the merge section. Friedrich (2016), use some
formula to find the impact of autonomous vehicles on the capacity of transportation networks. Also, in
this paper impact of autonomous vehicles on stability is investigated. Tilg et al. (2018) determined
impact of automated vehicles on the weaving section using a multiclass hybrid model and they
considered lane changing and reaction time in the simulation.
Method
This study has a specific goal, and the goal is to determine the capacity of a single lane road in the
presence of CAVs. To achieve this goal, we consider different scenarios that are shown in table 2 and
these scenarios are based on penetration rates of CAVs and regular vehicles in mixed traffic. Also, we
consider some phases. In the first phase, the data (including speed and density) is obtained using the
SUMO simulator. SUMO is a software that is open source, and it provides this possibility to
implements traffic simulation (Behrisch et al. 2011).in this phase we used car following model to
define drivers’ behavior in mixed traffic and information about car following model will be discussed
in the next section In the second phase, the data is aggregated in 1-minute intervals. The third phase is
using Papageorgiou speed-density relationship and macroscopic fundamental relationship to find
capacity and density that divided flow into a free-flow branch and congested flow branch. The
equations (1) and (2) show the speed-density relationship and macroscopic fundamental diagram
relationship, respectively (Lu et al. 2019; Krishna et al., .2019).in the first equation we tried to specify
the relationship between speed and density and specify the parameters and then we substituted
equation (1) in equation (2) to obtain flow for different time intervals. In Equation (1), Vf shows free-
flow speed; Km is critical density; k is density, and a is equation parameter. In Equation (2) Q shows
the flow (veh/hr) of a network; p determine density in (veh/km); and V means mean speed (km/hr).
(1)
a
m
fk
k
a
vV 1
exp
(2)
VpQ .
Table 2. Scenarios for simulations
Scenario
CAV penetration rate
Regular vehicle penetration rate
Scenario 1
0
100
Scenario 2
20
80
Scenario 3
40
60
Scenario 4
60
40
Scenario 5
80
20
Scenario 6
100
0
Car following model
For implementing traffic, simulation is necessary to determine the car following parameters. In this
study, we choose Krauss car-following model that is a default SUMO car-following model. For
regular vehicles, car-following models are taken from Lu et al. (2019), and for CAVs acceleration, tau
(minimum time headway) and minimum gap were taken from Atkins Ltd. (2016). To comply with
safety requirements deceleration, emergency deceleration for CAVs is equal to regular vehicles. (Lu et
al. 2019). Sigma (driver imperfection) for CAVs was taken from Lücken et al. (2019). Table 3 shows
the parameters for the car-following model for regular vehicles and CAVs.
In the car following model the parameters are defined as follows: Mingap is defined the offset to the
leading vehicle or Empty space after leader (in m). Acceleration is the acceleration ability of vehicles
(in m/s2). Deceleration is the deceleration ability of vehicles (in m/s2). Emergency Deceleration is the
maximum physically deceleration ability of vehicles (in m/s2). Sigma is The drtver imperfection .Tau
is the driver’s minimum time headway (in s) (Lu and Tettamanti, 2018).
Table 3. Car following models parameter
Parameters
Regular vehicle
CAVs
)
2
Acceleration (m/s
3.5
3.8
Deceleration (m/s2)
4.5
4.5
Emergency Deceleration (m/s2)
8
8
sigma
0.5
0
Tau
0.9
0.5
Mingap
1.5
0.5
Network and simulation setup
To determine the impact of CAVs on the transportation networks' capacity, it is necessary to define the
network. In this paper, we choose a single lane urban road. Figure 1 shows the network. In figure1
blue vehicles demonstrate the CAVs and red vehicles show the regular vehicles.
Figure1. Network in simulation environment
For this simulation we have 2 different branch as shown in figure 2.In the figure 2 there are two
different branch .The first branch is known as free flow branch that is starts from zero vehicles in the
network and continue until the network reaches its capacity and automatically can be built in SUMO.
The second branch is known as congested flow branch that is begin from capacity to jam density.
SUMO can’t create jam density by default. So there are some way to create jam density in SUMO.
Figure 1 shows a jam density. The way that we choose for this simulation is using variable speed sign
(VSS). In this method in some period of time the speed of network was reduced to create jam density.
For implementation the simulation the speed of vehicles should be specified. In this simulation we set
the speed of vehicles equal to 50 km/hr because the area of simulation is urban area the speed has a
logical value. In addition, the length of vehicles is 5 meters. Also, the length of simulation network is
set to 1 km.
Result
The simulation data were collected, and using equation (1) critical density (Km) and (a) were
obtained. Then, with the help of equation (2), the maximum flow for every scenario was determined.
Table 4 shows the different values for different scenarios. From equation (2), the flow density
relationship can be determined, and the diagram based on this relationship can help us understand the
free-flow branch and congested flow branch. The flow density diagrams are shown in figure 3 for each
scenario.
Figure2. Greenshield’s Fundamental Diagrams(Zaidi et al. 2014)
Table 4. Simulation result
Scenario
a
(critical density)
m
K
Flow
Flow changes (%)
(%) changes
m
K
1
3.447
63.566
2243
0
0
2
3.529
68.617
2426
8.16
7.94
3
3.605
74.538
2642
17.78
17.26
4
3.926
79.936
2897
29.11
25.75
5
4.255
86.869
3216
43.32
36.65
6
4.651
94.632
3603
60.57
48.87
Figure3. Flow density diagram
As shown in table 4 and figure 3, there are some changes in critical density and flow for each
scenario.in the figure 3 there are flow density relationships for every scenarios that are obtained from
equation (2). Critical density experienced a change from 63.563 to 94.632 that from this change can
we realized that CAVs could improve critical density substantially and this change also can be realized
from the figure 3.in addition, flow went up from 2243 to 3603 that we can realize that CAVs play a
vital role in improving the capacity of the road and redacting congested transportation networks.
Figures 4 and 5 respectively show changes in flow and density compared to percentage changes in
CAV.
On the other hand, there are interesting changes in density and flow changing. Table 1 shows that as
the penetration of CAVs increases, the percentage of changes in density and flow also increases. Also,
there is a comparison between changes in flow and changes in density compared with the change in
penetration rate in CAVs shown in figure 6. Figure 6 shows there is a similar change in density and
flow when the penetration rate of CAV is under 40 %. In contrast, after a 40% penetration rate,
changes in flow are higher than changes in density. At last, figure 7 shows the 3D plot of fundamental
diagrams and the percentage of CAVs.
Figure4. Flow change compared to percentage change in CAV
Figure5. Density change compared to percentage change in CAV
Figure6. Percentage change in critical density and flow compared to percentage change in CAV
Figure7. 3D plot of flow density diagram and percentage of CAV
Conclusion
The impact of CAVs on the capacity of a single road using macroscopic fundamental
diagrams have been investigated in this study. Results show that CAVs have provided a great
opportunity to increase the capacity of the road; therefore, these kinds of vehicles can be a
solution to the congested problem in the transportation network. Also, results show that CAVs
can improve the density that divided fundamental diagram to free-flow branch and congested
flow branch that is known as critical density.
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