Content uploaded by Frank Ekene Ozioko
Author content
All content in this area was uploaded by Frank Ekene Ozioko on Dec 05, 2022
Content may be subject to copyright.
Speed Harmonisation Strategy for Human-driven
and Autonomous Vehicles Co-existence
Ekene Frank Ozioko
e.f.ozioko@pgr.reading.ac.uk
Department of Computer Science,
University of Reading,
Reading, United Kingdom
0000-0001-7092-6261
Julian Kunkel
julian.kunkel@gwdg.de
Department of Computer Science,
University of Göttingen
Germany
0000-0002-6915-1179
Fredric Stahl
frederic.theodor.stahl@dfki.de
German Research Center for Artificial Intelligence
GmbH (DFKI), Laboratory Niedersachsen
Marine Perception, 26129 Oldenburg, Germany
0000-0002-4860-0203
ABS TR ACT
Autonomous vehicle emergence with the potential to improve
the traffic system efficiency and user comfort have made
the co-existence of human-driven and autonomous vehicles
inevitable in the near future. The different vehicle type co-
existence has facilitated vehicle speed harmonisation to en-
hance traffic flow efficiency and prevent vehicle collision risk
on the road. To a large extent, speed control and supervision
of mix-traffic behaviours will go a long way to ameliorate
the concerns envisaged in the autonomous vehicle integration
process. A model predictive control-based autonomous vehicle
speed adjustment technique with safe distance is developed
to optimise the flow of mixed vehicles based on estimated
driving behaviour. The main contribution of this work is
employing the autonomous vehicle speed adjustment to the
existing car-following model in mixed traffic. A mixed-traffic
simulator is developed to test the proposed method in a car
following model using a merging road to quantify the benefit
of the proposed speed control strategy. The proposed simula-
tion model is validated, and experiments are conducted with
varying traffic intersection control strategies and vehicle type
proportions. The obtained results demonstrate that the speed
adjustment strategy has about 18.2% performance margin.
KEY WO RD S:
Reservation node (RN), Traffic light (TL), Car-following
model, speed harmonisation, mix-traffic, vehicle cooperation
level, intersection capacity utilisation.
PAPE R STRUCTURE
This work is structured to provide a summary of the contri-
butions made by the contents of each section of the research
paper. This paragraph provides readers with a guide in under-
standing the organisation and relationships between the work
sections. This paper is organised as follows: Section Icovers
the general background introduction to the mix-traffic with
the state-of-the-art traffic management strategies, emphasising
the research problem and goals. Within this same section, we
have the motivation for the research, research questions, re-
search aims and objectives, and the contribution to knowledge.
Section II presents an overview of state of the art in traffic
management strategies and control architecture. These reviews
mainly involve traffic management schemes involving human-
driven and autonomous vehicles ( mixed-traffic environments).
The proposed mixed-traffic solution, covering the research
framework, research design methods, and strategy for speed
harmonisation in mixed-traffic, is presented in Section III.
The detailed experiment conducted, results obtained with
validation of data, and discussions are presented in Section IV.
Section VIII presents an n all-embracing conclusion of the
work and some encountered challenges with suggestions for
future research work on mix-traffic integration.
I. INTRODUCTION
The control and optimisation of mix-traffic flow at road in-
tersections are crucial as a baseline for the autonomous vehicle
integration process. Based on the emergence of autonomous
cars, mixed traffic problems have attracted researchers to
develop many related technologies to find solutions associated
with the autonomous vehicle integration process. Recently,
autonomous vehicles have been looked on as an alternative
way to solve road traffic problems. Autonomous vehicles have
the potential to share car movement parameter information or
with a central controller in real-time. This information-sharing
feature makes it possible to predict its velocities in managing
traffic at the intersection while human-driven vehicles use
traffic signals with the associated stochastic drivers’ behaviour.
The human drivers’ behaviour is unpredictable and associated
with a delay in making a driving decision, and autonomous
vehicles are in the sink with intelligent transportation Figure 1
systems where cars sense the environment via sensors and take
the best decision in real-time to avoid collision or accidents.
According to [1], the capacity of the road can be increased
with the increase of the cooperation level between vehicles
when their behaviours are homogeneous. This makes the
study of traffic mix more complex considering the under-
lining difference in the behaviour of the two cars category
of vehicles. Moreover, the simulation results from the survey
by [2] show that from mixing automated (AVs) and human-
driven (or manually-controlled vehicles), the road capacity can
be increased by 2.5 times when the percentage of automated
vehicles is more than 70 percent. Also, the works of [3]–[5]
show that vehicles forming a platoon can improve the stability
and efficiency of the traffic flow.
Developing a mix-traffic flow model is the first step towards
shaping a more sophisticated traffic management strategy to
midwife the transition period seamlessly. The proposed mix-
traffic management strategy aims to use the inter-vehicle
distance to make a judgement of vehicle position and predict
its movement. This strategy follows the safe distance model
to keep each car at a safe distance away from each other
(the safe distance is dependent on car type). Besides this,
the vehicles also check for nodes (where the Road-Vehicle
Communication comes into play) on the roads and how far
away each car is from its reference node position. In accessing
the intersection, our method uses a first-in-F-first out policy
approach; the right of way is assigned based on the vehicle
type and the car nearest to a merging node. An analysis from
the vehicle evolution and behavioural pattern indicates that
vehicles driven by a human being are more aggressive in
behaviour and has an associated delay in responding to the car-
following or at merging situation. Figure 2 model is defined by
using a T-junction with merging and priority road to simulate
the mix-traffic flow meticulously and realistically and review
the impact of our strategy on the alternatives. It is common
knowledge that HV’s are made up of radical drivers who
usually exhibit aggressive behaviours when they are in contact
with AVs. This design assigned HV the priority to access and
get rid of AVs by forcing the AVs to stop and give them the
right of way rather than waiting or following them from be-
hind. Inter-vehicle distance is usually considered at junctions
where a minor street (non-priority road) intersects a major
highway (priority road). If a priority road vehicle has just
arrived at the intersection, it may clear the intersection while
rolling; otherwise, it starts the movement from rest depending
on the car type. Human drivers intending to perform merging
maneuvers are presented with a space between vehicles in a
conflicting traffic movement. The pattern of arrivals of the
major street vehicles creates varying time gaps of different
values subject to when the vehicle mix is involved. From the
research of [6], the distance between the rear bumper of the
first vehicle and the front bumper of the following vehicle
and is usually measured in seconds and is called inter-vehicle
space. This space is the time interval between the arrivals
of vehicles at a stop line of the non-priority road and the
arrival of the first vehicle at the priority road. The earlier
study by [7] shows that modelling delays for homogeneous
traffic show a linear relationship with the same type of vehicle.
This may be caused by the reduction in the number of
available inter-vehicle spaces because of uniformity in vehicle
behaviours. There is a significant increase in the occupation
time of low-priority movements. However, such linear models
will not be suitable for mixed-traffic co-existence and non-
uniform car behaviour, leading to traffic collisions. According
to [8], intersection capacity is generally analysed either by
Fig. 1: A 4-way intelligent road intersection with double lanes
the regression method or gap-acceptance method. The Gap-
acceptance method is the widely used method in most of the
countries in their intersection capacity manual. However, in
earlier studies, it was reported that the gap-acceptance method
has a few drawbacks. The gap-acceptance strategy cannot
apply to the traffic streams which do not comply with the
uniform car behavioural pattern. The gap-acceptance theory
fails when a mixed behaviour of aggressive and gentle cars
co-exist.
a) Contribution Computing and Computation to Knowl-
edge::This work builds on the existing approaches by em-
ploying 1-dimensional homogeneous traffic control strategies
into a 2-dimensional complex traffic behaviour of the mix-
traffic environment. The work combined both traffic lights and
vehicle-vehicle/road infrastructure communications for con-
trolling the human-driven vehicle and autonomous vehicles,
respectively, at a road intersection. However, the main areas
of the contributions are as follows:
•Investigating the complicated behaviour involved in a mix
of AV and HV to fastract autonomous vehicle integration
process.
•Conduct as many simulated experiments to develop opti-
mal data as a basis for the AV and HV integration process.
•Development of a 2-D traffic model with the concept of
car-following models to comprehensively simulate both
lateral and longitudinal mix-traffic behaviour.
•Modelling driving behaviour with vehicle-type-
contingency and human psychological driving
characteristics.
•The method of adjusting the distance headway improves
the performance of a human-driven vehicle. This makes
the HVs yield to much smoother trajectories.
•A method for speed harmonisation algorithm for a traffic-
mix setting.
•A centralised traffic control method that controls both AV
and HV using one control unit with different proportion
of vehicle types to serve as an integration of autonomous
vehicle pattern.
II. REV IE W OF T HE S TATE OF T HE A RT
With traffic flow parameters, the behavioural pattern of
vehicles could be evaluated reasonably to suggest that the
co-existence of human and autonomous vehicles is possible.
The scenario of mixing different vehicle type behaviours in
a single traffic flow model brings a mountain of complex
variables into consideration. The co-existence of traffics lies
between the elements of human and machine co-existence. In
a mixed traffic flow at a road intersection, each vehicle type
are expected to behave in line with its default design, maintain
behavioural deviation and the essential objectives of traffics,
which is to safely reach its target destination or goal in the
shortest possible time. Mix-traffic flow management creates
room for vehicle co-existing by negotiating with other vehicle
types and traffic participants who have a different behavioural
pattern based on agreed set down rule to avoid a collision.
The platooning model of traffic management strategy is used
to optimise the traffic flow. Besides, the process of varying the
safe distance between autonomous and human-driven vehicles
is also deployed to enhance the optimal efficiency of the traffic.
[9], [10] proposed a real-time cooperative eco-driving scheme
for AV and HV mixed-vehicles using platoon. According
to [9], the lead vehicle receives timing and phase signal
information through (V2I) communication, while the preced-
ing vehicle on the reference platoon communicates via V2V.
Generally, mixed traffic is mainly comprised of road users,
which include vehicles, pedestrians, and cyclists. However, the
vehicles involved in [9] generally were termed "homogeneous"
traffic, but the vehicles have a wide variation in their static and
dynamic characteristics. The vehicle type for the purpose of
this research is human-driven (HV) and autonomous vehicles
(AV). The vehicles share the same right-of-way, resulting in
a jumbled traffic flow. The main distinguishing characteristic
of this mixed vehicle is based on their driving behaviour
and the means of communication among vehicles and road
infrastructure. These driving characteristics resulted in a wide
variation in behaviours of the vehicles, which makes the mix-
traffic management more complicated.
The emergence of autonomous vehicles has witnessed a
growing demand for mixed traffic research for the autonomous
vehicle integration process. The design concepts of managing
human and autonomous vehicles are because of the difficulties
and problematic areas of human-machine interaction and the
theoretical context of mental modelling. In contrast, the traffic-
mix model seeks to use existing homogeneous traffic manage-
ment techniques to manage a heterogeneous traffic system. The
approach first made use of the traffic flow models presented in
Figure 3, using the relative distance in a car-following model
and compared it with the alternative strategy. The core problem
in mix-traffic modelling, is the case of modelling the driver’s
behaviour.
The driving behaviour model predicts drivers’ intent, vehicle
and driver’s state, and environmental influence, to enhance
efficiency in driving experience [11]. [12], define "a driving
behaviour is aggressive if it is deliberate, likely to increase the
risk of collision and is motivated by impatience, annoyance,
hostility and an attempt to save time." non-observance to
successfully model drivers’ behaviour is a critical difficulty
in modelling microscopic traffic flows. Most drivers’ be-
havioumodelsel currently uses estimates. Modelling drivers’
behaviours predict human drivers’ psychological behaviour,
ranging from driver state, driver intention, vehicle, and en-
vironmental influence to enhance traffic safety and societal
well-being. It involves the design and analysis of drivers’
psychological and behavioural characteristics to predict their
capabilities in traffic and make an effort to acknowledge
and emphatically increase traffic throughput. This provides
an informed understanding of traffic and has the prospect
to improve driving behaviour, supporting safer and efficient
driving. Driver’s behaviour model is capable of generating a
classification that characterises the different profile levels of
drivers’ aggressiveness. According to [13], drivers’ behaviour
impacts traffic security, safety and efficiency, better under-
standing, and potentially improves driver behaviour. Attaining
a driving task is a mobility goal while avoiding obstacles and
collisions on the roadway. Aside from the mobility target,
there are several secondary goals, one of which has sparked
a long-running debate about drivers’ psychological behaviour
when driving to their destination. For a vehicle to get to its
destination, there is much decision-making based on feedback.
[14] considered driving behaviour with regards to the difficulty
of the driving task and the risk of collision. The work of
[14] classified driving risk into three main components: risk
is measured in three ways: quantitative risk, subjective risk
assessment, and risk perception. The most important aspects
of the driving role were avoiding potential adverse effects of
risky driving and maintaining a high level of safety. Also, the
work of [15], [16] proposed drivers maintain safety margins
to change their speed to cope more efficiently with any danger
or possible difficulty along the lane..
The advent of the autonomous vehicle has moved the role
of human drivers from active control operation to a passive su-
pervising role [17]. A closer look at the modern road vehicles,
one will observe that there is a high-level advancement in the
automation of most vehicle devices, like the adaptive cruise
control, obstacle sensor, and automated brake system [18],
[19]. [9], proposed a receding horizon model predictive control
(MPC) with dynamic platoon splitting and integration rules
for AVs and HVs, which mostly ease out the trajectory and
prevent any shock-wave but does not concurrently optimise
the trajectory and signal to time of the road intersection.
Currently, there is a large diversity of research going on
in mixed traffic generally and the co-existence of human-
driven and autonomous vehicles. However, most of these
applications are directed towards different types of human-
driven vehicles (car, bus, truck), motorcycles, bicycles, and
pedestrians, which exposes very few design details. Generally,
the state-of-the-art in traffic management was implemented
with the event-driven traffic control system. However, there
are drawbacks concerning throughput and safety when these
methods are implemented in a mixed scenario. There are some
traffic management techniques, [20]–[24] who investigated
the impact of integrating AV’s on the existing roads to co-
exist with the HV’s; how will the mix work concerning
traffic efficiency? The researcher looked critically at a high-
way road system using the following three traffic parameters:
Traffic flow characteristics (vehicle, driver behaviour and road
intersection, Merging entry, and Exit at intersections). This
work appears attractive, but it was only restricted at the
microscopic level. However, Tesla, Incorporation, based in
Palo Alto, California, developed electric cars with high-tech
features like autonomous vehicles and has been chaining the
growing impact of autonomous vehicle integration.
In a mix-traffic system, microscopic models are used to
model each vehicle as a kind of particle. The interactions
among cars are modeled with simulations with each com-
ponent of the proposed framework verified. Each car type
model with the cars and road interaction protocol system is
being implemented in the proposed mix-traffic framework.
This framework was verified through simulations involving 3-
way and 4-way intersection environments with a full detailed
assessment of the impact of each vehicle type. The critical
challenge in agent-based traffic simulation is re-creating prac-
tical traffic flow at both the macro and micro levels. By seeing
traffic flows as emergent phenomena, [25] proposed a multi-
agent-based traffic simulator. According to [26], car agent’s
behaviours are often implemented by applying car-following
theories using a continuous one-dimensional road model.
[27] proposed a multilevel agent composed of agents models
involving micro-meso, micro-macro, meso-macro simulation
framework to address a large scale road traffic mix system
using an organisational modelling approach. The multiple-
leader car-following model involves a heterogeneous mixture
of vehicle types that lack lane discipline. According to [28]–
[30], these traffic conditions lead to a complex driving maneu-
ver that combines vehicle motion in the lateral and longitudinal
direction that needed to address multiple-leader following. [28]
sought to simplify mixed traffic modelling by developing a
technique based on the concept of virtual lane shifts, which
centred on identifying major lateral changes as a signal of a
lane-changing situation.
Vehicle-to-vehicle (V2V)and vehicle-to-infrastructure
(V2I)communications are possible in a connected vehicle
system [31]. CACC systems can safely drive vehicles with
very short headways by forming platoons to increase road
traffic flow capability using V2Vcommunication. [32]–[34].
CAVs’ advanced technologies open up a world of possibilities
for developing novel traffic flow management approaches,
such as cooperative adaptive cruise control (CACC), speed
harmonisation, and signal control, to name a few. With much
room for improvement in terms of traffic safety, quality,
and environmental sustainability, the intersection coordination
scheme has obtained broad research interests. [3], [4], [35],
[36]. [37]–[40]. For several years, the idea of following a
vehicle with a short gap in CACC has been generalised to
provide a new intersection control model, in which nearly
conflicting vehicles approaching from different directions will
cross the intersection with marginal gaps without using a traffic
signal. This will enable automated vehicles to reach their
maximum potential to reduce traffic congestion, reduce travel
time, and increase intersection capability. However, Omae et
al. [34] suggested a virtual platooning system for automated
vehicle control at an intersection that allows vehicles to pass
through without pausing. Vehicles in both lanes are deemed
to be in a virtual lane situation, and their intersection inter-
ference is considered. They are separately managed so that
they can safely follow the platoon’s previous vehicle. The
system, which was tested using four electric vehicles fitted
with automated driving and V2V communication technologies
at a one-way intersection, resulted in a significant reduction
in traffic congestion.
The current literature confirms that typical constraints in
the car-following model is its rigidity to longitudinal vehicle
dynamics of safe- distance, average speed, and acceleration/de-
celeration rate. Most existing traffic models are only suitable
for describing a homogeneous traffic environment using a
firm lane behaviour. As a result, an in-depth analysis of
vehicle lateral and longitudinal movements are needed to
assess driver behaviour in a heterogeneous traffic flow system.
Currently, no widely used traffic theory could exhaustively
simulate a 2-dimensional mix-traffic flow involving a lateral
and longitudinal behavioural model because of the intricate
human driving behavioural pattern involved.
III. METHODOLOGY
Following the above-detailed review of the existing research
on the impact of an autonomous vehicle on traffic, and
considering the current gaps in collision avoidance method in a
car-following model, listed below are our reason for choosing
this method:
•Combining intelligent vehicle communications (IVC),
road vehicle communications (RVC), and Safe-distance
model produces a robust solution to the problem of the
safe distance model as well as collision avoidance in
traffic flow management.
•Autonomous Vehicles can be made to communicate with
other objects in their environment as well as visualise or
read some vital information of other objects, especially
how far away a car might be from a reference car position.
•human-operated vehicles can also tap into this approach
by engaging the sense of sight and looking out for traffic
control mechanisms, though at a less precise value than
autonomous cars.
•Efficiency of traffic management increases when cars
form a platoon
From the above motivations, we deemed it wise to propose a
speed harmonisation strategy for a mix of autonomous vehicles
(AVs) and human-driven vehicles (HVs) at a merging single
lane road with the priority lane.
The road model Figure 2 outlines a single lane merging road
system with its physical properties. Mix traffic involves cars
Fig. 2: Merging road model
with a different behavioural pattern but the same road system;
how can the co-existence work without heavily impacting traf-
fic flow efficiency? In this situation, a merging T-intersection
at an angle of 45◦is being considered for cars sharing space
to test the hypothesis. This is a scenario where cars are
coming from a separate road and will merge into a priority
road at a common node between them and cannot always
tell by their distance from each other if they are likely to
collide. They consider that they might eventually crash in a
situation where they are heading towards the same destination.
Naturally, the major problem will arise from human-controlled
vehicles because they do not possess the features of being self-
aware of their environment as their behaviour is stochastic
and more prone to prediction errors. The proposed model
considered the combination of the two traffic management
strategies of a centralised and decentralised approach. In the
centralised strategy, drivers and vehicles communicate with
a central controller and the traffic signal to assign right-of-
way access priority to the intersection. On the other hand, in
the decentralized strategy, drivers and vehicles communicate
and negotiate for right-of-way access priority. Several research
investigation works have been done in the area of the impact
of autonomous cars on the traffic flow at the intersection [41].
[42] proposes the Optimisation of traffic intersection using
connected and autonomous vehicles. Also, [43] considered the
impact of autonomous cars on traffic with consideration of
two-vehicle types, which are distinguished by their maximum
velocities; slow (Vs) and fast (Vf), which denotes the fraction
of the slow and fast vehicles respectively.
The mixed behaviour results in a very complex traffic
situation that significantly impacts the capacity and perfor-
mance of traffic intersections. Vehicles with one behavioural
pattern are treated with a unified protocol since each vehicle
behaves differently and observes a simple rule at the conflict
of intersection zones. However, investigation shows that car
accidents’ at merging roads are one of the most critical
common aspects of the traffic study because it is associated
with human life. Within the framework of our traffic model,
the co-existence of mixed behaviour, safe distance, and colli-
sion avoidance have been widely studied in this work. Most
models developed to study the traffic at the intersection with
mixed vehicles have been designed to avoid collisions among
autonomous vehicles and human-driven vehicles. In this work,
besides studying mixed traffic behaviour, we investigated the
impact of autonomous cars on merging roads in a mixed
environment. We propose a new traffic control model in a
mixed environment at the merging road using a safe distance
model to maximise the delay and reduce the probability of
accidents. Vehicle occupation time is the key parameter for
the required method, defined as the time a vehicle or vehicle
group crosses at the intersection area. The occupation time of
vehicles’ mixed ratio at these intersections was studied and
compared. The volume and the occupation time data by each
vehicle ratio were extracted from simulation.
The developed Mathematical relationships model describes
the two types of vehicle mixed behaviour to the occupation
time with the traffic flow in a merging single lane road
system. A proposal is made for a mix-traffic model at a
merging T-junction with a priority road section. In which
case, we have a vehicle mix of human-driven and driver-
less cars accessing the intersection simultaneously. Figure 2
is the proposed model of a one-way merging T-junction with
a priority road section and dimensions of the nodes considered.
The mix-vehicles on the two road system with start nodes (7
and 11) has a common destination or target at node 9. The
vehicle emerges from the two roads segment at node 8 and
joins the priority road. The fundamental work of intersection
is to direct vehicle trajectories from start to target. The driving
behavioural difference and the dynamic headway are taken
into account. Hence, the driving behaviour is classified into
two typical types: the aggressive driving style for humans
and the gentle driving for autonomous vehicles, respectively.
The equations obtained were used to estimate the critical
safe and inter-vehicle distances for aggressive driving(HV).
The queuing distance is calculated using an existing method
of clearing behaviour approach according to [6]. It is also
shown that the estimation of the safe distance is more realistic
if reaction time and the aggressive behaviour of drivers are
considered simultaneously.
Correspondingly, the safe distance, car-following, and pla-
tooning rules are used to optimise the traffic model. The
proposed mix traffic model considers the position and dynamic
headway of the leading and preceding vehicles. In this case,
both vehicles are on the current lane or will share a common
node upon merging, thereby using the safe distance and
car-following model. Based on the preceding, the following
protocols of the central controller determines the traffic flow
schedule under the below model underpinning protocols:
•The car movement priority is assigned to the road be-
tween nodes 7, 8, and 9 fig. 2.
•If the merging point (node 8) in fig. 2 of the road system
experiences vehicle arrivals at the same time, then the
priority to cross the merging point is given to the road
with a Human-driven vehicle in front.
•If both roads have the same vehicle types at the front,
the priority road takes precedence.
DES IG N OF T HE ROA D MOD EL
The length of the road in Figure 2 s determined by the addition
of all route lengths present in the model. The length of the
routes of the roads are calculated thus:
We assume that if the route is horizontally straight, like 1−
2−4−5then the route length is the difference of their x
coordinates:
5(x)−1(x)(1)
While if the route is vertically straight:
Therefore, the length of the road is calculated thus:
lroad = (1−2−4−5)+(11 −12−14−15)+(7−6−8−9)+
(17−16−18 −19) +(12−8)+(2 −18) +(16−4)+(6 −14) +
(12 −16) + (2 −6) + (8 −4)
lroad = 600 + 600 + 600 + 600 + 49.5 + 106.1 +
49.5 + 106.1 + 106.1 + 49.5 + 106.1
Therefore: lroad = 2972.9m(approximately)
lcar = 4.5m(Average)
v= 10m/s
ncars =lroad /(S+lcar)(2)
Where
safedistance, S is 5m for AVs,
S is 7m for HVs during platooning and
S is 3m after merging. The after merging time is when the
cars are on straight road and maintain a steady velocity.
Vehicle Model
There are two (2) types of vehicles being considered:
1) Autonomous Vehicles (AVs) with intelligent transporta-
tion systems (ITSs) features. These ITSs come in the
implementation of technologies like sensors and the
Internet of Things.
2) Human Driven Vehicles (HVs) with no intelligent trans-
portation system, but makes use of a human driver who
engages their sense of sight and hearing to watch for
traffic signals from traffic signalling devices.
Interaction between HV and AV:: The AV is modelled
with a gentle driving style where the car is responsible for
avoiding all obstacles and mitigates its movement through the
environment. The AV driving system has the following features
as implemented:
•High precision in obstacle avoidance and manoeuvring,
thereby controlling the velocity and acceleration seam-
lessly
•The AV has a safe distance 0f 3 seconds.
While the HV driving was implemented as a conventional
system of driving with features as listed below.
•The human drivers’ response to a stimulus is about 6
seconds when compared to the AV, which is a real-time
•The HV has a safe distance 0f 5 seconds.
•The braking distance for HD is higher than that AV, but
all are subject to the car’s current speed.
Because of these distinct differences between the AVs and
HVs, there will be challenges in implementing a safe distance
model that produces collision-free traffic flow due to the
different vehicle behaviours. Human drivers are unpredictable
with stochastic behaviour, less precise, and more prone to mis-
takes. [44] observed that human drivers respond to unforeseen
events in about 6 seconds, while autonomously driven vehicles
respond close to real-time, the distance to be kept between
autonomous vehicles will be:
sr=v·tr(3)
While that for human-driven vehicles will be:
sr=v·tr+ 6 (4)
Where 6 seconds is the reaction time for human drivers [45].
The developed model combined the microscopic and macro-
scopic vehicle level of vehicle modelling to address the
longitudinal and lateral mixed-vehicle behaviour process. [28],
observed that the roadway and traffic impact driving behaviour
features while the 2-dimensional behaviour of heterogeneous
vehicles impacts the intersection capacity. This condition
makes the driving behaviour control vehicles longitudinal and
lateral manoeuvre at the merging points. This bi-directional
behavioural feature is sophisticated when compared with the
car-following model for homogeneous traffic behaviour, giving
rise to abreast careful guide, filtering, tailgating, and co-
existence. Therefore, the need for a rigorous investigation
of the traffic parameters at the microscopic level to assess
the traffic behaviour and model an all-inclusive numerical
prototype.
The mix-traffic simulation strategies are subdivided into two
controlling routines or approaches:
1) Longitudinal Control for Car Following model: One of
the fundamental features of the car-following model is
that vehicles observe an average spacing, "S,"(m) that
one vehicle would follow another at a given speed,
"V"(mi/hr). This parameter is of interest in accessing
the throughput of the Car-following model. The average
speed-spacing relation in Equation (5) proposed by [46]
deals with the longitudinal features of the road and
has a relationship with the single-lane road capacity
’C’(veh/hr) estimation in the form:
C= (100)V
S(5)
Where the constant 100 represent the default optimal
capacity of the intersection.
However, the average spacing relations could be repre-
sented as:
S=α+βV +γV 2(6)
Where
α= vehicle length, L
β= the reaction time, T
γ= the reciprocal of the average maximum deceleration
of a following vehicle to provide enough space for
safety.
2) Lateral control of vehicle impacts macroscopic and
microscopic behaviours on a car-following model. The
lateral control causes a lateral interference in a car-
following model designed to impact its management
only on the longitudinal pattern [47]. The essence of the
lateral behaviour in this AVHVcontol model is to address
the driver behaviour characteristics in a mixed vehicle
environment. The AVHV control introduces the coupling
model between lateral and longitudinal vehicle dynamics
through velocity vxcontrol process and the front wheel
steering angle λiderived from the steering angle βv.
The relationship between the vehicle velocity v, the
longitudinal velocity components vx, and the vehicle’s
side slip angle θis represented in Equation (7)
vx=v·cos θ(7)
In addition, the steering angle θof the vehicle front
wheel λithe angle of the steering wheel, βvand steering
ration iuis represented in Equation (8).
λi=βv
iu
(8)
A mix of these two approaches is vital to modelling mix-traffic
flow simulations at road intersections to effectively manage
longitudinal and lateral driving behaviour. The longitudinal
car-following model used the optimal velocity function to
relax the equilibrium value of the gap between vehicles.
Besides, there are still high acceleration and deceleration
problems after a vehicle cuts in front, but the intelligent Driver
Model addressed this problem. The lateral model uses the
technique of maintaining the safe distance braking process
to decide the possibility, necessity, and desirability of lateral
control of vehicles. The lateral approach model is addressed
on a simplified decision-making process using acceleration
according to [48].
Algorithm 1: Car Behaviour Algorithm- Collision free
method
Data: Default Gentle behaviour of AV, Aggressiveness
in human drivers psychology (quantified by
random values)
Result: AVs and HVs Behaviour
1for Every HV : do
2Assign aggressiveness with the following attributes;
3Randomised Reaction time ;
4Randomised Safe distance (in time);
5if The Vehicle is AV then
6Maintain the constant Reaction time;
7Maintain the constant Safe distance (in time);
end
8if AV and HV having the same expected arrival
time (EAT),comes into conflict to share an
available road space (eg Reservation Node (RN),
Traffic Light (TL) or Cross Collision Point (CCP))
then
// (apply priority
considerations);
9Assign priority to HVs to move;
10 Decelerate the AV;
11 Then move the next Car (AV);
12 if the two Vehicle has different expected arrival
time (EAT) then
13 move the vehicle with the shortest EAT
first ;
end
14 At Intersection;
15 AV is guided by the Vehicle to Vehicle and to
infrastructural communication;
16 HV is guided by the traffic light control;
17 The control unit (CU) sync the 2 control
methods
end
18 if Emergency situation occurs then
The AV drives defensively by applying
deceleration/acceleration as necessary ;
end
end
A. Vehicle Movement Schedule
The car’s movement parameters are primarily controlled by
the longitudinal and lateral forces separately for acceleration
or deceleration and for turning, respectively. The prototype
simulator is developed in a virtual environment using a physics
engine to model the traffic system. The vehicle movement
schedule uses physics’ fundamental laws to move a car from
point A to point B in a straight or curved direction. Vehicle
movement involves two schedule:
•Straight movement schedule
•Curved Movement schedule
For the car to move, calculations of parameter values are based
on Newton’s second law of motion. The drag force Fdrag and
rolling resistance forces Frr resist the traction force Ftraction
while driving horizontally. If cruising at constant speed sce-
nario, then Fdrag ,Frr and Ftraction are in equilibrium, which
makes the longitudinal force Flong to be zero. To simulate car
movement at the curve Figure 3, one needs some geometry,
kinematics and need to consider forces and mass. The curved
Velocity Vi
Velocity Vi
Vehicle
Detectors
PS
PS
PS
PS
PS
PS
PS
r
PS
PS
Fig. 3: Model of curved vehicle movement
movement describes how vehicles move in relation to their
coordinate position. Without the curve movement model, this
experiment will fail because of the vehicles’ necessity to
maintain lane track.
a) Accessing the bend:: The angle of the curve is calcu-
lated thus:
θ= 360 ·v/lcircle(arc)(9)
θactual =time ·θ(10)
vmax(curve)=x·v·r(11)
The curve’s angle α= the angle between two intersecting
planes. Curved angle is a measure of the angle between two
intersecting straight lines and the lines perpendicular to the
intersection in respective lanes. This angle can be calculated
thus:
α=θactual
180 ·π(12)
The distance sin a curve can be calculated thus:
scurve =θactual −(θend ·l)
v(13)
Car Following Model With Safe Distance
The car-following model maintains the behaviour pattern of
the leading vehicle. The characteristics pattern of the model
analyses Figure 4 shows how a human being reacts in a
traffic situation, represented in drivers’ longitudinal behaviour
following a leading vehicle and maintaining a safe gap in
between vehicle groups. The driving behaviour does not
HV Safe_distance (m)
Car_1 Car_2 Car_3 Car_4 Car_5
AV Safe_distance (m)
AV AV
HV HV HV
Fig. 4: Car following model with safe distance
altogether depend on the leader in a car-following model,
but it depends on the immediate vehicle’s optimal velocity
in front. This model does not consider lane changing and
overtaking scenarios as that will involve lateral behaviour. The
car-following model behaviour could be described in detail
using the below three points:
•The leading vehicle can accelerate to its desired speed
because no vehicle can influence its speed.
•The leading vehicle’s speed primarily determines the
following vehicle state because drivers try to maintain
a reasonable interval of space or time.
•The braking process involves the use of varying degrees
of braking force to avoid the collision
Conditions for safe distance is dependent:
1) The braking manoeuvre is always executed with constant
deceleration b. There is no distinction between comfort-
able and maximum deceleration.
2) There is a constant Reactiontime trof 0.3 sec for Avs
and a randomised reactiontime of 0.3 to 1.7sec for HVs.
3) For safety reasons, all vehicle must maintain a constant
gap.
We propose a new mathematical model with aggressive
factors and adjustable inter-vehicle distance to describe the
hybrid vehicle moving behaviour in which the vehicle platoon
used to balance the traffic flow. This model deals with the
concept that a driver recognises and follows a lead vehicle
at a lower speed. According to [49]–[51], the potential to
observe and estimate the vehicle response to its predecessor’s
behaviour in a traffic stream is essential in evaluating what
impact the changes to the driving condition will have on traffic
flow. The car that follows the leader concept is dependent on
the below two assumptions:
•The collision avoidance approach demands that a driver
maintain a safe distance from other vehicles on the road.
•The vehicle speed is directly proportional to the spacing
between the vehicles.
Let δst
n+1 represent the distance available for (n+ 1)th
vehicle,
δxsaf e represent the safe distance
vt
n+1 and vt
nrepresents velocities
Therefore, the gap required for safety is given by
δst
n+1 =δxsaf e +T·vt
n+1 (14)
Where:
T= sensitivity coefficient.
However Equation (14) above could be expressed as:
xn−xt
n+1 =δxsaf e +T·vt
n+1 (15)
When the above equation is differentiated with respect to time
t:
vt
n−vt
n+1 =T·at
n+1 (16)
at
n+1 =1
T
·[vt
n−vt
n+1](17)
From the model prototype, the chosen random values of (0.3
to 1.7) for the human drivers’ safe distance based on the UK
transport authority [52] According to the sensitivity coefficient
term resulting from generations of models, we have
at
n+1 = [ αl,se(vt
n)m
xt
n−(xt
n+1)l][vt
n−vt
n+1](18)
Where l = headway
se= speed exponent
α=sensitivity coefficient
Figure 5 is a background description of the vehicle’s safe
distance as suggested by the UK Highway Code. The baseline
of the method indicates that a human-driven vehicle moving at
30mph will take approximately 23 metres for the braking and
stopping process. This is not the case with the autonomous
vehicle with about 0.1 seconds of thinking distance. This
stopping distance sis a component of the thinking distance
(the time it takes for a driver to activate brakes and time
involved in covering distance before the applied), and from the
time brake effect the car speed by initiating the deceleration
process. Also involved within the braking distance is the
stopping time (time/distance it takes the car to come to a stop).
According to [53], in the field of driving behaviour, many
researchers have devoted themselves to modelling driving be-
haviour, analysing conflict mechanisms, and improving traffic
safety. All values are based on the S.I units of metres, seconds,
and kilograms. Consideration is based on distinguishing be-
tween conservative driving and optimistic driving style to help
in the prediction of the car motion: In conservative driving, a
car must decelerate to a complete stop when the car in front
stops suddenly or entirely like in a crash-like scenario, and it
is the worst-case scenario. In this case, the distance gap to the
3m 5m
9m 14m
12m 24m
15m 37m
18m 58m
6m 10m
10mph
20mph
30mph
40mph
50mph
60mph
Thinking Distance
Braking Distance
Stopping Distance
Car Lenght = 4m
8 metres
(2 car lenght)
16 metres
(4 car lenght)
23 metres
(6 car lenght)
36 metres
(9 car lenght)
52 metres
(13 car lenght)
90 metres
(19 car lenght)
Fig. 5: Safe Distance Description for HV
leading vehicle should not become smaller than a minimum
gap of 30m [54], while in the optimistic driving style, it is
assumed that the car in front brakes as well, and the safe
distance takes care of the situation. During reaction time, the
vehicle moves by:
sr=v·tr(19)
However, based on the above assumptions, the safe distance
between vehicles is set to constant for the AVs and varies for
the HVs. The safe distance values are measured in seconds,
effectively describing the distance related to the current car
speed. Condition 1 implies that the braking distance that the
leading vehicle needs to come to a complete stop is given by
s=v2
1
2·a(20)
From condition 2 it follows that to come to a complete stop,
the driver of the considered vehicle needs not only braking
distance v2
2b, but also an additional reaction distance vδt
travelled during the reaction time (the time to decode and
execute the breaking instruction needed).
Consequently, the stopping distance is given by
δx =vδt +v2
2·b(21)
Finally, condition 3 is satisfied if the gap ’s’ exceeds the
required minimum final value of 0 by considering the stopping
distance.
δx =δt +v2
2b
−
v2
1
2·b(22)
The speed ’v’ for which the equal sign holds (the highest
possible speed) defines the “safe speed”
vsafe(s, v1) = b·δt +pb2δt2+ 2 ·(s−s0)(23)
What happens in a situation where the car in front applies
an automatic break? It would help if you had time (reaction
time) to use an automatic brake to avoid collision with the
available space and stop. If v = 40 m/s on the motorway, then
20 m distance to start braking time is ideal using the 2 secs
rule proposed by [55].
Condition for the minimum distance y[m] from the lead
vehicle
If the distance between the lead vehicle and the next is greater
than the calculated value of y, the merging AV decides to enter
the intersection.
b) For AV:
y=v·t(24)
Where
•t[s] = Transit time of the T-junction
•v[km/h]= velocity of coming vehicle
y can be related to the intersection capacity estimates by
c=v·y(25)
and
y=lcar +treaction ·v+a·v2·t(26)
Where
•lcar = vehicle length
•t = reaction time
•a= deceleration rate
•v = speed
Going by the above analysis equations, the inter-vehicle
distance for the different car categories can be driven as:
c) For HV:
y=v·(t+ 1.8) (27)
Where the constant 1.8 is the inter vehicle time of transit for
HV
However, considering the human anxiety due to AV by adding
a stopping distance d for safety.
We have
y=v·t·d(28)
where d is the safe distance.
The stopping, braking and reaction time were enumerated
for clarity
ss=v0·tl+v02
2
·aF(29)
Model Validation Process
Figures 6 and 7 represents two different speed graph scenar-
ios of two cars straight movement model without braking and
two cars straight movement model with braking, respectively.
This model validation is a confirmation that the developed
model is predictive under the conditions of its intended use.
From Figure 7, using the first in - first out approach, the first
human vehicle is followed by the first autonomous vehicle
and, so on, based on the first to arrive, has the right of way.
Also, note the similarities in the plots, where aggressive cars
1 and 2 approaching a curve have a similar velocity pattern to
gentle cars 1 and 2 that slow down to keep a safe distance.
Simulation Parameter Values
For a real traffic system behaviour and better control on the
parameters of the experiments given the dimensions of the
road stated in the Figure 2, the following parameter values
were used:
•Vmax = 10m/s (maximum velocity)
•Amax =9.9m/s2(maximum acceleration)
•Dmax =−9.9m/s2(maximum declaration)
•MCar = 1200kg (mass of car)
•Fm= 2200N (moving force)
•Fb= 1200N (braking force).
•C = 100 cars (intersection capacity)
Fig. 6: Two cars straight movement model
Fig. 7: Two cars straight movement model with braking
B. Traffic Flow Model
The traffic state
q=k.vt(30)
(where q = volume, v = speed and k = density)
vk=Vf−
vf
kmax
·k=vf(1 −
k
kmax
)(31)
where vf= free flow speed kmax = max traffic density
from equation 1 and 2 , we have :
qk=vf·(k−k2
kmax
)(32)
1) Traffic Flow Procedure:
•Autonomous and Human-driven vehicles are filled out;
let’s say HVs is on-road A and AVs, on-road B for
simplicity. Road A is a straight road, and the HVs proceed
without making any turns or bends.
•While road B merges or joins road A midway at node 8
after a curve and at an intersection.
•The AVs on approaching the curve, slow down con-
siderably and, depending on how close they are to the
intersection node 8, get a sense of how far the other car
(HV) might be from the nearest RVC server or node.
•More importantly, the RVC server judges how far away
both vehicles are from each other.
•The RVC then uses this information to grant RN to
vehicle. It signals the AV to decelerate, keep moving or
halt and displays a traffic signal for the human driver in
the HV that prompts them to move or slow down or halt.
•As a result of this, other cars behind the car that slows
down while communicating with an RVC node or due to
traffic or while arriving at an intersection will also slow
down to obey the safe-distance model by judging how
far they are from the car ahead of them (which is where
Inter-Vehicle Communication applies).
•At this point, two vehicles from different roads obey
the merging algorithm rule before fusing together and
forming a platoon.
Vehicle movement algorithm
However, looking ahead on how the cars will decide on
their movement to the target, each vehicle has a defined route
by identifying all the node-id along its trajectory or path
between the start node and the destination node, then analysing
each of the nodes within each identified route according to a
metric function value calculated for each identified route. The
measured function may include parameters associated with
each of the road nodes in the system, including a node-to-
node distance parameter, traffic movement rules, crossing time,
straight and curve movement model.
During Platooning, the safe distance is maintained at 5m
for AVs and 7m for HVs respectively.
For AVs:: ncars = 2972.9/(5 + 4.5)
ncars = 312.93(approx.)
Therefore, ncars = 312 cars for AVs
Algorithm 2: Car Movement Algorithm
function Start to destination node movement;
Assign vehicle type upon entering the intersection
zone ;
1for Car movement is equal true do
Carspeed =carv elocity multiply by the
carmagnitude;
carvelocity on xaxis = speed multiply by
cosine theta;
carvelocity on yaxis = speed multiply by sin θ.
2for Car movement is equal to False: do
3Decelerate by initialising the acceleration to
zero;
Stop
end
caracceleration on xaxis = 0.0;
caracceleration on yaxis = 0.0;
Carspeed =carv elocity multiply by the
carmagnitude;
carvelocity on xaxis = speed multiply by cosineθ;
4carvelocity on yaxis = speed multiply by sinθ;
5for All the next node is a Road node do
6if node is a valid RoadNode object;
7check edges and append connected nodes to
destination list;
8append this node to destination lists of
connected node;
9Decelerate the car by multiplying the
acceleration by 0;
Stop
end
end
For HVs:: ncars = 2972.9/(7 + 4.5)
ncars = 258.51 (approx)
Therefore, ncars = 258 for HVs
Based on the above calculations, the road capacity for the
different category of cars are calculated as follow:
•capacity for AVs = 396 cars
•capacity for HVs = 312 cars of the road
The vehicle describes a curved circular path perfectly when
the front wheels turn at an angle 0θ0, while the car maintains a
constant speed. For optimal performance, keep the car speed
constant while the physics of turning is simulated at low speed
and high speed. Car wheels can sometimes have a velocity
not aligned with the wheel orientation, and this is because,
at high speed, one observes that the wheel can be heading in
one direction while the car body is still moving in another
direction. This means a velocity component is at a right angle
to the wheel, which generates frictions.
capacity = max traffic volume:
q=k.vt(33)
density
k=1
vTh+L(34)
Th= time gap(temporal distance) L = length of vehicle
HA:
Ch=qmax =v
vTh+L(35)
a) VA:
Ca=v
vTa+L(36)
When HV and AV are combined togethe, one will be able o
generate the expected impact of AV on HV when implemented
on a graph with varying parameters.
Ca
Ch
=vTh+L
vTa+L(37)
For traffic mix, n represent Av
capacity cm is now dependent on n
n represent the ratio of AV integrated into the road.
cm =v
nvT a + (1 −n)vTh+Lpkw (38)
Considering an additional distance by AV to a vehicle
steered by HV to avoid harassment of drivers
cm =1
n2vT aa +n(1 −n)vTah + (1 −n)vThx +L(39)
Road traffic capacity estimation approach:
1) Shortening of headway between Av
2) Speed of the vehicle group. The higher the speed at a
constant density, the higher the traffic volume
IV. EXPERIMENTS
Collision Avoidance with Save Distance (CAwSD) Control
Method
The collision avoidance techniques describe how the inter-
action between traffics and the road system is represented as a
chain of conflict points as proposed by Gipps [56]. There is no
requirement for a phase assignment or cycle time compared
with the traffic light control method. At each time, traffic
arriving at the intersection check to know if another traffic
shares the collision points along its trajectory. The vehicle ar-
riving parameters of position, speed, time are used to calculate
which vehicle would be given way to the collision point in a
real traffic situation. On arrival at the intersection, conflicting
vehicles cannot enter the intersection simultaneously when
they share the same collision point but can move concurrently
on intersection as it provides that they do not share the same
collision point simultaneously. This method takes an analytical
approach by calculating the probability of traffics arriving
at a conflict point simultaneously and the subsequent delay.
When vehicles are sharing the same collision point from a
different route, they might eventually collide. Naturally, the
major problem will arise from human-controlled vehicles as
their behaviour is stochastic, and they are more prone to errors
in prediction. Consideration is based on two types of vehicles
which varies in their maximum velocities; slow (Vs)and fast
(Vf)which denotes the fraction of the slow and fast vehicles,
respectively.
Inter-vehicle space adjustment with reservation node technique
This proposed technique is a reservation-based algorithm
that schedules the vehicles’ entrances into the intersection
space by reserving a collision cell to one particular vehicle
every instance. The process of using the intersection collision
point is based on a request, and reservations are made based on
a predefined protocol before vehicles can pass. This efficient
schedule is formulated to calculate the vehicle’s relative speed
to the reservation cell and assign a vehicle sequence. Car’s
distances to other cars before it is calculated and the minimum
distance to the reservation node is found. After this, the
environment’s central collision avoidance system signals the
car to brake, decelerate, and, if not, to keep going. The safe
vehicle distance, reaction time, and relative distance model are
proposed to maximise the delay and reduce the probability of
accidents at cross collision points. This traffic management
strategy is a decentralised strategy where drivers and vehicles
communicate and negotiate for access to the cross collision
point based on their relative distance and access priority to
the intersection.
V. RESULT DISCUSSION AND EVA LUATION
To test the hypothesis, which states that vehicles move more
efficiently when the road intersection cell and reserved. With
the adjustment of the Avs inter-vehicle distance, the per-
formance of HVs increases, and the vehicle’s occupation
time increases with an increase in the ratio of human-driven
vehicles. An analysis of variance in the time analysis of
different ratio simulation tests is conducted fig. 10 which gives
statistics for the variation in time occupancy with vehicle mix
ratio. This is due to the difference in the behavioural aspects
of human-driven and driver-less cars.
Stability:
In the contest of this research, traffic flow stability as
represented in Figure 12 is analysed with the number of traffic
braking in response to the volume for the different control
methods under the same condition. The traffic flow efficiency
at road intersections depends partly on traffic flow stability
which is analysed with the number of braking associated with
a control method. The traffic stability could be accessed from
the uniformity of the flow speed. It is a state where all cars
move with an identical safe distance and optimal velocity. A
speed fluctuation impacts the vehicle flow stability when in
motion. It is observed that the different traffic control methods
are associated with varying levels of stability. The vehicle safe
distance process involves deceleration and acceleration, which
causes a perturbation in the stability of the overall flow.
Number of cars/hr
RN TL CAWSD
Experiment Method
50
100
150
200
250
300
Fig. 8: 50% Capacity
Number of cars/hr
RN TL CAWSD
Experiment Method
50
100
150
200
250
300
Fig. 9: 100% Capacity
Travel Time Delay
Figure 11 represents the travel time delay associated with
the different traffic control strategies. It is evident inFigure 11
Fig. 10: Vehicle Occupancy Matrix
Experiment Method
Waiting number of cars /min
TL
RN CAWD
10
20
30
40
50
Fig. 11: Travel time delay
that the RN traffic control strategy expenses the shortest
queues of cars. Depending on the intersection-specific condi-
tions, delay anal- yses for transportation system plans, trans-
portation planning rule (TPR) may be required for operational
research. Traffic congestion is often associated with stop-and-
go traffic, slower speeds, longer travel times, and increased
vehicular queuing as its characteristics. These characteristics
could be quantified by the number of vehicles waiting for
access permission around the intersection. It is the cumulative
effect of these delays that makes up the overall travel time.
DISCUSSIONS
The proposed methodology for analysing the impact of mixing
AVs and HVs will help determine the integration pattern of
an autonomous vehicle for the mixed vehicle transition period.
In addition, traffic engineers can use the models developed in
this study to estimate the capacity of a road intersection in a
mixed-traffic environment. This investigation discovered that
autonomous vehicles are much safer, time-efficient, and help
decongest roads. Figures 8 and 9 represents the simulation
result of the intersection performance under half number
of vehicle and full number of vehicles, respectively. It is
evident from Figure 9 that intersection efficiency increases
with an increase in the ratio of an autonomous vehicle. This is
because AVs combine and interpret their surroundings’ sensory
data to identify appropriate navigation paths, obstacles, and
appropriate signage. The measure of intersection efficiency
is conducted using traffic parameters performance metrics
relating to throughput and delay. The Performance for different
traffic control strategies is analysed using different parameter
values based on simulations to see the effect of their values
on the system’s throughput performance.
The values of the vehicle mixed ratio were increased in
every simulation to establish the impact of the ration variation
to guide the integration pattern. The Performance of different
ratio cases is analysed and compared under the three traffic
control methods. This trend makes the HV benefit inefficiency
from the AV in a co-existence scenario.
VI. CONTRIBUTIONS TO KNOWLEDGE
In the cause of this work, some new knowledge based on
the previously available knowledge has been created. They
include
•Guide to mixing traffic integration pattern
•Describe 2-D mix-traffic behaviour effectively
•Increases HVs performance when AV inter-vehicle dis-
tance is adjusted
•A speed harmonisation method for mixed traffic
•Serves as a mixed driving behaviour model
VII. FUTURE RESEARCH DIRECTION
Future research work could improve the mixed traffic man-
agement scheme in the following four main categories:
Drivers Behaviour Models
•Incorporate the drivers’ decision to accept or reject RN
offer
Number of braking per hr
Experimenet Method
RN TL CAWSD
500
1000
1500
2000
2500
0
Fig. 12: The Number of Braking Occurred
•Investigate the factors that influence the driver’s be-
haviour
Vehicle Models
•Model varying vehicle lengths to reflect the real city
traffic situation
Road Intersection Model
•Extend the strategy to a multi-lane, multi intersection road
network
•Investigate the cooperation level between AV and HV
Traffic Flow Model
•Investigate the effect of safe distance and reaction time
distribution
•Apply Machine Learning to control traffic and provide
real-life physics
•Investigate non-compliance to an emergency
VIII. CONCLUSION
The novelty of the mixed traffic speed adjustment strategy is
that it harmonise the AVs and HVs vehicle speed, thereby
increasing the flow efficiency. Secondly, by addressing a 2-
dimensional traffic flow problem in heterogeneous traffic,
an existing 1-dimensional car-following model compensates
for unexpected changes in human-driven vehicles. The al-
gorithm controls the mix-traffic variable speed bottleneck
to smooth the traffic flow effectively. Using the acceptance
safe distance model, this proposed model entails interpolating
human-driven and autonomous vehicles’ behaviour with inter-
vehicle distance adjustment. The above strategy has been
implemented on the developed model and calibrated with
realistic parameters, vehicle distribution, and vehicle ratio
mixes. The concept of the cell reservation method appears
to be efficient as it centrally synchronises both AH and HV
parameters simultaneously. The feature of real-time traffic
parameter sharing in AV makes predicting vehicle velocities
in managing traffic possible. This work provides scientific
support for the integration plan of autonomous vehicles and
a mixed traffic control system. It will improve mixed-traffic
efficiency, mitigate traffic congestion at road intersections, and
provide technical support for future research in traffic control
systems. A mix of human-driven and automated vehicles is
gradually becoming the norm around the world. The large-
scale advancement and application of new technologies in
vehicle and traffic management will greatly promote urban
traffic control systems and support a full-scale intelligent
transportation system. The developed AVHV model behaviour
appears to be able to reasonably mimic the behaviour of
mixed traffic with parameters consistent in the behaviour of
the mixed traffic and simulated flow. The combined behaviour
of the traffic is mainly controlled by the distribution of the
harmonised speed, safe distance distribution, and the number
of braking. In contrast, the reaction time distribution controls
the individual vehicle behaviour, and the vehicle length. The
experimental results show a well-harmonised vehicle group
speed at every instance of time.
The cell reservation method has investigated the effect of
driverless cars on human-driven cars at a merging road in-
tersection using inter-vehicle distance. The vehicle occupation
time is observed at a merging road, and mixed mathematical
relations relating to occupation time of different vehicle types
were developed. From our findings, a vehicle ratio occupancy
pattern was developed to serve as a valuable tool for evaluating
the integration process of autonomous cars on the road. The
key conclusions arising out of this study were:
1) Traffic flow efficiency increases when road intersection
cells are reserved.
2) It has been established that the integration of au-
tonomous cars on the road will positively impact the
efficiency of human-driven cars.
3) The vehicle occupancy time depends on the traffic mixed
ratio.
A. Summary
Related traffic technologies have been developed to support
the autonomous vehicle integration process, which is essen-
tial for effectively utilizing autonomous vehicles’ benefits. A
Mathematical model describes the two types of vehicle mixed
behaviour to the occupation time with the traffic flow in a
merging T-junction. It has been observed that the vehicle
occupation time in a mixed traffic flow increases with a
higher ratio of an autonomous vehicle. Also, the throughput
increases by adjusting the inter-vehicle distance. The proposed
methodology will be helpful to determine the integration
pattern of an autonomous vehicle for the mixed vehicle
transition period. Also, the models developed in this research
can be used by traffic engineers to estimate the capacity of a
merging road intersection in a mixed traffic environment. The
investigation discovered that autonomous cars are much safer,
time-efficient, and help decongest roads. The work done so far
represents steps towards a system of safe and efficient mixed
traffic management schemes to implement a mixed traffic
integration environment. It is an important goal as reliance
on these autonomous cars is ever increasing, the objectives
of this project have been identified, autonomous cars have
come to stay and co-exist with human-driven cars inevitable.
Towards this end, a promising method of managing traffic mix
is realisable. The generated experimental results promise to
produce a traffic schedule that will sustain state of art in mixed
traffic environment management.
The results obtained are based on an intersection capacity
of 100 cars with a varying ratio mixed of autonomous and
human-driven cars. Looking at the result in fig. 10, it is
observed that the obtained result shows that an increase in
the ratios of autonomous cars is inversely proportional to a
decrease in the simulation time, and this supports the research
hypothesis. Hence, we conclude that the intersection efficiency
increases with the ratio of autonomous cars to human-driven
cars, which shows that autonomous cars improve traffic effi-
ciency. We have examined the potential impact of integrating
autonomous cars to co-exist with human-driven cars on the
road. The assessment was carried out under parameters that
align with the realistic operating environment of the city traffic
flow system. Modern traffic lights use real-time event-driven
control models but are designed to model a homogeneous
traffic system. However, the AVHV control model supports
a traffic schedule with a traffic signal light to control HVs
and wireless communications for controlling AVs. This control
method involves the dynamic representation of a mix-traffic
system at road intersections to help plan, design better, and
operate traffic systems moving it through time. The research
direction taken was the utilisation of reservation cells to
improve the traffic flow performance. By reserving any of the
12 intersection reservation cells for a vehicle at every instance,
the traffic flow throughput increases better than when using
traffic light or collision avoidance methods. To quantify the
benefit of the proposed Node Reservation strategy, a simulator
is developed, and three traffic management strategies are in-
tegrated: traffic light control method, collision avoidance with
safe distance method, and the node reservation method. The
proposed simulation model is validated, and experiments are
conducted with varying traffic intersection control strategies
and vehicle type proportions. The obtained results demonstrate
that the node reservation strategy has a high throughput with
minimal delay and braking.
ACK NOW LE DG EM EN TS
This research is part of the outcome of my PhD research
which was funded by the Nigerian Tertiary Education Trust
Fund.
AUTHOR INFORMATION
Computer Science Department, University of Reading, Uk.
Ekene Ozioko, Dr. Julian Kunkel and Dr. Fredrick Stahl
CORRESPONDING AUTHOR
Correspondence to e.f.ozioko@pgr.reading.ac.uk
IX. AUTHORS’CONTRIBUTION
REFERENCES
[1] G. M. Arnaout and J.-P. Arnaout, “Exploring the effects of cooperative
adaptive cruise control on highway traffic flow using microscopic traffic
simulation,” Transportation Planning and Technology, vol. 37, no. 2, pp.
186–199, 2014.
[2] S. Huang and W. Ren, “Autonomous intelligent vehicle and its perfor-
mance in automated traffic systems,” International Journal of Control,
vol. 72, no. 18, pp. 1665–1688, 1999.
[3] S. Gong and L. Du, “Cooperative platoon control for a mixed traffic
flow including human drive vehicles and connected and autonomous
vehicles,” Transportation research part B: methodological, vol. 116, pp.
25–61, 2018.
[4] E. Chan, P. Gilhead, P. Jelinek, P. Krejci, and T. Robinson, “Co-
operative control of sartre automated platoon vehicles,” in 19th ITS
World CongressERTICO-ITS EuropeEuropean CommissionITS Ameri-
caITS Asia-Pacific, 2012.
[5] J. J. B. Vial, W. E. Devanny, D. Eppstein, and M. T. Goodrich, “Schedul-
ing autonomous vehicle platoons through an unregulated intersection,”
arXiv preprint arXiv:1609.04512, 2016.
[6] M. Dutta and M. A. Ahmed, “Gap acceptance behavior of drivers at
uncontrolled t-intersections under mixed traffic conditions,” Journal of
modern transportation, vol. 26, no. 2, pp. 119–132, 2018.
[7] G. Asaithambi and C. Anuroop, “Analysis of occupation time of vehicles
at urban unsignalized intersections in non-lane-based mixed traffic
conditions,” Journal of Modern Transportation, vol. 24, no. 4, pp. 304–
313, 2016.
[8] S. Tripathy, K. Asaithambi, P. Jayaram, and R. Medhamurthy, “Analysis
of 17β-estradiol (e 2) role in the regulation of corpus luteum function
in pregnant rats: involvement of igfbp5 in the e 2-mediated actions,”
Reproductive Biology and Endocrinology, vol. 14, no. 1, p. 19, 2016.
[9] W. Zhao, D. Ngoduy, S. Shepherd, R. Liu, and M. Papageorgiou,
“A platoon based cooperative eco-driving model for mixed automated
and human-driven vehicles at a signalised intersection,” Transportation
Research Part C: Emerging Technologies, vol. 95, pp. 802–821, 2018.
[10] Z. Yang, Y. Feng, and H. X. Liu, “A cooperative driving framework for
urban arterials in mixed traffic conditions,” Transportation research part
C: emerging technologies, vol. 124, p. 102918, 2021.
[11] N. AbuAli and H. Abou-zeid, “Driver behavior modeling: Developments
and future directions,” International journal of vehicular technology, vol.
2016, 2016.
[12] M. S. Young, S. A. Birrell, and N. A. Stanton, “Safe driving in a green
world: A review of driver performance benchmarks and technologies to
support ‘smart’driving,” Applied ergonomics, vol. 42, no. 4, pp. 533–
539, 2011.
[13] J. Ferreira, E. Carvalho, B. V. Ferreira, C. de Souza, Y. Suhara,
A. Pentland, and G. Pessin, “Driver behavior profiling: An investigation
with different smartphone sensors and machine learning,” PLoS one,
vol. 12, no. 4, p. e0174959, 2017.
[14] R. Fuller, “Towards a general theory of driver behaviour,” Accident
analysis & prevention, vol. 37, no. 3, pp. 461–472, 2005.
[15] Y. Liu and U. Ozguner, “Human driver model and driver decision making
for intersection driving,” in 2007 IEEE Intelligent Vehicles Symposium.
IEEE, 2007, pp. 642–647.
[16] D. D. Salvucci, “Modeling driver behavior in a cognitive architecture,”
Human factors, vol. 48, no. 2, pp. 362–380, 2006.
[17] F. Biondi, I. Alvarez, and K.-A. Jeong, “Human–vehicle cooperation
in automated driving: A multidisciplinary review and appraisal,” Inter-
national Journal of Human–Computer Interaction, vol. 35, no. 11, pp.
932–946, 2019.
[18] J. Van Brummelen, M. O’Brien, D. Gruyer, and H. Najjaran, “Au-
tonomous vehicle perception: The technology of today and tomorrow,”
Transportation research part C: emerging technologies, vol. 89, pp. 384–
406, 2018.
[19] G. Prescinotti Vivan, N. Goberville, Z. Asher, N. Brown et al., “No cost
autonomous vehicle advancements in carla through ros,” SAE Technical
Paper, pp. 01–0106, 2021.
[20] B. Friedrich, “The effect of autonomous vehicles on traffic,” in Au-
tonomous Driving. Springer, 2016, pp. 317–334.
[21] M. L. Maitre and A. Prorok, “Effects of controller heterogeneity on
autonomous vehicle traffic,” arXiv preprint arXiv:2005.04995, 2020.
[22] P. Dro´zdziel, S. Tarkowski, I. Rybicka, and R. Wrona, “Drivers’ reaction
time research in the conditions in the real traffic,” Open Engineering,
vol. 10, no. 1, pp. 35–47, 2020.
[23] R. Liao, “Smart mobility: Challenges and trends,” Toward Sustainable
And Economic Smart Mobility: Shaping The Future Of Smart Cities,
p. 1, 2020.
[24] L. C. Bento, R. Parafita, and U. Nunes, “Intelligent traffic management at
intersections supported by v2v and v2i communications,” in 2012 15th
International IEEE Conference on Intelligent Transportation Systems.
IEEE, 2012, pp. 1495–1502.
[25] K. Benhamza, S. Ellagoune, H. Seridi, and H. Akdag, “Agent-based
modeling for traffic simulation,” in Proceedings of the International
Symposium on Modeling and Implementation of Complex Systems
MISC2010, Constantine, Algeria, 2010, pp. 30–31.
[26] H. Fujii, H. Uchida, and S. Yoshimura, “Agent-based simulation frame-
work for mixed traffic of cars, pedestrians and trams,” Transportation
research part C: emerging technologies, vol. 85, pp. 234–248, 2017.
[27] I. T. Haman, V. C. Kamla, S. Galland, and J. C. Kamgang, “Towards an
multilevel agent-based model for traffic simulation,” Procedia Computer
Science, vol. 109, pp. 887–892, 2017.
[28] B. N. Matcha, S. N. Namasivayam, M. Hosseini Fouladi, K. Ng,
S. Sivanesan, and S. Y. Eh Noum, “Simulation strategies for mixed
traffic conditions: A review of car-following models and simulation
frameworks,” Journal of Engineering, vol. 2020, 2020.
[29] A. K. Budhkar and A. K. Maurya, “Multiple-leader vehicle-following
behavior in heterogeneous weak lane discipline traffic,” Transportation
in developing economies, vol. 3, no. 2, p. 20, 2017.
[30] T. V. Mathew, C. R. Munigety, and A. Bajpai, “Strip-based approach
for the simulation of mixed traffic conditions,” Journal of Computing in
Civil Engineering, vol. 29, no. 5, p. 04014069, 2015.
[31] M. A. S. Kamal, J.-i. Imura, A. Ohata, T. Hayakawa, and K. Aihara,
“Coordination of automated vehicles at a traffic-lightless intersection,”
in Intelligent Transportation Systems-(ITSC), 2013 16th International
IEEE Conference on. IEEE, 2013, pp. 922–927.
[32] B. Van Arem, C. J. Van Driel, and R. Visser, “The impact of cooperative
adaptive cruise control on traffic-flow characteristics,” IEEE Transac-
tions on Intelligent Transportation Systems, vol. 7, no. 4, pp. 429–436,
2006.
[33] J. Ploeg, A. F. Serrarens, and G. J. Heijenk, “Connect & drive: design
and evaluation of cooperative adaptive cruise control for congestion
reduction,” Journal of Modern Transportation, vol. 19, no. 3, pp. 207–
213, 2011.
[34] M. Omae, T. Ogitsu, N. Honma, and K. Usami, “Automatic driving
control for passing through intersection without stopping,” International
Journal of Intelligent Transportation Systems Research, vol. 8, no. 3,
pp. 201–210, 2010.
[35] Y. Zhou, S. Ahn, M. Chitturi, and D. A. Noyce, “Rolling horizon
stochastic optimal control strategy for acc and cacc under uncertainty,”
Transportation Research Part C: Emerging Technologies, vol. 83, pp.
61–76, 2017.
[36] D. Swaroop, J. K. Hedrick, C. Chien, and P. Ioannou, “A comparision
of spacing and headway control laws for automatically controlled
vehicles1,” Vehicle system dynamics, vol. 23, no. 1, pp. 597–625, 1994.
[37] B. Khondaker and L. Kattan, “Variable speed limit: A microscopic
analysis in a connected vehicle environment,” Transportation Research
Part C: Emerging Technologies, vol. 58, pp. 146–159, 2015.
[38] Y. Feng, K. L. Head, S. Khoshmagham, and M. Zamanipour, “A
real-time adaptive signal control in a connected vehicle environment,”
Transportation Research Part C: Emerging Technologies, vol. 55, pp.
460–473, 2015.
[39] S. Knorn, A. Donaire, J. C. Agüero, and R. H. Middleton, “Passivity-
based control for multi-vehicle systems subject to string constraints,”
Automatica, vol. 50, no. 12, pp. 3224–3230, 2014.
[40] M. Wang, W. Daamen, S. P. Hoogendoorn, and B. van Arem, “Rolling
horizon control framework for driver assistance systems. part ii: Coop-
erative sensing and cooperative control,” Transportation research part
C: emerging technologies, vol. 40, pp. 290–311, 2014.
[41] F. Duarte and C. Ratti, “The impact of autonomous vehicles on cities:
A review,” Journal of Urban Technology, vol. 25, no. 4, pp. 3–18, 2018.
[42] R. Hussain and S. Zeadally, “Autonomous cars: Research results, issues,
and future challenges,” IEEE Communications Surveys & Tutorials,
vol. 21, no. 2, pp. 1275–1313, 2018.
[43] D. Chen, A. Srivastava, S. Ahn, and T. Li, “Traffic dynamics under
speed disturbance in mixed traffic with automated and non-automated
vehicles,” Transportation research procedia, vol. 38, pp. 709–729, 2019.
[44] K. van Wees and K. Brookhuis, “Product liability for adas; legal
and human factors perspectives,” European Journal of Transport and
Infrastructure Research, vol. 5, no. 4, 2020.
[45] N. M. Pawar and N. R. Velaga, “Modelling the influence of time pressure
on reaction time of drivers,” Transportation research part F: traffic
psychology and behaviour, vol. 72, pp. 1–22, 2020.
[46] R. W. Rothery, “Car following models,” Trac Flow Theory, 1992.
[47] D. Miloradovic, J. Glišovi´
c, N. Stojanovi´
c, and I. Gruji´
c, “Simulation
of vehicle’s lateral dynamics using nonlinear model with real inputs,” in
IOP Conference Series: Materials Science and Engineering, vol. 659,
no. 1. IOP Publishing, 2019, p. 012060.
[48] A. Kesting, M. Treiber, and D. Helbing, “General lane-changing model
mobil for car-following models,” Transportation Research Record, vol.
1999, no. 1, pp. 86–94, 2007.
[49] N. N. N. Azlan and M. M. Rohani, “Overview of application of traffic
simulation model,” in MATEC Web of Conferences, vol. 150. EDP
Sciences, 2018, p. 03006.
[50] T. Mathew, “Lecture notes in transportation systems engineering,”
Indian Institute of Technology (Bombay), http://www. civil. iitb. ac.
in/tvm/1100_LnTse/124_lntse/plain/plain. html, 2009.
[51] W.-X. Zhu and H. Zhang, “Analysis of mixed traffic flow with human-
driving and autonomous cars based on car-following model,” Physica A:
Statistical Mechanics and its Applications, vol. 496, pp. 274–285, 2018.
[52] U. transport autority, “Driving test success is the uk’s copyright
2020 - driving test success,” https://www.drivingtestsuccess.com/blog/
safe-separation- distance, May 2020.
[53] H. Li, S. Li, H. Li, L. Qin, S. Li, and Z. Zhang, “Modeling left-
turn driving behavior at signalized intersections with mixed traffic
conditions,” Mathematical Problems in Engineering, vol. 2016, 2016.
[54] P. Lertworawanich, “Safe-following distances based on the car-following
model,” in PIARC International seminar on Intelligent Transport System
(ITS) in Road Network Operations, 2006.
[55] M. Saifuzzaman, Z. Zheng, M. M. Haque, and S. Washington, “Re-
visiting the task–capability interface model for incorporating human
factors into car-following models,” Transportation research part B:
methodological, vol. 82, pp. 1–19, 2015.
[56] P. G. Gipps, “A behavioural car-following model for computer simula-
tion,” Transportation Research Part B: Methodological, vol. 15, no. 2,
pp. 105–111, 1981.
