muntaser a. salman, estimating intersection traffic ...muntaser a. salman, college of computer...
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REVISTA AUS 26-2 / Muntaser A. Salman et al.,/ DOI:10.4206/aus.2019.n26.2.25/ www.ausrevista.com/ [email protected]
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ABSTRACT/ Vehicular networks have become an attractive traffic conditions surveillance method. Ratio of number of vehicles equipped with
communication capability to the total number of vehicles with time, known as penetration rate, is the major factor that influence this
method. Traffic congestion can be estimated based on either static or dynamic measurements. For static measurements, such as count of
vehicles or average speed of vehicles can be utilized through vehicle to vehicle (V2V) communication. V2V communication based traffic
congestion estimation can be represented as an optimization problem (i.e. finding minimum PR with good estimation accuracy). In dynamic
measurements, such as period of sensing or vehicles' presence can be utilized through vehicle to infrastructure (V2I) communication. In the
same time an estimation problem can be represented as a real time model designing (i.e. finding time-dependent model cover the lack of
knowledge of vehicles information). In this context, traffic congestion estimations that utilize vehicle to everything (V2X) communication
require both static and dynamic measurements to be taken into consideration. To fulfill these measurements requirements, a new approach
has been proposed in this paper based on delay time estimation model under different PR. Average delay time is the major indicator for such
measurements requirements. Delay time can be measured and estimated based on three categorized: acceleration, deceleration and stopped
delay. To estimate these categories fuzzy system using average speed of vehicle or group of vehicles (and its derivative) is proposed in this
paper. The proposed approach is simulated using COLOMBO framework with suitable modifications and investigated under different PR.
Simulation results reveal that the proposed approach can estimate traffic delay for the whole intersection as well as for each incoming and
outgoing edge. These results, encourage us to propose a simple procedure for traffic congestion estimation and evaluation, that is suitable
for traffic light controller in future work even under low PR.
Keywords: Traffic congestion; estimation; V2X communication; intersection; fuzzy system; acceleration, deceleration and stopped delay time.
RESUMEN/ Las redes vehiculares se han convertido en un método atractivo de vigilancia de las condiciones del tráfico. La relación entre el
número de vehículos equipados con capacidad de comunicación y el número total de vehículos con tiempo, conocida como tasa de penetración,
es el factor principal que influye en este método. La congestión del tráfico puede estimarse en base a mediciones estáticas o dinámicas. Para
mediciones estáticas, como el recuento de vehículos o la velocidad promedio de los vehículos se pueden utilizar a través de la comunicación
de vehículo a vehículo (V2V). La estimación de congestión de tráfico basada en la comunicación V2V puede representarse como un problema
de optimización (es decir, encontrar un PR mínimo con buena precisión de estimación). En mediciones dinámicas, como el período de
detección o la presencia de vehículos, se puede utilizar a través de la comunicación de vehículo a infraestructura (V2I). Al mismo tiempo, un
problema de estimación puede representarse como un diseño de modelo en tiempo real (es decir, encontrar un modelo dependiente del
tiempo que cubra la falta de conocimiento de la información de los vehículos). En este contexto, las estimaciones de congestión de tráfico
que utilizan la comunicación del vehículo a todo (V2X) requieren que se tengan en cuenta las mediciones estáticas y dinámicas. Para cumplir
con estos requisitos de medición, se ha propuesto un nuevo enfoque en este documento basado en el modelo de estimación del tiempo de
retraso bajo diferentes PR. El tiempo de retraso promedio es el indicador principal para tales requisitos de medición. El tiempo de retraso
puede medirse y estimarse en función de tres categorías: aceleración, desaceleración y retraso detenido. En este documento se propone
estimar el sistema difuso de estas categorías utilizando la velocidad promedio del vehículo o grupo de vehículos (y su derivada). El enfoque
propuesto se simula utilizando el marco COLOMBO con modificaciones adecuadas y se investiga bajo diferentes PR. Los resultados de la
simulación revelan que el enfoque propuesto puede estimar el retraso del tráfico para toda la intersección, así como para cada borde entrante
Muntaser A. Salman, College of Computer Sciences and Information Technology, University of Anbar, Iraq [email protected] Suat Ozdemir, Computer Engineering Department
Gazi University, Turkey [email protected] Fatih Vehbi Celebi Computer Engineering Department Ankara Yildirim Beyazit University, Turkey [email protected]
Estimating Intersection Traffic Congestion through
V2X Communication
Estimación de la congestión del tráfico de intersección a
través de la comunicación V2X
Recepción/ 27 junio 2019
Aceptación/ 25 agosto 2019
REVISTA AUS 26-2 / Muntaser A. Salman et al.,/ DOI:10.4206/aus.2019.n26.2.25/ www.ausrevista.com/ [email protected]
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y saliente. Estos resultados nos animan a proponer un procedimiento simple para la estimación y evaluación de la congestión del tráfico, que
sea adecuado para el controlador del semáforo en el trabajo futuro, incluso bajo PR bajo.
Palabras clave: congestión del tráfico; Estimacion; Comunicación V2X; intersección; sistema difuso aceleración, desaceleración y tiempo de
retraso detenido.
1. Introduction
An intersection is the key node to urban
scenario where space is shared by more than
one edge at a time. Traffic signals used for
such intersection to solve its sharing in time
and space. Estimating traffic congestion of
such intersection, with time and space sharing,
is a difficult task. There are a number of
measures that have been used in this context,
delay is the most important one. This is
because it is directly related to the time loss
that a vehicles experience while crossing an
intersection. Another reason may be it is an
essential indicator of level of service (LOS) in
a signalized intersection.
However average delay time is a static
measure that is not easily determined due to
the dynamic behavior of vehicles at the
intersection. Most of the traditional
technologies (i.e. inductive loop, camera,
radar … etc.) used mathematical models to
describe arrival and departure of vehicles in
dynamic manners. These models have been
proved to work under specific traffic condition
with an assumption to simplify the complexity
of model’s behavior. On the other hand,
recently emerged technologies (more
specifically vehicular communication networks
based) proposed with higher potential to
monitor dynamic behavior of vehicles. Main
factor that influence this technology is PR.
From dynamic point of view, with high PR the
stability of clustering algorithm that is required
for dynamic behavior consideration is
increased, but wireless channel traffic load will
increase as well (i.e. decrease the accuracy of
communications). This is done through either
the continuous exchange of information
between vehicles with V2V communications or
between vehicles and infrastructure nodes with
V2I communications or cooperative of them
with V2X communications. On the other hand,
i.e. from static point of view, with high PR
average delay time for vehicle or group of
vehicles is increased, but the problem of
finding suitable dynamic model for measuring
delay time for vehicle or group of vehicle will
increase as well. This is because there are no
direct measurements for delay time. Though
estimation based on static measurements as
well as dynamic measurements are required.
Both of these points of view should be
considered. In this context, research is
required to estimate traffic congestion through
V2X communication while addressing static
and dynamic measurements under different
PR. This paper follow characteristics of both
traffic congestion and V2X communication with
different PR. More specifically, the dynamic
delay time under different PR is estimated
using fuzzy model. This is based on static
measurements using V2X communication
protocol with vehicles speed averaging.
Vehicles speed is effected with low PR. Thus,
more investigation is required in compared
with the existing literature for traffic
congestion estimation.
This is done here with many steps. First,
average speed for vehicle or group of vehicles
detected under low PR with V2X
communication protocols given in COLOMBO
framework is analyzed. Since delay time is the
summation of acceleration, deceleration and
stopped delay time. Thus, fuzzy delay
estimation system is proposed with three
outputs that represent delay categories. This is
done per edge per moment for each incoming
and outgoing edge based on its vehicles
average speed and their derivatives. In order
to have dynamic behavior for such estimation,
each incoming and outgoing edge averaged
delay time is accumulated with suitable
adaptation procedure. This procedure should
take into consideration the low PR issue. The
traffic congestion for each incoming and
outgoing edge, as well as for the intersection
as a whole, can be estimated with online
procedure based on their estimated average
delay time. In this context, a novel indicator
called accumulated delay percent (ADP) is
proposed with suitable adaptation procedure.
Where ADP is defined as the ratio of average
delay time estimated to vehicles sensed time
under communication coverage area.
The remainder of this article is organized as
follows. Section 2 presents related works on
traffic congestion estimation methods. Section
3 describes the proposed approach in details.
Section 4 analyzes the primary simulated
results collected so far. Evaluation of the
proposed approach is presented in Section 5.
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Discussions on conclusive remarks are
provided at the end of the paper.
2. Related Works
Recently European Framework Programme EU
FP has funded many projects in the field of
traffic surveillance method under vehicular
communication networks.
For instance, in V2V communication context,
the EU FP7 iTETRIS (2007-2010) project [1]
has developed six traffic efficiency intelligent
transportation system ITS applications. One of
them, the CoTEC distributed cooperative traffic
surveillance system [2] propose to rely on
cooperative V2V communications to guess the
density and speed of the neighboring vehicles.
They use fuzzy logic based on estimated traffic
in different LOS to map the density/speed to
the occurrence of a traffic jam without
deploying additional infrastructure nodes. The
traffic surveillance solutions shown to be
capable of detecting traffic congestion very
efficiently and at very little overhead (as it is
based on cooperative awareness messages,
CAMs). However, this solution has been
evaluated only on highway scenario based on
LOS defined by [3].
In V2I communications context, the EU FP6
SAFESPOT (2006-2010) project [4] has
demonstrated and tested a large number of
applications via vehicle and/or infrastructure
based. One of infrastructure based
applications, intelligent cooperative
intersection safety ICIS [5] propose to rely on
V2I communications to identify a safety
situation as fast as possible to prevent traffic
conflict and collision to be happened. Although
effective dynamic model of the vehicle’s
surrounding environment can be achieved, this
clearly has limits with low PR.
In V2X communications context, the EU FP7
COLOMBO (2012-2015) project [6] has
developed new protocols under urban
scenario. One of them, [7] propose to
determine traffic surveillance information
about local traffic conditions near traffic lights.
To update traffic surveillance information at
the RSU, a novel protocol is introduced. The
main idea of which is to group vehicles in traffic
light proximity in order to reduce the
communications needed. The traffic
surveillance solution is shown to be capable of
detecting average speed efficiently even under
low PR. However, this solution has been
simulated and evaluated for an abstract of
traffic conditions without neither traffic
congestion nor dynamic model estimation.
Most related solutions in the literature, based
on the powerful enabler of cooperative
vehicular communications, assume the
complete penetration rate over the targeted
vehicle population, thus making them not
applicable nowadays. Few research deals with
this issue. It is started with iTETRIS project for
traffic congestion estimation with highway
scenario and developed by COLOMBO project
for an intersection scenario. Recently,
Bellavista et al. [8] proposes an innovative
solution for cooperative traffic surveillance
based on vehicular communications capable of
working with low penetration rates and
collecting a large set of monitoring data about
vehicle mobility in targeted areas of interest.
They presents insights and lessons learnt from
the design and implementation work of the
proposed solution. Moreover, they reports
extensive performance evaluation results
collected on realistic simulation scenarios
based on the usage of iTETRIS platform with
real traces of vehicular traffic of the city of
Bologna. Their proposal solution capable to
estimate the real vehicular traffic till 10% of
penetration rate. This is done by direct effect
with measurements based on number of
vehicles counting. In our proposal, to
overcome the low PR issue, average traffic
delay is estimated independently on number of
vehicles (i.e. based just on their existing).
From the over mentioned projects, it is clear
that for vehicular communication networks
under low PR a dynamic delay model is
required to estimate traffic congestion at
signalized intersections. A lot of delay models
have been proposed but the oldest and the
most popular one is Webster’s delay model [9].
Although many researchers modified this
model (e.g. [10-13]), but all of these modified
models were developed for specific traffic
conditions. Modelling the relationship between
control delay and stopped delay of vehicles
under mix traffic conditions is done in [14].
Also researchers of [15-16] developed a model
to estimate average overall delay to mixed
traffic conditions. But acceleration and
deceleration delay component was not
considered in the modelling. Study done in
[17] used artificial neural networks with fuzzy
logic to estimate traffic delay. Another study in
[18] used data fusion model to handle more
types of data but demands less data transfer
for online traffic condition evaluation.
Most of the above-mentioned models analyze
delay time separately from its categories.
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Moreover, total delay alone does not reflect
traffic congestion dynamic at an important
time characteristics. Therefore, it is hard for
such analyses to draw deeper conclusions on
the true causes and patterns of intersection
delay. With the development of vehicular
communication networks reviewed, now it is
time to focus on the above issue with a novel
approach. In which, both static and dynamic
measurements can be included.
Promising solution to do that in an intersection
is the intersection-based geographic routing
protocol. Few surveys have been done in this
field, e.g. [19] and [20]. One of these surveys
done in [20], address some issues (one of
them traffic light at intersections) and suggest
important guidelines for network designers. In
this paper, a fuzzy system to estimate the
categories of signalized intersection delay
utilizing V2X communication is proposed.
Then, the proposed approach investigated
under different PR with suitable adaptation and
accumulation procedure to reflect traffic
congestion dynamic. Finally, simple criteria for
traffic congestion evaluation is extracted based
on LOS criteria. To the best of our knowledge,
this is the first attempt for traffic congestion
estimation and evaluation utilizing V2X
communication under different PR for an
intersection. The following subsection describe
our approach in details.
3. Proposed Approach
Our approach use V2X communications to
estimate the traffic congestion of a signalized
intersection by RSU. This is done by estimating
average delay time of vehicles as a direct
indicator while number of cars as a constraint.
First, vehicles’ average acceleration,
deceleration and stopped time is estimated
based on average speed (and its derivative) for
each edge of an intersection using fuzzy
system. This will be done per second to provide
the static measurements (i.e. an average) of
the estimated model. Since average delay time
is basically the sum of average stopped time,
acceleration and deceleration losses; then it
can be determined using the summation of
them respectively. The dynamic
measurements of our model can be provided
by accumulating average delay time through
suitable adaptation procedure. This adaptation
should be not sensitive to low PR. Thus,
existing of vehicle or group of vehicles (i.e.
group leader) will be considered as a constraint
for adaptation procedure instead of their
count. Therefore, the accumulated average
delay per edge, called group time delays
(GTD), can be calculated. A new concept called
average delay percent (ADP) is also proposed
to evaluate our estimation for each incoming
and outgoing edge. ADP is defined as the ratio
of GTD for each incoming and outgoing edge
to the total vehicle sensed time. To evaluate
our model estimation for all the incoming and
outgoing edges (as well as for the intersection
as a whole), GTD per all incoming and outgoing
edges are averaged separately per direction.
Finally, the whole intersection average delay
time is determined by summing accumulative
average delay time for all directions
respectively. There is no need to stress here
that all the above steps are done
instantaneously (i.e. second by second) under
RSU communication coverage area without
any additional communication required.
3.1. Average delay estimation
Average delay at signalized intersections are
associated with the time loss to vehicles and/or
drivers/pedestrians because of the operation
of the signals, the geometric of the intersection
and traffic conditions present at the
intersection. In the literature review models,
delay can be essentially computed with
knowledge of arrival rates and departure rates
of vehicles. However, this knowledge required
exact number of arrival and departure vehicles
per time which is difficult to obtain with
vehicular communication networks even under
full PR. Instead of that, an approach with fuzzy
system proposed to estimate average delay
dynamically. Our aim is to characterize
average delay as a time-dependent model (i.e.
dynamic) when a vehicle or group of vehicles
becomes under RSU communication coverage
area. With vehicles grouping protocol used in
COLOMBO project, it is assumed that average
speed of vehicles is less affected by PR. With
this assumption, average delay can be
estimated based on average speed. Average
delay is basically the sum of an average
acceleration, deceleration and stopped time as
shown in the following equation: 𝐷𝑒𝑙𝑎𝑦(𝑘) = 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛(𝑘)
+ 𝐷𝑒𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛(𝑘)+ 𝑆𝑡𝑜𝑝𝑝𝑒𝑑(𝑘)
(1)
Where, 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛(𝑘) is the time determined
with low speed and increase acceleration of
vehicle or group of vehicles entered to the
edge under the RSU communication coverage area per moment. While, 𝐷𝑒𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛(𝑘) is the
time determined with high speed and decrease
acceleration of vehicle or group of vehicles
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entered to the edge under the RSU
communication coverage area per moment.
Finally, 𝑆𝑡𝑜𝑝𝑝𝑒𝑑(𝑘) is the time determined with
zero speed and/or no acceleration of vehicle or
group of vehicles entered to the edge under
the RSU communication coverage area per
moment. As it is clear, the uncertainty in the
definitions of acceleration, deceleration and
stopped delay (i.e. low and high) can be
managed with simple fuzzy system. To this
point, the average delay will be estimated per
moment (e.g. per second) for each edge of the
incoming and outgoing edges of an
intersection without counting the number of
vehicles. The following subsections describe
the above steps in details.
3.1.1. Fuzzy system
As described previously, fuzzy system is
proposed to estimate the average acceleration,
deceleration and stopped delay of vehicle or
group of vehicles for each incoming and
outgoing edge of an intersection. This is done
based on the average speed of vehicles, as well
as its derivative, which can be easily obtained
from the protocol presented in [7] and used by
COLOMBO framework. Since COLOMBO
framework is discrete, we make use of a
discrete derivative (as used by COLOMBO
framework but without historical knowledge),
which is computed as the difference between
the average speed at two subsequent time
instants divided by the interval between them.
In our approach (in order to compare our
results with COLOMBO’s), time steps with fix
length of one second have been used and the
division is always by one. The input/output
variables, as in any fuzzy system, are first
classified into different categories or fuzzy
sets. Possible inputs in our case are average
speed and their derivative. Where average
speed fuzzy sets are L for low, M for medium,
and H for high (see Figure 1.(a)); and for the
average speed derivative, the defined fuzzy
sets are N for negative, Z for zero, and P for
positive (see Figure 1.(b)). The required
outputs, corresponding to average
acceleration, deceleration and stopped delay
time respectively, have also been defined for
one second time span, with L for low, M for
medium and H for high (see Figure 1.(c)).
Figure 1. Fuzzy delay estimation system (a)
Average speed (m/s/veh) (b) Average speed
derivative (m/s2/veh) (c) Average
acceleration, deceleration and stopped delay
(s/veh).
The degree of membership of the input and
output values to each fuzzy set are determined
using membership functions. In our approach,
membership functions implemented based on
simple rating system, are illustrated in Figure
1. (where d, a and max is the average
deceleration, average acceleration and
maximum allowed speed respectively for
vehicles used in the simulated scenario).
Fuzzy rules that relate the inputs (average
speed and its derivative) with the outputs
(average acceleration, deceleration and
stopped delay per second) are established
based on logical input/output relations (see
Table 1.).
Table 1. Fuzzy rules relating inputs (average
speed and its derivative) with outputs
(average acceleration, deceleration and
stopped delay time).
Average
accelerat
ion,
decelerat
ion and
stopped
Average
speed
derivative
N Z P
1
0
L M H
0 max/2 max
Deg
ree
of
mem
ber
ship
1 N Z P
-d 0 a
Deg
ree
of
mem
ber
ship
1
0
L M H
0 1/2 1
Deg
ree
of
mem
ber
ship
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delay
time
Avera
ge
Speed
L L,
H,
L
L,
L,
H
H,
L,
L
M L,
M,
L
L,
L,
M
M,
L,
L
H L,
L,
L
L,
L,
L
L,
L,
L
Delay estimation is done per second for each
edge. The estimation of the average delay for
the whole intersection should be rather
insensitive to very short peaks, like a singular
platoon in one edge, but should react rapidly
to more persistent traffic changes where we
expect a burst in traffic from a single edge that
will last for specific period (e.g. fifteen to
twenty minutes). In order to do that, a novel
accumulation and adaptation procedure is
proposed here with the following details.
3.1.2 Adaptation and accumulation
procedure
As described previously, every RSU in an
intersection monitors the individual average
delay for each incoming and outgoing edge,
and estimates through fuzzy based system the
delay time per moment. Every edge has a
counter associated to it, called group times
delay (GTD). This GTD represent accumulated
average delay per edge if vehicle or group of
vehicles through group leader is sensed
according to the following equation. 𝐺𝑇𝐷𝑒(𝑘)
= {𝐺𝑇𝐷𝑒(𝑘 − 1) + 𝐷𝑒𝑙𝑎𝑦𝑒(𝑘) 𝑖𝑓 𝑐𝑎𝑟𝑒(𝑘) > 0 𝑎𝑛𝑑 𝑘 ≠ 0
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (2a)
𝑤𝑖𝑡ℎ 𝐷𝑒𝑙𝑎𝑦𝑒(𝑘) =∑ 𝐹𝑖 (𝑣𝑒(𝑘),𝑑𝑣𝑒(𝑘)
𝑑𝑘)
3
𝑖=1 (2b)
Where 𝐺𝑇𝐷𝑒(𝑘) and 𝐺𝑇𝐷𝑒(𝑘 − 1) are the new and
the previous value of accumulative GTD for edge e at time-step (𝑘)and previous time-step (𝑘 − 1) respectively. 𝐷𝑒𝑙𝑎𝑦𝑒(𝑘) is the summation
of estimated average acceleration 𝐹1, deceleration 𝐹2 and stopped delay
𝐹3 respectively based on the fuzzy inference 𝐹
with edge average speed 𝑣𝑒(𝑘) and its
derivative 𝑑𝑣𝑒(𝑘)/𝑑𝑘 as an inputs. Finally,
𝑐𝑎𝑟𝑒(𝑘) is the number of vehicles in edge e at
time-step (𝑘).
To this point, for each incoming and outgoing
edge, GTD is estimated based on the averaged
speed and its derivative with respect to their
sensed vehicles. In order to determine the
average GTD for all incoming and all outgoing
edges separately, the average GTD for each
edges’ direction are averaged as given in the
following equations. 𝐴𝑣𝑔 𝐺𝑇𝐷𝑒(𝑘)
= {𝐴𝑣𝑔 𝐺𝑇𝐷𝑖𝑛(𝑘) 𝑓𝑜𝑟 𝑖𝑛𝑐𝑜𝑚𝑖𝑛𝑔 𝑒𝑑𝑔𝑒
𝐴𝑣𝑔 𝐺𝑇𝐷𝑜𝑢𝑡(𝑘) 𝑓𝑜𝑟 𝑜𝑢𝑡𝑔𝑜𝑖𝑛𝑔 𝑒𝑑𝑔𝑒
(3a)
=
{
1
𝑛∑ 𝐺𝑇𝐷𝑒(𝑘)
𝑛
𝑒=1𝑓𝑜𝑟 𝑛 𝑖𝑛𝑐𝑜𝑚𝑖𝑛𝑔 𝑒𝑑𝑔𝑒
1
𝑚∑ 𝐺𝑇𝐷𝑒(𝑘)
𝑚
𝑒=1𝑓𝑜𝑟 𝑚 𝑜𝑢𝑡𝑔𝑜𝑖𝑛𝑔 𝑒𝑑𝑔𝑒
(3b)
Where n and m is number of incoming and
outgoing edges with sensed vehicles
respectively.
How to use these estimated average delays as
a direct indicator for traffic congestion
estimation is going to be explained in the next
subsection.
3.2. Traffic congestion estimation and
evaluation
Although average delay considered as a major
indicator for estimating and evaluating the
traffic congestion but total estimation and
evaluation time interval should be taken into
consideration as well. Predefined threshold
value may be used and corresponds to the LOS
to be evaluated for each incoming and
outgoing edge or for the intersection as a
whole. For example, left hand side of Table 2.
summarizes the LOS criteria for signalized
intersections, as described in [12].
Table 2. LOS versus BAYAN criteria.
LOS criteria
[12]
BAYAN criteria
LOS
Control
delay
(sec/veh)
𝑨𝑫𝑷𝒆(𝒌)% Traffic
congestion
A ≤ 10 ≤ 10 No congestion
B 10 − 20 10 − 20 Little congestion
C 20 − 35 20 − 35 Low congestion
D 35 − 55 35 − 55 Medium congestion
E 55 − 80 55 − 80 High congestion
F > 80 > 80 Sever congestion
Signalized intersection LOS is stated in terms
of average control delay (in sec/veh) during a
specified time period, typically for a 15- minute
analysis period. It may be calculated per
intersection, per edge, or per lane group. In
order to determine the time period for vehicles
sensed under RSU communication coverage
area per edge, the following equation is used. 𝑇𝑖𝑚𝑒𝑒(𝑘)
= {𝑇𝑖𝑚𝑒𝑒(𝑘) + 1
0 𝑖𝑓 𝑐𝑎𝑟𝑒(𝑘) > 0 𝑎𝑛𝑑 𝑘 ≠ 0
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(4)
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From which, ADP per edge can be determined
using the following equation.
𝐴𝐷𝑃𝑒(𝑘)% =𝐺𝑇𝐷𝑒(𝑘)
𝑇𝑖𝑚𝑒𝑒(𝑘) (5)
Where 𝐴𝐷𝑃𝑒(𝑘)% is the ADP per edge e
measured in % at time-step (𝑘). 𝑇𝑖𝑚𝑒𝑒(𝑘) is the
accumulated total time for edge e where
vehicles have been sensed till time-step (𝑘). The proposed approach for estimating the
traffic congestion for each edge of an intersection, based on 𝐴𝐷𝑃𝑒(𝑘)%, is extracted
from LOS criteria of [12] as displayed in the
left side of Table 2. With these threshold value
an evaluation procedure, called BAYAN (Basic
traffic Acceptance via Yes and No evaluation),
can be derived for specific 15-minutes (i.e. 900
sec) period as follows. 𝐴𝑒(𝑘)
= {𝑌𝑒𝑠 𝑖𝑓 𝐴𝐷𝑃𝑒(𝑘)% ≤ 𝑡ℎ 𝑎𝑛𝑑 𝑇𝑖𝑚𝑒𝑒(𝑘) ≥ 900 𝑁𝑜 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(6)
Where 𝐴𝑒(𝑘) is the acceptance logic Boolean
value (i.e. either Yes or No) and 𝑡ℎ is one of
the acceptable average delay percent
threshold values shown in Table 2. For example, 𝐴𝑒(𝑘) ≤ 35% (i.e. for low, little and no
traffic congestion) can be considered as an
accepted traffic congestion and not accepted
otherwise.
The same proposal can be used for traffic
congestion estimation of the intersection as a
whole. Since control delay for the whole
intersection is basically the sum of average
delays in the incoming and outgoing edges (as
well as in the intersection overlap area); then
it can be determined using the summation of
them respectively, as given by the following
equation. 𝑎𝑣𝑔𝐺𝑇𝐷(𝑘) = 𝑎𝑣𝑔𝐺𝑇𝐷𝑖𝑛(𝑘)
+ 𝑎𝑣𝑔𝐺𝑇𝐷𝑜𝑢𝑡(𝑘) (7)
In the same time, since RSU is assumed to be
located in the center of an intersection area, delay in the intersection overlap area is
assumed already included by 𝑎𝑣𝑔𝐺𝑇𝐷𝑖𝑛(𝑘) and
𝑎𝑣𝑔𝐺𝑇𝐷𝑜𝑢𝑡(𝑘) respectively.
BAYAN procedure allows online evaluation of
the individual local traffic congestion estimated
for each incoming and outgoing edge as well
as for the intersection as a whole.
4. Results
Although our approach could be investigated in
different traffic scenarios (highways, urban,
rural … etc.), an intersection from urban
scenario is selected to be simulated.
Traffic simulator SUMO used to produce
realistic vehicular movement traces. Network
simulator version-3 (NS3) used to implement
vehicular communication networks under
different PR. Finally, fuzzylite libraries for fuzzy
logic control [21] used to implement the
proposed fuzzy system. Then, COLOMBO
framework is selected to connect the above
simulators with the proposed approach
algorithm. An intersection with four (incoming
and outgoing) edges from COLOMBO
framework (called RILSA intersection [22], as
shown in Figure 2.) has been used. With this
intersection, a traffic conditions configured to
be realistically reflect urban intersection traffic
with varying intensity and duration in different
edges. Neither infrastructure nor traffic light
settings (i.e. traffic signal controller with
predefined time intervals) are assumed to
influence the quality of the performed
approach.
Figure 2. RiLSA Intersection with incoming and
outgoing direction.
For simulation purpose, V2X communications
are performed by ns-3 standard WiFi model
using IEEE 802.11p with ETSI ITS G5
standards. A fixed 170m transmission range
are assumed. This value is chosen to match the
same range used in COLOMBO framework. A 6
Mbps bandwidth rate with OFDM and finally to
compute signal loss default log-distance
propagation model is used.
In the simulation study, RSU periodically
receive messages from group leader (if exist)
within one second sampling resolution
indicating existing of vehicle or group of
vehicles and average speed per incoming and
outgoing edge respectively. All simulations
were performed in the same one hour time
span. Vehicle densities are changed during
time according to a wave trend that follows the
green and red timings controlled by the traffic
light. The main simulation parameters and
configurations used here are reported in Table
3.
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Figure 3. GTD estimated per incoming edge with (a)180o, (b)90o, (c)0o and (d)-90o direction
respectively.
Figure 4. Average GTD estimated for all the incoming edges of an intersection.
0
4
8
12
16
20
24
0
200
400
600
800
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400
Num
ber
of
veh
icle
s (v
eh)
GT
D (
sec/
veh
)
Time (sec)
(a)GTD
Number of vehicles
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0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400
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ber
of
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icle
s (v
eh)
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sec/
veh
)
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(b)GTD
Number of vehicles
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0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400
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s (v
eh)
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veh
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Number of vehicles
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0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400N
um
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of
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icle
s (v
eh)
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D (
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veh
)
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(d)GTD
Number of vehicles
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icle
s (v
eh)
Aver
age
GT
D (
sec/
veh
)
Time (sec)
Average GTD
Number of vehicles
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Figure 5. ADP estimated per incoming edge with (a)180o, (b)90o, (c)0o and (d)-90o direction
respectively.
Figure 6. Average ADP estimated for all the incoming edges of an intersection.
0
4
8
12
16
20
24
0
0.2
0.4
0.6
0.8
1
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400
Num
ber
of
veh
icle
s (v
eh)
AD
P %
Time (sec)
(a)ADP
Number of vehicles
0
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s (v
eh)
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P %
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Number of vehicles
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eh)
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P %
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um
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icle
s (v
eh)
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P %
Time (sec)
(d)ADP
Number of vehicles
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Num
ber
of
veh
hic
les
(veh
)
Aver
age
AD
P %
Time (sec)
Average ADP
Number of vehicles
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Figure 7. GTD estimated per outgoing edge with (a)180o, (b)90o, (c)0o and (d)-90o direction
respectively.
Figure 8. Average GTD estimated for all the outgoing edges of an intersection.
0
4
8
12
16
0
5
10
15
20
25
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400
Num
ber
of
veh
icle
s (v
eh)
GT
D (
sec/
veh
)
Time (sec)
(a)GTD
Number of vehicles
0
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s (v
eh)
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D (
sec/
veh
)
Time (sec)
(b)GTD
Number of vehicles
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s (v
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sec/
veh
)
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(c)GTD
Number of vehicles
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ber
of
veh
icle
s (v
eh)
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sec/
veh
)
Time (sec)
(d)GTD
Number of vehicles
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ber
of
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icle
s (v
eh)
Aver
age
GT
D (
sec/
veh
)
Time (sec)
Average GTD
Number of vehicles
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Figure 9. ADP estimated per outgoing edge with (a)180o, (b)90o, (c)0o and (d)-90o direction
respectively.
Figure 10. Average ADP estimated for all the outgoing edges of an intersection.
0
4
8
12
16
0
0.2
0.4
0.6
0.8
1
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400
Num
ber
of
veh
icle
s (v
eh)
AD
P %
Time (sec)
(a)ADP
Number of vehicles
0
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8
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Num
ber
of
veh
icle
s (v
eh)
AD
P %
Time (sec)
(b)ADP
Number of vehicles
0
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8
12
16
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1
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400
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ber
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veh
icle
s (v
eh)
AD
P %
Time (sec)
(c)ADP
Number of vehicles
0
4
8
12
16
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1
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400N
um
ber
of
veh
icle
s (v
eh)
AD
P %
Time (sec)
(d)ADP
Number of vehicles
0
4
8
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Num
ber
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veh
icle
s (v
eh)
Aver
agr
AD
P %
Time (sec)
Average ADP
Number of vehicles
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Table 3. Simulation parameters.
Parameter Value
Wi-Fi mode 802.11p/ETSI ITS 5G
Transmission
mode
6 Mbps (OFDM)
Node radius 170 m
Propagation loss Logarithmic
Propagation
speed
Constant (3x108 m/s)
Penetration rate 100,50,20,10,5,2,1%
Simulation time 1 hour
In the first step, we simulate the selected
scenario with constant traffic light control
setting (i.e. fixed time) and real number of
vehicles (i.e. with no error position). This
produce benchmark traffic conditions against
which to compare those estimated through our
proposal with different PR. This step is depicted
in Figure 3. for GTD estimated versus real
number of vehicles for each incoming edges.
The average GTD estimated for all the
incoming edges of an intersection is shown in
Figure 4. Then, ADP is determined (as
described previously) for each incoming edge
(see Figure 5.) as well as for all the incoming
edges (see Figure 6.) respectively. The same
steps are done for outgoing edges as shown in
Figure 7. - Figure 10. respectively.
4. Evaluation
To evaluate the proposed fuzzy delay
estimation system, results shown previously
with real number of vehicles have been
compared with the proposed approach results
under different PR. In this phase, Figure 11(a).
depicts the estimated delay for each incoming
edge by our approach with different PR as well
as the average for all the incoming edges. The
same thing shown in Figure 11(b). for outgoing
edges. Figure 12. and Table 4. depicts the
estimated delay for the intersection as a whole
(as well as for all incoming and outgoing
edges) by our approach with different PR as
well as delay measured from SUMO output.
Figure 11. Delay estimated with different PR for (a) incoming and (b) outgoing directions
respectively.
Figure 12. Delay estimated with different PR for the intersection as a whole.
0
10
20
30
40
50
Real 100 50 20 10 5 2 1
Del
ay (
sec/
veh
)
PR%
180 90 0 -90 incoming
0
0.5
1
1.5
2
2.5
Real 100 50 20 10 5 2 1
Del
ay (
sec/
veh
)
PR%
180 90 0 -90 outgoing
0
20
40
Real 100 50 20 10 5 2 1 PR%
incoming outgoing all sumo
(a)
(b)
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To evaluate the overall performance of our
approach, a simple summarizing metric can be
introduced. Delay difference between the one
determined from SUMO output and the one performed by our approach, called delta (∆).
Its value is referred to a single direction of
interest computed using data from a whole
batch of simulation runs for one hour under
different PR (see Table 4.).
Table 4. Delta evaluation with different PR.
PR% 𝐃𝐞𝐥𝐚𝐲 ∆
Incoming Outgoing All SUMO
Real 24.9807 0.1959 25.1766 21.942 -3.2346
100 23.7271 0.2360 23.9632 21.942 -2.0212
50 24.1915 0.8187 25.0103 21.942 -3.0682
20 29.6518 0.4097 30.0615 21.942 -8.1195
10 27.2398 0.3763 27.6161 21.942 -5.6741
5 26.4994 0.1814 26.6808 21.942 -4.7388
2 22.3421 0.1115 22.4536 21.942 -0.5117
1 22.2213 0.0000 22.2213 21.942 -0.2793
4. Discussion
Results are depicted with real number of cars
in Figures 3 – 6. for incoming edges and in
Figure 7–10. for outgoing edges. To effectively
measure the performance of our proposed
approach, we compare the group time delay
GTD (and average delay percent ADP)
estimated by our approach (solid line) with
dynamic behavior of the number of vehicles
sampled via a real-mode procedure (dashed
line). In real-mode procedure, the real position
of every vehicle in a 170 meters range from
the RSU is detected with full accuracy and
precision. As it can be observed, the tendency
of the GTD simulation results follows the
dynamical change of real number of vehicles
with time, although a drift is clearly visible.
This is due to two major aspects: first, the
exact number of vehicles cannot be precisely
estimated through vehicular communication
networks even under real-mode procedure.
Second, our proposed dynamical delay model
does not include the vehicles count, which
change (increasing or decreasing) gradually
with time. Both aspects shall be more
investigated in future work. Nevertheless, we
can see that beside the drift, curves are
capable of providing an average delay given a
traffic flow speed.
One central result of high relevance is that the
proposed approach has the ability to estimate
the dynamic delay with different PR. This very
positive dynamic behavior of increasing and
decreasing of delay with the existing of actively
cooperating vehicles made the proposed
approach suitable even when one vehicle is
sensed. One obvious issue is the lack of data
for intervals where no equipped vehicle was
sensed. The probability to have no data for an
interval depends on the aggregation interval’s
duration and the PR. For this reason, low PRs
show data absence at times where no equipped
vehicle has been within the communication
range. Further investigations should be
performed to evaluate the performance of the
proposed approach under more realistic
scenarios with different interval periods.For evaluating results, Table 4. shows delta (∆) where higher values indicate poorer system
performance. It is clear that our approach has
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good performance under low PR (i.e. <5%)
while not for others. In fact, even under real
vehicle position have less performance than PR
with 100%. On the other hand, negative values
indicate overestimation in delay with our
approach. This result from accumulating
previous delay time if traffic light cycle fail to
pass waiting vehicles even if only one vehicle
stayed. Optimizing fuzzy system parameters
with suitable threshold for accumulative
procedure may help to solve this problem. This
require keeping accumulative errors as small
as possible and should be considered for future
work.
5. Conclusions
A novel time dependent approach for
estimating and evaluating traffic congestion of
an intersection is proposed and investigated
under different PR. The proposed approach is
simulated using COLOMBO framework through
V2X communication. The simulation results
reveal that the proposed approach can
estimate traffic delay with low PR (till 1%) over
time for the whole intersection as well as for
each incoming and outgoing edge. These
results are based on traffic delay estimation
with fixed time interval for evaluation. In fact,
using threshold values for traffic congestion
estimation is not preferred. This should be
considered in future work, under traffic light
control algorithm.
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