=Paper=
{{Paper
|id=Vol-2332/paper-10-003
|storemode=property
|title=
On modeling the traffic of vehicles through the road intersection of a smart city
|pdfUrl=https://ceur-ws.org/Vol-2332/paper-10-003.pdf
|volume=Vol-2332
|authors=Elena Y. Bogdanova,Viktoriya A. Khalina,Vladimir V. Rykov,Konstantin E. Samouylov
}}
==
On modeling the traffic of vehicles through the road intersection of a smart city
==
https://ceur-ws.org/Vol-2332/paper-10-003.pdf
88
UDC 519.872
On modeling the traffic of vehicles through the road
intersection of a smart city
Elena Y. Bogdanova* , Viktoriya A. Khalina* ,
Vladimir V. Rykov*† , Konstantin E. Samouylov*‡
*
Department of Applied Probability and Informatics
Peoples’ Friendship University of Russia
6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
†
Department of Applied Mathematics and Computer Modeling
Gubkin Russian State University of Oil and Gas
65 Leninsky Prospekt, Moscow, 119991, Russian Federation
‡
Federal Research Center “Computer Science and Control”
of the Russian Academy of Sciences (FRC CSC RAS)
44-2 Vavilov St, Moscow, 119333, Russian Federation
Email: elenabogdanova1@gmail.com, viktoriya.khalina@gmail.com, rykov-vv@rudn.ru, samuylov-ke@rudn.ru
The relevance of the research topic is determined by the increasing role of information and
communication technology (ICT) systems and services usage in all spheres of life - culture,
education, healthcare, transport and trade. We live in a society where mobile, broadband
and cloud computing change the structure of society and promise the great opportunities for
its inhabitants. The development of the human activity field will depend on the progress
achieved through the information and communication technology (ICT) systems and services
usage. ICTs can play a key role in smart transport management; utilities and electricity
supplying; measuring pollution levels; health care and education management, innovative
management of agriculture. All of the above-mentioned systems form a "smart" society. By
2050, a significant part of the world’s population will be living in cities, and the proportion
of urban residents will reach approximately 70%. For the timely provision of quality urban
services requires the introduction of various information systems.
Key words and phrases: infocommunication system analysis, smart city, traffic flow,
transport network, traffic flow modeling.
Copyright © 2018 for the individual papers by the papers’ authors. Use permitted under the CC-BY license —
https://creativecommons.org/licenses/by/4.0/. This volume is published and copyrighted by its editors.
In: K. E. Samouylov, L. A. Sevastianov, D. S. Kulyabov (eds.): Selected Papers of the 12th International Workshop on
Applied Problems in Theory of Probabilities and Mathematical Statistics (Summer Session) in the framework of the
Conference “Information and Telecommunication Technologies and Mathematical Modeling of High-Tech Systems”,
Lisbon, Portugal, October 22–27, 2018, published at http://ceur-ws.org
Bogdanova E. Y. et al. 89
1. Introduction
The phrase "smart society" is often used as a term describing the vision of a plan for
the future of a nation or region to achieve a developed information society. An analysis
of the various approaches to the definition of "smart" society shows that in this diversity
the emphasis is placed on different aspects. Let’s give some examples:
Society 5.0 is a society that will contribute to the prosperity of humanity. This
society is able to provide the necessary data and services to people at a given time and
only in the right quantity; society, capable of engaging a wide range of social needs; a
society in which all people can easily receive high-quality services, despite their age,
gender, region and language, as well as live an energetic and comfortable life [1].
The term “smart” means a society that is economically and environmentally sustain-
able without sacrificing the comfort and quality of life of its citizens. It is a convergence
of physical and digital infrastructure, where the use of ICT makes life more efficient and
sustainable.
The majority of the world’s population lives in cities, which leads to the creation of
a complex urban environment with complex processes. It is precisely these difficulties
and the importance of their solution that determine such attention to the concept of
smart cities.
Smart Sustainable City is an innovative city that uses information and communication
technologies and other means to improve the quality of life, work efficiency, service and
competitiveness, while meeting the needs of city residents in relation to economic, social
and environmental aspects.
The trend of urbanization and the increase in the planet population leads to problems
that can be solved through the effective resources allocation and the urban system
rational management. Thus, many countries set themselves the task of implementing an
intelligent society projects.
Congestion can completely paralyze the movement of vehicles in a large area and on
a single road. Owners of cars and passengers of public transport suffer from traffic jams.
The problem of car congestion negatively affects on the economic and environmental
situation, as well as the health of people.
There are several causes of traffic jams: the number of vehicles exceeds the capacity
of the road; the road network inefficient operation (road markings, signs, operation
mode of traffic lights), inconvenient road interchanges, the lack of overhead/underground
passages and detours for freight transport; violation of traffic rules by vehicles and
pedestrians; repair and construction work; accidents and inadequate technical condition
of cars and poor road conditions; lack of parking spaces; adverse weather conditions [2].
The transport flow is considered as the result of the interaction of vehicles on the
elements of the transport network in mathematical models. Due to the rigid nature of
network restrictions and the massive passage in a traffic flow, distinct patterns of queue
formation and intervals, loads along the road lanes etc. are defined.
Thanks to transport modeling, rational management of the urban system, construction
of new and reconstruction of existing roads are possible. In this case, the queueing
theory is used to build a mathematical model of a regulated intersection. Although,
automobile traffic has been studied for half a century, but these studies are not often
used in practice due to instability, the diversity of traffic flow and the need to expand the
number of parameters [3]. To obtain the optimal solution of transport issues, specialized
equipment and software are required, which makes it difficult to quickly implement such
systems in Russia.
Lifestyle and workflow change due to technological advances. More and more, physical
and virtual areas of our life are becoming intertwined due to the introduction of the
interconnection of machines (Internet of Things, M2M, wearable technology, intelligent
live and wireless computing).
In addition to things that can be connected to each other, neural networks will play
a special role - technologies that are capable of self-learning, receiving the necessary
information from the Internet. The Internet, based on artificial neural networks, is called
neuronet.
90 APTP+MS’2018
Figure 1. The lifecycle of the city
Data prediction, analytics, large data sets, open data, data availability and manage-
ment, data security, mobile broadband, wireless sensor networks - all these aspects have
become essential in society.
Due to the significant role of ICT in solving the problems of creating smart cities and,
moreover, smart societies, it is necessary to emphasize the important role of software
tools used to introduce relevant services. The criteria for such applications include the
following: expediency, reliability, security, confidentiality, practicality.
The above four pillars work through the physical and service infrastructures that
form the lifecycle of the city (Fig. 1).
Nowadays, the rapid growth of cars leads to the decrease in the capacity of the
road network. For many large cities, this problem is the painful one and that is why it
requires an urgent solution [4]. The main reasons of traffic jams are improper operation
of traffic lights and inconvenient interchanges, as well as adverse weather conditions that
make driving difficult.
That is why, this task is relevant in the framework of the well-known concept of the
smart city [5]. The definition of "smart" transport system is related to the system that
consists of separately modeled sections, which are then compiled and transported into a
single knowledge base. Due to the continuous monitoring and incoming information from
the road management services, the information and mathematical model is periodically
adjusted and the level of service provision in cities increases. The simulation allows
to evaluate the effectiveness of the city’s transport network management and identify
potentially problematic areas for their repid elimination [6]. This paper gives a brief
overview of the method and numerical analysis, which will then be used in further
studies on the optimization of traffic flows in a smart city [7].
Bogdanova E. Y. et al. 91
Figure 2. Stream of cars at a crossroad
2. Main section
In this article a model that describes the vehicles passage through a regulated
intersection as a queuing system with variable service intensity and a limited queue is
described (Fig. 2).
We consider that the traffic light has two states: the red light is on, then the passage
is prohibited, and the green light is on. The number of service channels is determined
based on the number of lanes for the intersection passage in one direction and is equal
to one.
The model has a limited capacity 𝑁 that can fit throughout the selected quarter. In
this way,
𝑁 = 𝐿𝑙 𝑚
where 𝐿 – is the length of the block, 𝑙 – is the average length of the car, 𝑚 – is the
number of lanes. The number of places in the queue varies from 10 to 30 cars on average.
It should be considered that the car, which has occupied the whole quarter, will leave
the system.
The main parameters of the system are: 𝑇 - the length of the full traffic light cycle
(the length of the "green" phase 𝜏 = 𝑇2 ); 𝜆 is the intensity of the arrival stream; 𝜇0 is
the intensity of the service flow in the "green" phase; 𝑁 is the maximum queue length.
For instance, the service intensity 𝜇(𝑡) has an periodical form and shown in Figure 3:
{︃
𝜇0 , 𝑘𝑇 ≤ 𝑡 < 𝑘𝑇 + 𝜏 ,
𝜇(𝑡) =
0 , 𝑘𝑇 + 𝜏 ≤ 𝑡 < 𝑘𝑇 + 𝑇 .
where 𝑘 = 𝑘(𝑡) = [𝑡/𝑇 ] – the quantity of traffic light cycles, [𝑥] – the integer part of
number 𝑥, 𝜇0 – an intensity of passage through intersection on a green traffic signal.
According to the fact that the service intensity is piecewise constant, the Queuing
System can be in different states:
92 APTP+MS’2018
Figure 3. The intensity of the car passage through the intersection
Figure 4. System state graph for the one direction
𝑆 (0) – there are no cars in front of the stop line,
𝑆 (1) – one car drives through a crossroads,
𝑆 (2) – one car drives through a crossroads, one is in front of the stop line and so on,
𝑆 (𝑁 ) – all places in the queue are occupied.
The state graph of the system is shown in the Figure 4.
The probability of the 𝑛-th state of the system 𝑆 at a 𝑡 moment of time is denoted
as 𝑝𝑛 (𝑡). In this case, the normalization condition 𝑝0 (𝑡) + 𝑝1 (𝑡) + ... + 𝑝𝑁 (𝑡) = 1 is
necessarily satisfied. The system can be solved numerically for different input data using
well-known software tools, and the main characteristics of the Queueing System can be
determined for it at a given operation mode of a traffic light.
The considered queuing system makes three quality decisions: 1. Free passage in a
given direction. The mode is characterized by high probabilities of states 𝑆0 and 𝑆1 at
the end of the green phase 𝑁1 < 𝑁2 .
2. Difficult passage. The mode is characterized by a low probability state 𝑆( 𝑛 + 1)
at the beginning of the inhibit signal 𝑁1 = 𝑁2 .
3. Clogging. The mode is characterized by a high probability of the state 𝑆𝑛 at the
beginning of the inhibit signal 𝑁1 > 𝑁2 .
𝑁1 = 𝜆𝑇
𝑁2 = 𝜇𝜏
𝑁1 - the average number of approaching cars for a full cycle,
Bogdanova E. Y. et al. 93
Figure 5. The average number of cars in the queue at 𝜏 = 30
𝑁2 - the average number of cars driving on the green light.
The paper also provides an example of numerical analysis. The average length of the
machine queue at the intersection
𝑁
∑︀
𝑟(𝑡) = (𝑛 − 1)𝑝𝑛 (𝑡),
𝑛=1
was calculated. To do so, the system of Kolmogorov’s differential equations was
solved and a stationary distribution was found.
To calculate the parameters of the model, the closed to real life baseline data were
taken. The intensity of the arrival stream is 𝜆 = 0.15 cars per second, the average time
of the intersection passage equals to (𝜇)−1 = 2.5 seconds, the length of a full cycle of
traffic lights is T=60 seconds, the permissible queue length of cars is 𝑁 = 10.
In order to investigate the dependence of the queue length on time, several cases with
different duration of the green phase were considered. In the first case, let‘s consider
that the green phase is 𝜏 = 30 seconds.
At the same time, at the initial moment of time the quarter is empty, therefore the
initial probability distribution of the systems states: 𝑝(0) = (1, 0, ..., 0)𝑇 .
Figure 5 presents the results of finding the main characteristics of the system - the
average number of cars waiting to travel through the intersection.
In the second case, by changing the duration of the green signal to 𝜏 = 0.8𝑇 = 48
seconds, the average queue length will decrease. So, it does not go beyond the limits of
one car, as can be clearly seen in Figure 6.
The last considered case (𝜏 = 0.2𝑇 = 12 seconds) shows that cars have not enough
time to cross the road in such a short period of time. This leads to a blockade of cars at
the intersection, forming a traffic jam that consists of 6-8 cars in average (Fig. 7).
94 APTP+MS’2018
Figure 6. The average number of cars in the queue at 𝜏 = 48
Figure 7. The average number of cars in the queue at 𝜏 = 12
Bogdanova E. Y. et al. 95
3. Conclusions
Traffic modelling plays an important role in improving the traffic situation. The
paper presents the results of monitoring the time distribution of the intersection crossing
by cars. It depends on the time elapsed from the beginning of the enabling signal.
Also, the methods of mathematical modeling were used. In the future, it is planned to
study models that allow creating routes which takes into consideration the indication
of stopping places, overtaking. Moreover, the team would like to implement a data
processing system and coordinating schedules [8, 9].
It is impossible to create an intellectual society without using digital inclusion
technologies. They allow to achieve maximum efficiency by combining vast distances
in order to bring in a sustainable way the knowledge, help and resources to those who
need it.
It is expected that such a society will develop and implement an environment in
which people, robots and artificial intelligence will coexist and work to improve the
quality of life, offering finely differentiated personalized services that meet the diverse
needs of users. The trend of urbanization and the increase in the population of the
planet leads to problems that can be solved through the effective allocation of resources
and the rational management of the urban system. But every year the development of
cities faces a lot of problems: provision of water, electricity, transport, etc. Thus, many
countries set themselves the task of implementing projects of an intelligent society.
Summing up the research on “smart” services, we concluded that despite the great
interest of scientists in this issue, not all countries are ready to provide an adequate level
of infocommunication support and a legislative framework for the introduction of modern
technologies into life. The main obstacles to the development of this issue are: firstly,
the lack of clearly defined economic goals and objectives of innovation, secondly, the
insignificant involvement of universities and research centers for the implementation of
plans, and thirdly, the lack of a working process management system and the development
of the digital economy. However, we are on the right track, and the development of
the future depends on our ability to build an information-friendly culture, support the
development of digitalization and invest in key infrastructure elements to create new
open platforms and markets.
Acknowledgments
The publication has been prepared with the support of the “RUDN University
Program 5-100” and funded by RFBR according to the research projects No. 18-00-
01555, 19-07-00933.
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