Spatial Characteristics of Communication in Urban Vehicular System

Antal Ily

es, Tomaj Kov

acs, Gr

eta Tisza and Imre Varga

Department of IT Systems and Networks, University of Debrecen, Kassai str. 26, Debrecen, Hungary

Keywords:

Trafﬁc, VANET, Information Spreading, ABM, Radius of Gyration, Bounding Box.

Abstract:

We propose a model of information spreading based on urban trafﬁc, where smart vehicles can carry data of

sensor measurements and share them by short-range wireless communication. The spreading of information

can be quite fast and widespread without central control within this ad hoc network. In this position paper,

we want to characterize some spatial aspects of the spreading process. We planned to analyze the radius

of gyration and the bounding box of the 2D positions of informed agents and communication events. First

simulation results show a crossover in the time evolution of the system.

1 INTRODUCTION

Over the last decade, we have witnessed many re-

search efforts that have investigated various aspects

of Vehicular Ad hoc NETworks (VANET). Due to the

equipped On Board Units (OBU) of modern smart

vehicles they can continuously perform Vehicle-to-

Vehicle (V2V) communication. Besides, vehicles

can also exchange information with Road Side Units

(RSU) via Vehicle-to-Infrastructure (V2I) communi-

cation. Messages related to trafﬁc information, road

conditions, local utility information are carried and

forwarded by vehicles, thus the key component of the

infotainment services in VANETs is the data dissem-

ination. It is the base of several applications, such

as adaptive navigation, vehicle safety, trafﬁc manage-

ment or different location-based services.

These systems attract industrial and scientiﬁc in-

terest as the number of research papers shows. The

trafﬁc ﬂow was analyzed and simulated in different

scenarios (Fiore et al., 2007; Zeadally et al., 2012;

Meignan et al., 2006). Wireless communication pro-

tocols (e.g. IEEE 802.11p) were developed and their

performance were measured (Malla and Sahu, 2013;

Ramakrishna, 2012; Sanguesa et al., 2016). Af-

ter the communication is available within an urban

system the topology of this network was also in-

vestigated (Zhang and Le, 2015; Kocsis and Varga,

2019). In intelligent transportation systems, vehicles

can play the role of routers, not just simple senders

or receivers. Thus special routing protocols were de-

veloped and introduced (Mtech and Malhotra, 2016;

https://orcid.org/0000-0003-3921-2521

Malla and Sahu, 2013; Rehman et al., 2013; Ramakr-

ishna, 2012) as well. The statistical physics of the

information spreading processes was also published

(Varga et al., 2018).

In this work, we would like to ﬁnd the answers

to further open questions. Where are the vehicles

carrying information packets? How large is the area

concerned by the dissemination? How does its size

change in time? What is the shape of the affected

area? Does it have almost circular symmetry or elon-

gated prolate shape due to primary roads? Is the den-

sity of informed vehicles constant or are they spatially

centralized? Is communication only on the perimeter

of the area?

The rest of the paper is organized as follows. Sec-

tion 2 provides our own model of urban trafﬁc and the

spreading of information. Section 3 presents the spa-

tial characteristics we interested in and our hypothe-

ses. Some preliminary results are in section 4. Fi-

nally, we conclude the paper.

2 MODEL

In order to study the spreading of information

in VANET, an agent-based model (ABM) is pro-

posed describing both the urban trafﬁc and the self-

organized communication of vehicles.

2.1 Trafﬁc

An urban road map can be modeled by straight road

segments, where a connection between two neighbor-

108

Ilyés, A., Kovács, T., Tisza, G. and Varga, I.

Spatial Characteristics of Communication in Urban Vehicular System.

DOI: 10.5220/0009464001080112

In Proceedings of the 5th International Conference on Complexity, Future Information Systems and Risk (COMPLEXIS 2020), pages 108-112

ISBN: 978-989-758-427-5

Figure 1: The urban road map of Debrecen (left) was con-

verted to a weighted graph connecting real geographical

locations with different kinds of straight road segments

(right).

ing crossroads can be represented as a concatenated

segment list. Thus the road map of Debrecen (Open-

StreetMap, 2019) was converted to a graph, where

the nodes are planar geographical locations, the end-

points of straight road segments as it is illustrated in

Figure 1. The length of a link is deﬁned by the dis-

tance of the nodes connected by the given link. The

links also differ in other sense because the average

speed of vehicles varies on different types of roads

(primary route, living street, highway, etc.). In our

model we assume that point-like vehicles move with

a constant velocity determined by only the road type.

In this way, it is a mesoscale approach of the traf-

ﬁc, where microscale objects (e.g. trafﬁc lights, junc-

tions, pedestrian crossing, etc.) are taken into account

only by the average speed.

Each vehicle have a randomly selected departure

and arrival location within the city and between them

they proceed along the shortest travel time routes.

They derive from the lengths of links and the average

speed on them using the Dijkstra’s algorithm (Dijk-

stra, 1959). The amount of vehicles in the model is

constant since the simulated time intervals are short

(circa 10 minutes) compared to the duration of the

different phases of the daily life periods of the ur-

ban trafﬁc. Thus rush-hours or off-peak periods can

be modeled only separately. If a vehicle arrives at

its destination, a new one will be launched, just for

simplicity. The left side of Figure 2 demonstrates the

motion of three vehicles using discrete timescale for

computer simulation.

This model is quite similar to the model intro-

duced by Varga et al. (2018), but there is a huge differ-

ence. The recent model is based on the real geograph-

ical locations contrary to the former model which was

a simpliﬁed model ignoring the shape of roads and fo-

cusing on only the connections of crossroads. There

the Cartesian coordinates of vehicles were not man-

aged just the distances from the two neighboring junc-

Figure 2: (Left) Colored circles illustrate the positions of

3 vehicles in different discrete-time moments along their

routes during the time evolution. Distinct distances between

consecutive circles show the various average speed on dif-

ferent ranked road segments. (right) A time moment of the

system, where the communication ranges R of agents are

presented by green areas. Blue and red circles refer unin-

formed and informed agent, respectively, while the newly

informed agents have gradient color.

tions. In the recent work, there are nodes with degree

k = 2 along bent roads between junctions. Thus the

number of nodes is much higher resulting in more

computational effort but makes us able to study the

geographical properties of spreading.

2.2 Information Spreading

Vehicles can be equipped with smart on-board units.

Their sensors can perform different measurements

and then they are able to share this information via

short-range wireless communication. After the mea-

surement, the given car can carry the information and

in the vicinity of other vehicles, it is shared. In this

way, the source of information packets are the ve-

hicles themselves, there are no road-side units just

vehicle-to-vehicle communication. Thus useful infor-

mation (e.g. trafﬁc or weather alerts) can spread in

this complex system. For the sake of simplicity in this

work we consider only one measurement and follow

the spreading of this information packet.

Vehicles are the agents of this ABM, having only

two states. Initially, all the agents are in an unin-

formed state denoted by S

= 0 because they have not

received information yet. Due to the sensor measure-

ment, one of the agents becomes informed (S

= 1).

It is the T = 0 time moment of the simulation. Since

agents are moving they can meet. If the uniformed

agent j is within the R communication range of the in-

formed agent i, then j becomes informed S

= 1. Thus

both of them can carry and share the information later.

See the right side of the Figure 2. There is only one

state change in this model similar to the Susceptible-

Infected epidemic model (Newman, 2010).

Spatial Characteristics of Communication in Urban Vehicular System

109

3 SPATIAL FEATURES

In order to capture the geographical features of the

spreading process, we planned to study the spatial dis-

tribution of three different location sets.

• Recent locations of informed agents,

• Spots of all the information exchanges in the past,

• Spots of information exchanges in the recent time

moment.

All of them mean a set of 2D points, which are in the

focus of our analysis to describe the spreading pro-

cess. We are going to calculate four quantities of the

above-mentioned position sets:

• Radius of gyration (R

• Area of the bounding box (A),

• Ratio of the side lengths of the bounding box

(L/W ),

• Largest distance between an informed agent and

the information source (d

max

The radius of gyration R

is mathematically the

root mean square distance of the points from the cen-

ter of mass at ~r

(assuming unit mass for all points).

Formally it deﬁned as

∑

i=1

(~r

−~r

), (1)

where N is the number of points and ~r

is the posi-

tion of location i. It can be interpreted as an average

coverage of the set of points. Additionally, in poly-

mer physics is it used to describe the shape. When

the radius of gyration is proportional to the number of

points it refers to linear shape, while if R

∝ N

have a planar structure.

A minimal bounding box of planar structure can

be deﬁned as the smallest rectangular area, where the

longer line of symmetry is parallel to the line segment

connecting the two furthermost points. In Figure 3,

the length and width of this rectangular is denoted by

L and W , respectively. The area of the bounding box

is A = L × W . The A denotes the planar size of the

system (similar to R

) and the L/W ratio of the side

lengths refers to the shape.

The location of the sensor measures, where the

initial source agent starts to share the information

packet can be far from later informed agents, which

get the packet via multiple information exchanges.

The recent distance of agent i from the source is de-

noted by d

(t). The distance of the furthermost agent

max

≥ d

can be also an interesting characteristic of

the system.

100

0 10 20 30 40 50 60 70 80 90 100

100

0 10 20 30 40 50 60 70 80 90 100

=40.0

L/W=1.00

A=6400

100

0 10 20 30 40 50 60 70 80 90 100

100

0 10 20 30 40 50 60 70 80 90 100

=27.4

L/W=1.15

A=5540

100

0 10 20 30 40 50 60 70 80 90 100

100

0 10 20 30 40 50 60 70 80 90 100

=30.7

L/W=1.00

A=6400

100

0 10 20 30 40 50 60 70 80 90 100

100

0 10 20 30 40 50 60 70 80 90 100

=24.0

L/W=5.50

A=1164

Figure 3: Regular arrangements of 24 planar points to illus-

trate various spacial properties. a) A circular structure with

large radius of gyration. b) Radial structure with square-like

bounding box (L/W ≈ 1) and lower R

. c) A square grid

structure where the uniform distribution results in lower R

then in case of circular structure nevertheless the value of

A is the same. d) A prolate structure, which is dense (low

value of R

and A) and longish (high value of L/W ).

By these quantities, we can capture differences be-

tween the structures in Figure 3, although all of them

contain the same amount of points. The small value

of R

refers to a dense structure. (Compare Figure 3a

and Figure 3b.) Similarly, a smaller value of A can

be found in a more concentrated structure. (Compare

Figure 3c and Figure 3d.) The large L/R ratio can

be observed in Figure 3d because the shape is linear

rather than planar.

3.1 Hypotheses

The number of informed agents increasing very inten-

sively and quickly reach a saturation. Sooner or later

the majority of agents will be in informed states. The

information spans the whole city within a short time

interval.

At a given time moment the communication takes

place not only at the peripheral region of the area

covered by the informed agent because there are uni-

formed agents within this area, so the area is not com-

pact.

We suppose that at the beginning of the spreading

process, the informed agents are within a linear area

due to the relatively straight road segments. However

later it still remains linear for intervals longer than

distances between junctions due to the neighboring

priority roads, which have precedence in case of long

COMPLEXIS 2020 - 5th International Conference on Complexity, Future Information Systems and Risk

110

rides. After a long time of dissemination, the bound-

ing box of the affected area starts to be square-like.

Thus there will be a crossover between the linear and

planar phase.

4 FIRST RESULTS

Our self-developed agent-based software is over the

tests. We plan to carry out a lot of simulations in or-

der to discover the parameter space. We are at the be-

ginning of this long process, but some interesting fea-

tures of the system have been already reported. The

following results are obtained by the simulation of a

few ten-thousand vehicles and using a communication

range covering a few meters wide area.

Figure 4: A snapshot of the system covering just the central

part of Debrecen. The black and blue spots represent the

uninformed and informed vehicles, respectively. The red

circle in the middle marks the location of the information

source when it triggered off the spreading process. As one

can see the main roads are very crowded while residential

ones have low loads. The information dissemination is more

dominant along the primary roads.

At ﬁrst sight, the general behavior of the system is

very realistic even though the model is quite simple.

However real-life measurements and statistics are not

available, the distribution of vehicles is very similar to

the trafﬁc, we experience every day as local drivers.

After an agent starts to share information as an ini-

tial source neighboring agents receive and forward it.

Thus more and more agents become informed until

we reach saturation, where almost all the smart vehi-

cles are informed within a few minutes. A snapshot

of the spreading process is shown in Figure 4.

All the studied quantities have two distinct phases.

At ﬁrst, the linear spreading dominates the system.

The radius of gyration and the maximal distance of in-

formed agents from the source are increasing rapidly.

The length L and the width W of the minimal bound-

ing box are deﬁnitely different. Later, as more agents

carry the information all over the city the slopes of

the R

(t), A(t) and the d

max

(t) are decreasing signif-

icantly and the bounding box becomes more square-

like (see Figure 5). The reason for this can be the

local topology. In the former phase, the affected area

covers only one almost straight main road. Contrary

later the informed agents mainly proceed on several

primary roads in different directions of the 2D plane.

distances [km]

100

area [km

]

0 100 200 300

t [s]

[km]

max

[km]

A [km

]

1.0

1.2

1.4

1.6

1.8

2.0

2.2

L / W

0 100 200 300

t [s]

Figure 5: A) A crossover can be observed in several quanti-

ties. Both the radius of gyration, the maximal distance from

the source and the area of the bounding box changes quali-

tatively in time. The presented curves are obtained from the

recent locations of informed vehicles. b) The shape of the

bounding box is gradually changing from rectangular form

to square-like form as the L/W ratio is converging to a value

close to 1.

5 CONCLUSIONS

Our self-developed software implements a simple but

efﬁcient mesoscopic model of urban trafﬁc. Based on

this, one can observe an ad hoc communication net-

work of moving devices, which can accomplish infor-

mation dissemination. We would like to analyze the

spatial features of the spreading process observing the

sets of different locations.

We found empirical correspondence of the sim-

ulations and the real observations. A lot of simula-

Spatial Characteristics of Communication in Urban Vehicular System

111

tions and the evaluation of their results are ahead of

us. However we are just at the beginning of a long,

detailed analysis, some interesting features of the sys-

tem have already been found. The spreading process

is not uniform, one can observe two distinct phases

of the time evolution of the spreading caused by the

local urban topology.

ACKNOWLEDGEMENTS

This work was supported by the construction EFOP-

3.6.3-VEKOP-16-2017-00002. The project was sup-

ported by the European Union, co-ﬁnanced by the Eu-

ropean Social Fund.

Map data copyrighted OpenStreetMap contributors

and available from https://www.openstreetmap.org.

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