Intersection Traffic State Estimation using Speed Transition Matrix and

Fuzzy-based Systems

ˇ

Zeljko Majstorovi

´

c

a

, Leo Ti

ˇ

sljari

´

c

d

Faculty of Transport and Traffic Sciences, University of Zagreb, Vukeli

´

ceva street 4, 10000 Zagreb, Croatia

Keywords:

traffic demand. Thus, a better approach for solving the problem of city congestion is by optimal management

of the existing infrastructure. Timely detection of traffic congestion on the road level can prevent congestion

formation and even improve road network capacity when used for appropriate traffic control actions. Detecting

congestion is a complex process that depends on available traffic data. In this paper, for traffic state estimation,

including congestion level, at the intersection level, a new method based on Speed Transition Matrix and

Fuzzy-Based System is presented. The proposed method utilizes the Connected Vehicle environment. It is

tested on a model of an isolated intersection made in SUMO simulation software based on real-world traffic

data. The validation results confirm the successful detection of traffic state (congestion level) at intersections.

1 INTRODUCTION

In recent years, the world has faced an increased num-

flicting traffic flows are safely resolved using traffic

lights.

In general, urban congestions can be divided into

recurrent and non-recurrent. Physical limitations of

infrastructure, daily repeating periods of increased

traffic demand, and infrastructure management cause

recurrent congestions, and non-recurrent congestions

are mainly caused by traffic incidents, special events

(e.g., sports events, concerts, vehicle breakdown, traf-

fic accident), roadworks, etc (Chow et al., 2014). Re-

c

https://orcid.org/0000-0002-2083-0672

d

https://orcid.org/0000-0001-8564-4304

alleviate them. For the latter, good traffic state esti-

mation is crucial because the first step towards the so-

lution of congestion is its detection. By successfully

detecting the congestion, appropriate actions for con-

gestion soothing like changing the signal or rerouting

vehicles can be taken.

Urban roads can operate longer in stop-and-go

count for multiple input parameters and describe them

with a single value to have reliable data to estimate

the traffic state. Researchers often use fuzzy logic

because it is close to human reasoning and can also

process vague input information. Fuzzy logic is used

to describe the uncertainty of things and has wide ap-

plication in fuzzy reasoning which allows application

in different fields (Maldonado et al., 2021). Because

of its properties, fuzzy logic has also found its ap-

plication in traffic engineering (Koukol et al., 2015).

variable speed limits, and adaptive traffic signal con-

trol. (Pozna and Precup, 2014) created an algorithm

for modeling expert systems. The advantage of this

lyzes. Unlike historical traffic data that needs to be

collected over a period of time to observe patterns in

traffic behavior covering only specific measurement

points, each CV can provide real-time data. Thus,

spatio-temporal traffic data can be collected. While

existing infrastructure uses traffic monitoring sensors

and cameras to detect congestion and manage traf-

fic infrastructure, networked vehicles can communi-

cate with infrastructure using Vehicle to Infrastructure

(V2I) communication and other vehicles using Vehi-

tion (Shuttleworth, 2019). SAE Level 0 implies ve-

hicles without automation to SAE Level 5 which im-

plies full vehicle autonomy. According to the same

standard almost fully self-driving (Level 4) and even

fully autonomous vehicles (Level 5) are expected

within a decade including city driving.

CVs have significant advantages. Modern equip-

ment such as radars, lidars, cameras, and many

other sensors makes them excellent mobile data traf-

fic sources. To optimize the driving strategy of

Moreover, CVs have advantages over existing traffic

sensor technology because they are not limited by line

of sight like cameras, and are collecting large amounts

of data at the microscopic level which is convenient

for studying traffic. However, the motivation for this

research stems from the question of how to process

large amounts of data quickly and efficiently. Such

data amounts of data will be generated by future traf-

fic flows containing classic and CVs. The share of

the later will rise decreasing the need for classic traf-

as well. The motivation for this research stems from

the question of how to process large amounts of data

quickly and efficiently using the potential of mobile

during simulation, and are represented as a speed

probability distribution of vehicles traveling between

two consecutive road segments. Thus, the scientific

contributions of this paper are as follows:

estimation is proposed based on the attributes ex-

tracted from the traffic patterns represented with

the STMs;

dated on an isolated intersection in the Simulation

of Urban Mobility (SUMO) software.

The rest of the paper is organized as follows. In

section 2, existing traffic state estimation methods are

described. The proposed methodology applied inter-

fic states based on features found in historical data.

Depending on historical data has its drawbacks.

These methods are prone to failure if an irregular

events. They rely on streaming data and weak as-

sumptions without capabilities for future prediction.

For accurate estimation, these methods require large

amounts of streaming data (Seo et al., 2017).

For traffic analysis, the Global Positioning System

(GPS) is commonly used as a data source. Needed

traffic data are mostly collected by GPS-equipped taxi

or delivery vehicles. GPS cannot always provide ac-

curate data. Thus, it is mostly used to determine con-

ditions on the road level. (Kan et al., 2019) detected

speed thresholds. Another example of applying GPS

data to estimate queue length and level of service for

an intersection is (Ti

c et al., 2018). All of these

methods rely on features such as vehicle speed and

position extracted from GPS data, which depend on

the number of tracked vehicles and valid GPS data

samples. Also, it is important to consider the time de-

lay caused by data processing because it takes some

time to collect enough GPS data and process it.

(He et al., 2019) relayed on probe vehicle data

estimation of queue lengths on intersection based on

detectors data which resulted with reliable estimation

of queue lengths in real-time.

Fusion from multiple data sources can also pro-

vide timely and accurate information, which are im-

portant for applications such as driver information

systems and traffic control systems (Papageorgiou

et al., 2003). To estimate queue tail location, (Rostami

Shahrbabaki et al., 2018) fused detector data with the

location and speed of the CVs in a mixed traffic flow

3 METHODOLOGY

The model is made based on real-world data, it is part

of the arterial road network of the City of Zagreb, and

it is known for congestions during peak hours.

peak hours without significant congestions.

model as proposed in (Ti

ˇ

sljari

´

c et al., 2020). The

STM is a matrix that represent the probability of the

speed change when vehicles are traveling between

two consecutive road segments in the observed time

period ∆t. Every transition is defined with two con-

secutive road segments, e

segment, and e

tion segment. Fig. 4 shows two representative exam-

ples of the extracted STMs. Thus, the final form of

the STM is:

X(∆t) =

.

.

.

p

where p

represents the probability of the speed

After processing the road traffic data creating

the STMs, the fuzzy-based traffic state estimation

method, adopted from (Ti

sljari

c et al., 2022) is ap-

served traffic parameter type, which implies the traf-

fic state. In Fig. 4a, congestion as one of the traf-

fic states can be detected because transitions indicate

small speeds on origin and destination segments.

traffic flow

(b) Extraction of attributes from STM

Figure 4: Examples of STMs representing road traffic

states.

There are two attributes extracted from the STM

as input parameters for the fuzzy-based traffic state

estimation (shown in Fig. 4b): distance from the

STM’s source d

, and distance from the STM’s diag-

onal d

, both computed as the Euclidean distances.

estimation, and d

parameter for the anomaly poten-

tial (Ti

sljari

computation process is described in (Ti

Table 1: Set of fuzzy rules used for bottleneck probability

estimation (Ti

ˇ

sljari

´

c et al., 2022).

The membership functions of the input and out-

put variables of the fuzzy-based system are shown

in Fig. 5. The bottleneck probability is the output

of the system with input variables modeled with d

and d

ables are represented as linguistic variables with val-

value from the interval [0, 1] (Ti

ˇ

sljari

Figure 5: Fuzzy-based system setup for the bottleneck prob-

ability estimation.

4 RESULTS

A representative example of intersection state estima-

tion results are shown in Fig. 6. The Fig. 6a shows

speeds of vehicles captured with SUMO simulator

case, direction East-West). It can be observed that the

speeds in front of a traffic light (edge JS6 presented

in Fig. 6a) are lower during the whole day, which is

Fig. 6b is the result of fuzzy inference system

where peak hours can be observed. Additionally, it

can be observed that during the day, the bottleneck

probability is increased on edge JS7. Increased bot-

tleneck probability on edge JS7 is because an STM

reflects speed change. When the vehicles start mov-

ing on the green traffic light signal, the CoM of that

STM will be positioned in the upper right corner. In

that case, d

and d

are high which results with in-

towards the left side of the figure in the same way in

Figs. 6a and 6b.

Figure 7: Example of results of TimeLoss parameter.

The validation process was conducted using confu-

sion matrices, and results were presented using a con-

fusion matrix and a classification report. The classifi-

cation report contains the total accuracy of the model,

precision, recall, and F1-score for each class. In this

case, class is particular traffic state, and two classes

The accuracy parameter is used to measure the

accuracy of the model. It is computed as the number

of data instances that were predicted correctly divided

5 CONCLUSIONS

pean Regional Development Fund under the grant

KK.01.1.1.01.0009 (DATACROSS). This research

has been carried out within the activities of the Center

of Research Excellence for Data Science and Coop-

erative Systems supported by the Ministry of Science

and Education of the Republic of Croatia. The author

and Ph.D. student

´

of Zagreb Faculty of Transport and Traffic sciences

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