identifying the range of threshold for fuzzy input in a traffic flow

1. DEPARTMENT OF CIVIL ENGINEERING BAYERO UNIVERSITY KANO
IDENTIFYING THE RANGE OF THRESHOLD FOR FUZZY
INPUT IN A TRAFFIC FLOW
BY
Salisu IBRAHIM
(SPS/21/MCE/00024)
December, 2023
SPS/21/MCE/00024

2. PRESENTATION OUTLINE
▪ Introduction
▪ Problem Statement
▪ Aim and Objectives
▪ Literature Review
▪ Range of threshold for fuzzy input in a traffic flow
▪ Conclusion
▪ Recommendation
▪ References
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3. INTRODUCTION
An increase in traffic results in congestion growth, but also more accidents and air pollution. Even though traffic
congestion might be inevitable, there are ways to deal with this phenomenon. While many support the idea of improving
transportation systems through building new roads or repairing aging infrastructures, others argue that the future of
transportation lies not only in concrete and steel, but rather increased application of information technology. This
approach enables elements within the transportation system (e.g., vehicles, roads, traffic lights, message signs, etc.) to
become intelligent by embedding them with microchips and sensors and empowering them to communicate with each
other through wireless technologies (Ezell, 2011). Moreover, traffic and transportation engineers emphasizes on the
importance of implementing traffic guidance and control using the road resources effectively. These ideas evolve into the
discipline known as Intelligent Transportation Systems (ITS) whose general aim is to fulfill increasing traffic demands and
facilitate efficient utilizations of transport infrastructure. Therefore, the use of fuzzy inference model for detecting traffic
congestions at specific road segments or entire transportation networks was suggested. Moreover, it is interested to
investigate which traffic parameters (e.g. traffic flow, velocity, density) are most suitable for detecting traffic congestions
and to which degree the choice of these parameters influence the output interpretations.
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4. INTRODUCTION (cont’d….)
• Threshold: A threshold, in a general sense, is a point at which a physical or abstract property changes or
crosses a limit, leading to a significant effect or result.
• Fuzzy logic: The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by US-based
Iranian-Azerbaijani mathematician Lotfi Zade. Fuzzy Logic can be considered to be a generalization of a
logic system that includes the class of all logic systems with truth-values in the interval (0, 1). “In a broader
sense, fuzzy logic is viewed as a system of concepts, principles, and methods for dealing with modes of
reasoning that are approximate rather than exact.” Klir, St. Clair, and Yuan (1997).
• Fuzzy Input: The input to the fuzzy operator is two or more membership values from fuzzified input
variables. The output is a single truth value.
• Traffic flow: Traffic flow is the systematic study of the movement of vehicles, including cars, trucks,
bicycles, and pedestrians, as they navigate through a transportation network. It encompasses the examination
of factors such as vehicle speed, density, volume, and the interactions between different modes of
transportation. May, A. D. (1990). "Traffic Flow Fundamentals." Prentice Hall).
• Parameters in traffic flow: Fuzzy inference model input parameters are at the same time measures that
explain traffic congestion events. Based on the traffic flow theory, there are three traffic flow characteristics
which are most suitable for describing congestion phenomena – Density (k), Flow (q) and Mean speed (v)
(Wardrop, 1952).

5. PROBLEM STATEMENT
Traffic flow management is a critical aspect of urban planning and transportation engineering. In the context of
fuzzy logic systems, accurately defining the range of thresholds for fuzzy inputs such as speed, volume, and
density is essential for creating a responsive and effective traffic control system. However, the challenge lies in
determining precise threshold values that appropriately represent the diverse and dynamic conditions of traffic
flow on different road segments.
AIMS AND OBJECTIVES
The primary aim of this study is to develop a comprehensive understanding of the range of threshold values for
fuzzy inputs, specifically focusing on speed, volume, and density, in the context of traffic flow.
The objective is to define the range of threshold values for the linguistic terms "Low," "Medium," and "High"
for speed, volume, and density based on the analysis of traffic data and expert input.
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6. LITERATURE REVIEW
Fuzzy has been very popular for more than forty years in transport engineering applications such as speed control on
expressways (Ngo et’al 1994), signalization for traffic control (Zhao et’al 20ll), seaport (John, A et’al 2014) and transit
operations (Li, X et’al 2016), lane-changing simulation models (Li, Q et’al 2015) and congestion-related applications
(Kukadapawar, S.R et’al 2015). In (Kukadapawar, S.R et’al 2015), the authors measured the level of congestion by
using the same fuzzy approach with inputs such as speed reduction rate, the proportion of delay time within total travel
time, and traffic volume to road capacity. Patel and Mukherjee 2014 classified the traffic according to a fuzzified index
of congestion and the average speed Future Transp. 2023, 3 842 level on the urban road network. Here, the congestion
index was calculated as an output of the relationship between actual and free-flow travel time. The authors showed that
the fuzzy approach was better at showing the real congested situation than other traditional congestion index values.
Another fuzzy congestion evaluation study considering average speed as the input variable was presented by Hamad
and Kikuchi 2002. They used travel speed, free-flow speed, and the proportion of very low speed in the total travel
time as input variables to determine the congestion situation. Additionally, in 2006, Kikuchi and Chakroborty studied a
fuzzy approach for handling the uncertainty embedded in the definition of the level of service (LOS).

7. RANGE OF THRESHOLD FOR FUZY INPUT IN A TRFFIC FLOW
SPEED: The range of threshold values for speed as a fuzzy input in traffic flow can vary based on the specific
context, road characteristics, and the goals of the fuzzy logic system.
Let's consider a linguistic variable "Speed" with terms "Low," "Medium," and "High." Here's a hypothetical
example of threshold ranges:
a). Low Speed:
• Threshold Range: 0 km/h to 40 km/h
b). Medium Speed:
• Threshold Range: 30 km/h to 70 km/h
c). High Speed:
• Threshold Range: 60 km/h to 100 km/h
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8. SPS/21/MCE/00024
VOLUME: Defining the range of threshold values for a fuzzy input in traffic flow involves considering
factors like the type of road, local regulations, and the desired granularity of the fuzzy logic system.
Here's a hypothetical example with linguistic terms "Low," "Medium," and "High":
a). Low Traffic Volume:
• Threshold Range: 0 vehicles per hour (veh/h) to 500 veh/h.
b). Medium Traffic Volume:
• Threshold Range: 400 veh/h to 1000 veh/h
c). High Traffic Volume:
• Threshold Range: 800 veh/h to 1500 veh/h

9. SPS/21/MCE/00024
DENSITY: Defining the range of threshold values for a fuzzy input in traffic flow, such as "Traffic
Density," involves considering factors like road type, lane configuration, and local traffic regulations.
Here's a hypothetical example with linguistic terms "Low," "Medium," and "High," along with reference
values:
a). Low Traffic Density:
• Threshold Range: 0 vehicles per unit length to 20 vehicles per unit length
b). Medium Traffic Density:
• Threshold Range: 15 vehicles per unit length to 40 vehicles per unit length
c). High Traffic Density:
• Threshold Range: 35 vehicles per unit length to 60 vehicles per unit length

10. CONCLUSION/RECOMMENDATIONS
In conclusion, the defined threshold ranges for speed, volume, and density in a traffic flow provide a basis for
creating a fuzzy logic system that can model and respond to different traffic conditions. These ranges are
illustrative and should be adjusted based on the specific characteristics of the road and local traffic patterns.
The following recommendations are made:
1. Validate the fuzzy logic system with real-world data to ensure that the chosen threshold values accurately
represent the observed traffic conditions.
2. Collaborate with traffic engineers and local authorities to refine the threshold values based on their expertise
and insights into the specific road network.
3. Adopt an iterative approach, refining the fuzzy logic system based on continuous monitoring and feedback
to improve its accuracy and responsiveness to changing traffic dynamics.
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11. REFERENCE
1) Amini, M.; Hatwagner, M.; Mikulai, G.; Koczy, L. An intelligent traffic congestion detection approach based on fuzzy inference.
2) Eze, U.F.; Emmanuel, I.; Stephen, E. Fuzzy logic model for traffic congestion. IOSR J. Mob. Comput. Appl. 2014, 1, 15–20.
[CrossRef]
3) Kikuchi, S.; Chakroborty, P. Frameworks to Represent Uncertainty when Level of Service is Determined. Transp. Res. Rec. 2006,
4) Kukadapwar, S.R.; Parbat, D.K. Modeling of traffic congestion on urban road network using fuzzy inference system. Am. J. Eng.
5) Li, Q.; Qiao, F.; Yu, L. Socio-demographic impacts on lane-changing response time and distance in work zone with drivers’ smart
6) Ngo, C.Y.; Victor, O.K.L. Freeway traffic control using fuzzy logic controllers. Inform. Sci. 1994, 1, 59–76. [CrossRef]
7) Zhao, D.; Dai, Y.; Zhang, Z. Computational intelligence in urban traffic signal control: A survey. IEEE Trans. Syst. Man Cybern.
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