Traffic Signal Control Using Fuzzy Logic

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A

SEMINAR REPORT ON

TRAFFIC SIGNAL CONTROL USING FUZZY LOGIC

A B S T R A C T

Traffic congestion has become a serious problem in the urban districts. This is mainly due to the rapid increase in the number and the use of vehicles. Travel time, travel safety, environmental quality, and life quality are all adversely affected by traffic congestion. Many traffic control systems have been developed and installed to alleviate the problem with limited success. Traffic demands are still high and increasing. The main focus of this paper is to introduce a versatile traffic flow model capable of making optimal traffic predictions. This model can be used to evaluate various traffic-light timing plans. More importantly, it provides a framework for implementing adaptive traffic signal controllers based on fuzzy logic technology.

This paper simulates the control logic of experienced human traffic controllers such as police officers who supersede signal controls at over-saturated intersections during special events. Given real-time traffic information, the FLC controller decides on whether to extend or terminate the current green phase based on a set of fuzzy rules.

The FLC strategy was compared with pretimed and actuated control strategies using a typical intersection with varying traffic volume levels. Based on delay, speed, % stops, time in queue and throughput-to-demand ratio statistics, the FLC strategy produced

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significant improvements over pretimed and actuated control strategies under heavy traffic volumes. This indicates that FLC has the potential to improve operations at over-saturated intersections.

C O N T E N T S

Page No

1. INTRODUCTION

1

1.1 GENERAL 1

1.2 OBJECTIVES 2

1.3 Types in traffic signal control 2

2. FUZZY SET AND FUZZY LOGIC 4

2.1Fuzzy Set 4

2.2 Fuzzy Logic 5

3. TERMINOLOGY AND NOTATION 7

3.1 Terminology 7

3.2 Notation 8

4. MODELING A SINGLE INTERSECTION 10

5. METHODOLOGY 12

6. INVESTIGATING OF FUZZY LOGIC SIGNAL

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8. CONCLUSION 25

REFERENCES 26

LIST OF FIGURES FIG NO DESCRIPTION PAGE NO 2.1 Fuzzy logic system 6

3.1 Single 4- leg intersection 7

3.2 Illustration of the traffic phases 8

4.1 The 4- phases of the c-th signal cycle 11

4.2 Determination of coefficient aln using a linear regression model 11

5.1 Fuzzy sets for QC,QN and AR 13

5.2 Initial threshold values for fuzzy sets for QC,QN and AR 15

6.1 Comparison of fuzzy logic model values with traffic actuated model values for two phasing control and equal traffic volumes. 17

6.2 Comparison of fuzzy logic model values with traffic actuated model values for two phasing control and different (not equal) traffic volumes. 18

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6.3 Comparison of fuzzy logic model values with traffic actuated model values for three phasing

control and equal traffic volumes. 19

6.4 Comparison of fuzzy logic model values with traffic actuated model values for three phasing control and different (not equal) traffic volumes. 19 7.1 Geometry of the Intersection 21

7.2 Pretimed signal 22

7.3 Actuated signal 23

7.4 Results of case study 24

LIST OF TABLES TABLE NO DESCRIPTION PAGE NO 5.1 Fuzzy Rules 14

5.2 Fuzzification of Input Traffic 16

5.3 Fuzzy Inference using Max- Min Composition Method 16

7.1 Traffic volumes(veh/hr) 21

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1. INTRODUCTION

1.1 GENERAL

Intersections are common bottlenecks in roadway systems. More intelligent traffic signal control would make the current roadway system operate more efficiently without building new roadways or widening existing roadways which is often impossible due to scarce land availability and public opposition to roadway expansion in many locations. It has been recognized that signal improvement is one of the most useful and cost-effective methods to reduce congestion

While controlling the traffic flows at signalized intersections, it is aimed to decrease delays of vehicles and environmental effects and also increase intersection capacity at same time.

Most signal controls are implemented with either pretimed controls or actuated controls. A pretimed controller repeats preset signal timings derived from historical traffic patterns. An actuated controller computes phase durations based on real-time traffic demand obtained from the detection of passing and stopped traffic on all lanes leading into an intersection.

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Fuzzy logic is one of these new methods introduced in 1960 by Lutfi Askerzade (Zadeh) at University of California (Berkeley) and it was based on set theory.

The main benefit of fuzzy set theory is the opportunity to model the ambiguity and the uncertainty of decision making. The basic idea of fuzzy traffic signal control is to model the control based on human expert knowledge, rather than the modelling of the process itself. Fuzzy logic has the ability to comprehend linguistic instructions and to generate control strategies based on a priori communication.

1.2 OBJECTIVES

The main goal of traffic signal control is to ensure safety at signalized intersections by keeping conflicting traffic flows apart. Traffic signal control can contribute to this as part of a wider traffic management system with consistent and well-defined aims. Some of the areas where changing the objectives of traffic signal control could make a difference are:

- pedestrian friendly signals, - separate signals for cyclists, - public transport priorities, - heavy vehicle priorities, - Environmental sensitivity.

The objectives of fuzzy signal control were:

- to present fuzzy logic as a control method in adaptive traffic signal control, - to make a general theoretical analysis of fuzzy traffic signal control,

- to formulate generalized fuzzy control rules for traffic signal control in different cases using linguistic variables,

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Fixed time signal control is based on the historical traffic data, assuming traffic conditions are unchanged in the time periods. A local field signal controller uses the preset timing plan to control intersection signals. Since the traffic demands are changing all time in the real world, the fixed time signal control is obviously not satisfactory.

b. Adaptive signal control

As an improvement over fixed time control, this control scheme uses the online data that are collected from sensors and detectors installed at an intersection. The operation of signal control depends on the actual traffic situation.

Vehicle-actuated Signals, in many cases, for isolated intersections, the fixed time control when abandoned and replaced by vehicle-actuated control. The most important elements of actuated control are demand and extension. The traditional vehicle-actuated control of isolated intersections attempts continuously to adjust green times. The main disadvantage is that the control algorithm looks only at the vehicles on green while not taking into account the number of vehicles waiting at red. The simplest type of vehicle-actuated installation has a detector located at a distance A ahead of the stop line at an intersection approach, and a controller sensitive to signals sent by the detector.

It follows that simple traffic-actuated signals suffer from some of the same weaknesses as those of fixed-timed signals. They will work well if the actual traffic flow matches the flow assumed when the unit extension of green was selected. An obvious direction of improvement is to design traffic-actuated signals with variable unit extension, varying with the length of green and/or with the changes in flow rate. Such improvements are, in fact, operational.

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2. FUZZY SET AND FUZZY LOGIC

Fuzzy set theory is suitable for systems that involve imprecise and vague information. The fuzzy set theory was first introduced by Zadeh in 1965 as a mathematical method for representing vagueness in everyday life. It has been recognized as a useful mathematical tool in a variety of research fields, including transportation engineering and planning.

Based on basic fuzzy set theory, Zadeh first introduced fuzzy logic in 1973. Fuzzy logic is a mathematical representation of human concept formulation and reasoning. In recent years, fuzzy logic has been applied to practical problems with controls and decisions which involve or are similar to the imprecise human reasoning process. It is a promising mathematical approach for modelling traffic control processes which are characterized by subjectivity, ambiguity and imprecision.

2.1Fuzzy Set

In the classic theory of sets, also known as crisp set theory, very precise bounds separate the elements that belong to a certain set from the elements outside the set. In other words, it is easy to determine whether an element belongs to a set or not. The membership of

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element x in set A is described in the classic theory of sets by the membership function

α

A

(x)

,as follows:

α

A

(x)

= 1, if and only if x is not a member of A

= 0, if and only if x is a member of A

However, many sets encountered in real life do not have precisely defined bounds that separate the elements in the set from those outside the set. For example, if we denote by A the set of “long delay at a signal,” how could we establish which element belongs to this set? Does a delay of 40 sec. belong to this set? What about 30 sec. or 60 sec.? It is obvious that the binary logic of having each single element to either belong to a set (membership = 1) or not belong to a set (membership = 0) is not appropriate for most categories describing real-world situations that do not possess well-defined boundaries. Fundamentally then this initiates the development of fuzzy set theory.

In contrast to the classical set theory, fuzzy sets admit intermediate values of class membership. A fuzzy set is represented by a membership function which expresses the degree that an element of the universal set belongs to the fuzzy set: larger values denote higher degrees of membership, smaller values indicate lower degrees of membership. The most commonly used range of values of membership functions is the unit interval [0,1]. Each membership function maps elements of a given universal set X into real numbers in

[0,1]. In other words, themembership function of a fuzzy set A,

α

A

(x)

, is defined as

α

A :

X

[

0,1

]

2.2 Fuzzy Logic

The development of fuzzy logic dates back to 1973. Introducing a concept he called “Approximate reasoning”, Zadeh successfully showed that vague logical statements enable the formation of algorithms that can use vague data to derive vague inferences.

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Fuzzy logic makes it possible to compute with words, which enables complex analysis reflecting the human thinking process. Each fuzzy logic system can be divided into three elements (Figure 2.1): fuzzification, fuzzy inference and defuzzification.

Figure 2.1 Fuzzy logic system

Input data are most often crisp values. Fuzzification maps crisp numbers into fuzzy sets. The fuzzifier decides the corresponding membership grades (or degrees of membership) from the crisp inputs. The resulting fuzzy values are then entered into the fuzzy inference engine. Fuzzy inference is based on a fuzzy rule base which contains a set of If →Then fuzzy rules. A typical fuzzy rule would be:

If {Queue Length is Long} and {Arriving Rate is High} and {Queue length on the cross street is Short}

Then {Green Light is extended}

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3. TERMINOLOGY AND NOTATION

To facilitate the discussion in the subsequent sections, some special terminology and notation are introduced.

3.1 Terminology

Without loss of generality, it is sufficient to consider a single four-leg intersection, which usually arises from two intersecting arteries (roadways). As shown in Figure 3.1, a typical intersection has the configuration described below.

- Four approaches: south (I = l), east (I = 2), north (I = 3), and west (I = 4). - Three lanes in each approach: left-turn (n = l), straight-forward (n = 2), and Right- turn (n = 3).

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Figure 3.1. Single 4- leg intersection

In addition, it is assumed that each signal cycle of the traffic light consists of four phases. Referring to Figure 3.2, each phase signifies the duration of the green signal intended for the traffic in specific lanes and specific approaches. Specifically,

- Phase 1: For left-turn, south (approach 1) and north (approach 3) traffic. - Phase 2: For straight-forward and right-turn, south (approach 1,) and north (approach 3) traffic.

- Phase 3: For left-turn, east (approach 2) and west (approach 4) traffic. - Phase 4: For straight-forward and right-turn, east (approach 2) and west (approach 4) traffic.

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Figure 3.2 Illustration of the traffic phases

3.2 Notation

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A traffic state vector, denoted by

is a 3D vector, which is used to describe the number of queue vehicles in approach 1 at time t. The term approach refers to an artery or roadway that converges to an intersection. The components x1l(t) , x2l(t) , and x3l(t) denote the number of queue vehicles in the left-turn lanes, straight-forward lanes, and right-turn lanes, respectively. The queue vehicles at an intersection with four approaches are depicted in Figure 2.

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A traffic flow vector, denoted by

is a 3D vector, which specifies the flow rate of incoming traffic for approach l at time t. The three components J1l(t), J2l(t) and J3l(t) represent the traffic flow rate (vehicle/second) in the left-turn lanes, straight-forward lanes, and right-turn lanes, respectively.

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Green signal parameters

For an intersection where each signal cycle has I phases, the parameter

Specifies the length of green signal in phase i for approach I during signal cycle c. The duration of signal cycle c is denoted as Tc.

4. MODELING A SINGLE INTERSECTION

In this section, a dynamic model is formulated to describe the traffic flow at an intersection. The purpose is to acquire capability to adequately predict the traffic flow process. Without loss of generality, it is sufficient to consider a single four-leg

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It is of great practical interest to maintain an accurate count of queue vehicles at the intersection. Accordingly, the number of queue vehicles at time t in lane n of approach I during signal cycle c is modelled by the following differential equation:

Where,

Figure 4.1 The 4- phases of the c-th signal cycle

Intuitively, this model stipulates that the rate of traffic flow in a lane of any approach is proportional to the current number of queue vehicles plus the flow rate of incoming traffic.

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In this formulation, it is taken that the signal cycle c starts at t = T, which is the total duration of (c-1) cycles. The green signal parameters gil

(c), are read from the stored

timing plans, which are optimally calculated using Webster's theory.

It may be mentioned that the coefficients

a

ln, are determined by fitting a linear regression

model to simulate the relationship between the vehicles crossing intersection per unit time and the number of queue vehicles. This procedure is depicted in Figure 4.2

Figure 4.2 Determination of coefficient aln using a linear regression model

5. METHODOLOGY

Signal control is basically a process for allocating green time among conflicting movements. Alternatively, signal control is a process for determining whether or to extend or terminate the current green phase. The proposed fuzzy logic controller (FLC) works in the same way but it is significantly different from actuated control. Actuated control extends green time based on an extension interval, a maximum green time and the vehicular actuations on the subject approach. No examination of the conditions on

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The proposed fuzzy logic controller determines whether to extend or terminate the current green phase based on a set of fuzzy rules. The fuzzy rules compare traffic conditions with the current green phase and traffic conditions with the next candidate green phase. The set of control parameters is:

QC = Average queue length on the lanes served by the current green, in veh/lane. QN = Average queue length on lanes with red which may receive green in the next phase, in veh/lane.

AR = Average arrival rate on lanes with the current green, in veh/sec/lane TMIN = minimum green time for each phase, in sec.

TMAX_ TH = maximum green time for through lanes which can vary for different approaches, in sec.

TMAX_LT = maximum green time for left-turn lanes which can vary for different approaches, in sec.

The fuzzy logic controller determines whether to extend or terminate the current green phase after a minimum green time of TMIN has been displayed. If the green time is

extended, then the fuzzy logic controller will determine whether to extend the green after a time interval Δt. The interval Δt may vary from 0.1 to 10 sec. depending on the controller processor speed. Δt = 5 sec. in this study. If the fuzzy logic controller determines to terminate the current phase, then the signal will go to the next phase. If not, the current phase will be extended and the fuzzy logic controller will make the next decision after Δt and so forth until the maximum green time is reached.

The decision making process is based on a set of fuzzy rules which takes into account the traffic conditions with the current and next phases. The general format of the fuzzy rules is as follows:

If {QC is X1} and {AR is X2} and {QN is X3} Then {E or T}. Where,

X1, X2, X3 = natural language expressions of traffic conditions of respective variables

E = Extension of green phase T = Termination of green phase

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QC and QN are divided into four fuzzy sets: “short,” “medium,” “long” and “very long.” AR is divided into three fuzzy sets: “low,” “medium” and “high.” The number of fuzzy rules is dependent on the combinations of fuzzy sets for X1, X2, and X3. A total of 4⋅ 3⋅4 = 48 fuzzy rules are listed in Table 5.1

The parameters QC, QN, and AR are characterized by fuzzy numbers as shown in Fig 5.1 Trapezoidal fuzzy numbers are used in this study. Q1 to Q6 are threshold values to define fuzzy sets for QC and QN; AR1 to AR4 are threshold values to define fuzzy sets for AR.

Figure 5.1 Fuzzy sets for QC,QN and AR

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The input data (traffic conditions) are first fuzzified using the proposed fuzzy sets for QC, QN, and AR. Then the fuzzified input data are entered into the fuzzy inference system which is composed of a set of fuzzy rules as described above. The max-min composition method is applied for making inferences. The membership grades (or degrees of membership, between 0 and 1) for E (Extend) and T (Terminate) are compared. The one with the highest membership grade is chosen as the control action.

The initial threshold values for fuzzy sets for QC, QN, and AR are shown in Figure 5.2

Figure 5.2 Initial threshold values for fuzzy sets for QC,QN and AR

The entire fuzzy logic control process can be represented with a simple example as follows. Suppose that after a time interval Δt = 5 sec. (within the maximum green time), the fuzzy logic controller needs to make a decision whether to extend or terminate the current green phase based on the following traffic conditions:

QC = 7.5 veh/lane AR = 0.18 veh/sec/lane QN = 10.5 veh/lane

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and 36 in Table 5.1 are involved in this fuzzy inference. The fuzzy inference procedure using max-min composition method is shown in Table 5.3. Based on the fuzzy logic inference procedure, the fuzzy logic controller will decide to extend the green time for the current phase.

Table 5.2 Fuzzification of Input Traffic Data

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6. INVESTIGATING OF FUZZY LOGIC SIGNAL CONTROL

MODEL PERFORMANCE

Performance of Fuzzy Logic Signal Control Model is investigated using simulation studies. Fuzzy logic signal control model is compared with traffic actuated model for two and three phased controlled intersections with respect to average delays. Average delay values are calculated by using weighted average method considering traffic volumes of approaches and it is expressed as seconds per vehicle unit for each flow.

Comparisons are done by considering two cases of traffic volumes; equal and different (not equal) values at approaches of intersection. Results for two phasing situation are given in Figure 6.1 and Figure 6.2, respectively.

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Figure 6.2. Comparison of fuzzy logic model values with traffic actuated model values for two phasing control and different (not equal) traffic volumes.

Second situation which is considered for researching the performance of the fuzzy logic controller is not equal or different traffic volumes on approaches of intersection at the same time. Some experimental studies are made for determining considered traffic volumes and results of comparisons are indicated in Figure 6.2

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Results for three phasing situation are given in Figure 6.3 and Figure 6.4 respectively.

Figure 6.3 Comparison of fuzzy logic model values with traffic actuated model values for three phasing control and equal traffic volumes.

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Figure 6.4 Comparison of fuzzy logic model values with traffic actuated model values for three phasing control and different (not equal) traffic volumes.

According to the simulation studies, it is understood that results of the fuzzy logic controller is the same as the traffic actuated controller when considering two phasing controlled situation and little traffic volumes. But if the variation and values of traffic volumes are bigger, the fuzzy logic controller decreases the delays of vehicles and increases performance about 15 percent. When considered three phasing controlled situation, fuzzy controller also decreases the delays and increases the capacity for equal and different traffic volumes.

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7. CASE STUDY

FLC was evaluated against pretimed and actuated control strategies. The MOE used in the evaluation were (1) network delay, (2) network speed, (3) % stops, (4) network time in queue, and (5) network throughput-to-demand ratio. The best control strategy is the one that provides the lowest delay, highest speed, lowest % stops, lowest time in queue, and highest throughput-to-demand ratio.

The geometry of the intersection is illustrated in Figure 7.1 Left-turn lanes were made long enough to accommodate left-turning traffic queues. Traffic volumes varying from 20% to 100% of the highest volume are shown in Table 7.1 The 100% traffic volume level represents a condition where two conflicting movements have a volume-to-capacity ratio greater than 1.0, thus, the intersection is substantially over-saturated

Figure 7.1 Geometry of the Intersection Table 7.1 Traffic volumes(veh/hr)

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Two simplifications were applied: no right turn on red and no pedestrian demand. The pretimed signal timings shown in Figure 7.2 were optimized with TRANSYT-7F using “delay and stops” as the objective function. Figure 7.3 displays the actuated control phases and phase timing. For all phases minimum green time is 8sec and maximum green time is 40sec.Vehicle extension intervals of 2, 3 and 4 sec. were tried and the value that produced the best performance in terms of speed and delay was used to compare actuated control with FLC.

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Figure 7.3. Actuated signal

Table 7.2. Parameters for Fuzzy logic controller

Five different combinations of control parameters (Q1-Q6, AR1-AR4, TMAX_TH, TMAX_LT,

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The simulation results for FLC are listed in the lower half of Table 7.2. The columns with shaded background are the best FLC control for each volume level. As expected, FLC control parameters increase with increasing traffic volumes.

FLC is compared with pretimed and actuated control as summarized in Figure 7.4. The summary table in Figure 7.4(a) shows average proportional differences of FLC’s MOE over pretimed and actuated control for the test intersection. FLC produced the best performance for all MOE examined.

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A basic fuzzy logic control (FLC) algorithm for full intersections with two-way streets and left-turn lanes was developed. The FLC strategy simulates the control logic of experienced humans such as police officers directing traffic who often replace signal controls when intersections experience unusually heavy traffic volumes (e.g., during special events.) The FLC controller makes the decision whether to extend or terminate the current green phase based on a set of fuzzy rules and real-time traffic information.

FLC was compared with pretimed and actuated control strategies using a typical intersection with varying traffic volume levels. Measures of effectiveness including delay, speed, % stops, time in queue, and throughput-to-demand ratio were examined. FLC showed substantial improvements over pretimed and actuated control strategies for all MOE except % stops under heavy traffic volumes. Overall, the simulation results indicated that FLC has the potential to improve operations at oversaturated intersections.

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[1] Lin Zhang, Honglong li, Panos D Prevedours, 2004 ,”Signal Control for over saturated intersections using Fuzzy Logic” , A presentation for publication in the Transportation Research Record.

[2]Yetis Sazi Murat, Ergun Gedizlioglu, “Approach for Fuzzy Traffic Signal Control”, Istanbul Technical University, Turkey

[3] Qinghui lin, B. W. Kwan, L.J.Tung ,”Traffic Signal Control Using Fuzzy Logic”, FAMU-FSU College of Engg ,U S A

[4] Klir, G. J., and B. Yuan,1995, “Fuzzy Sets and Fuzzy Logic: Theory and Applications”. Prentice Hall, Englewood Cliffs, New Jersey .

[5] Teodorovic, D,1999, “Fuzzy Logic Systems for Transportation Engineering: the State of the Art”. Transportation Research, Part A, Vol. 33, pp. 337-364.

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