FUZZY LOGIC APPROACH FOR ESTIMATING 85

PERCENTILE SPEED BASED ON ROAD ATTRIBUTE DATA

Bayzid Khan

and Yaser E. Hawas

1,2

Roadway, Transportation and Traffic Safety Research Center,

United Arab Emirates University, Al Ain, United Arab Emirates

Department of Civil and Environmental Engineering, United Arab Emirates University, Al Ain, United Arab Emirates

Keywords: 85

Percentile Speed, Posted Speed Limit, Fuzzy Logic, Neuro-Fuzzy Training.

Abstract: This paper discusses the development of fuzzy logic model for estimating the 85

percentile speed of urban

roads. Spot speed survey was conducted on four randomly selected urban road segments for a typical

weekday and a weekend. The considered road segment attribute data are length of the road segment, number

of access points/intersecting links, number of pedestrian crossings, number of lanes, hourly traffic volume,

hourly pedestrian volume and current posted speed limits of the selected roads. Such attribute data were

collected and used as input variables in the model. Two models for weekday and weekend were developed

based on the field survey data. Both models were calibrated using the neuro-fuzzy technique for optimizing

the fuzzy logic model (FLM) parameters. Analyses of estimated results show that the FLM can estimate the

percentile speed to a reasonable level.

1 INTRODUCTION

Determining a safer posted speed limit for any given

roads/links is one of the major challenges for the

researchers and professionals all around the world.

Many studies tried to identify the safer speed limit

for a road (Manual on Uniform Traffic Control

Devices [MUTCD], 2003; Department for

Transportation [DfT], 2006; Global Road Safety

Partnership [GRSP], 2008). Setting a speed limit is a

multi-criteria task. Many road and roadside factors

such as the road alignment, section length, traffic

volume, pedestrian volume, current speed limit,

number of lanes, weather condition, time of the day,

law enforcement, purpose and length of the trip,

vehicles’ characteristics are to be incorporated.

(TRB, 1998; Srinivasan, Parker, Harkey, Tharpe and

Summer, 2006). Setting the speed limits also

requires understanding the drivers’ characteristics

and their driving pattern. As such, most of the

studies suggested the 85

percentile of the operating

speed to be set as the posted speed limit (Fitzpatrick,

Carlson, Wooldridge and Miaou, 2003).

Studies showed that the chances of involving in a

crash is least at 85

the percentile traffic speed

(Minnesota Department of Transportation

[MNDOT], 2002; American Association of State

Highway and Transportation Officials [AASHTO],

1985).

Developing a model to estimate the 85

percentile speed by incorporating all the factors is

quite challenging. The individual driver’s operating

speed depends on individual driver’s perception

about all of the above mentioned factors. For a given

road characteristics, every driver may choose

different operating speed. Therefore, it is very

important to develop a method to estimate the 85

percentile speed which will also address such

uncertain choice behaviour.

Many studies were conducted to determine the

factors that influence the choice of the operating

speed. Poe, Tarris and Mason (1996) showed that

access points, land-use characteristics and traffic

engineering features have influences on vehicle

speed on low speed urban streets. Haglund and

Aberg (2000) showed that the posted speed limit has

influence on drivers’ speed choice behaviour.

Fitzpatrick, Carlson, Brewer and Wooldridge (2001)

evaluated the influence of geometric, roadside and

traffic control devices on drivers’ speed on four-lane

suburban arterials and found that posted speed limit

was the most significant variable for both curve and

straight sections. Wang (2006) demonstrated that the

number of lanes, sidewalks, pedestrian movements,

Khan B. and E. Hawas Y..

FUZZY LOGIC APPROACH FOR ESTIMATING 85TH PERCENTILE SPEED BASED ON ROAD ATTRIBUTE DATA.

DOI: 10.5220/0003716300460054

In Proceedings of the 4th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2012), pages 46-54

ISBN: 978-989-8425-95-9

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

and access density have significant influences on the

drivers’ behaviour of choosing operating speed.

Fildes, Fletcher and Corrigan (1987) and Fildes,

Leening and Corrigan (1989) found that the road

width and the number of lanes have the greatest

influence on speed choice. Tignor and Warren

(1990) showed that the number of access points and

the nearby commercial development have the

greatest influences on the vehicle speeds. Most of

these studies used different model approaches range

from simple linear regression models to complex

curvilinear regression equations (Wang, 2006;

Tarris, Poe, Mason and Goulias, 1996; Poe and

Mason, 2000). Most of the existing models attempt

to quantify the operating speed based on physical

conditions such as road geometric design, roadside

development and traffic control devices. All of these

models used 85

percentile speed as a representative

measures for operating speed.

No studies on the use of FLM to estimate the

percentile speed have been found. The FLM

approach has the premise to tackle the imprecise,

vague and uncertain relationship between the inputs

and outputs. The proposed system can be regarded

as an expert system or a knowledge base. It is

critically important that the design of such system

should account for the imprecise, incomplete or not

totally reliable information (Zadeh, 1983). The key

feature of the FLM is the suitability to incorporate

intuition, heuristic and human reasoning (Hawas,

2004) and such technique is useful for problems that

entail probabilistic or stochastic uncertainty (human

behaviour modeling), or problems that cannot be

easily represented by mathematical modeling

because of the complexity of the process (Kikuchi

and Pursula, 1998). Fuzzy set theory provides a

strict mathematical framework in which vague

conceptual phenomena can be precisely and

rigorously studied (Zimmermann, 1996). The word

imprecise or vague does not mean the lack of

knowledge of data; rather it indicates the sense of

vagueness of the value of parameters.

The objective of this paper is to develop a fuzzy

logic based approach to estimate the 85

percentile

speed for different urban road segments based on

road segments attribute data for weekday and

weekend. In doing so, four urban road segments

(one local and three arterial roads) of Al Ain city of

United Arab Emirates have been selected randomly

(termed as ‘Site 1’ to ‘Site 4’). Only four road

segments were selected because of limited time and

resources for conducting the study. The authors do

recognize that the limited data collection cannot be

used to make general conclusions on the validity of

the devised FLM for a general network. We

emphasize here that the main contribution of this

study is the introduction of the concepts and the

procedure to develop the FLM that can be

generalized to any network given that adequate data

collection on a representative sample size is

fulfilled.

This paper is divided into five sections. The

second section provides a brief overview on data

collection methodology. In third section, the

structure of the proposed FLM is discussed in brief.

The inference engine and fuzzy operators, and

neuro-fuzzy training procedure are also discussed.

The fourth section discusses the FLM validation and

analysis of results. Concluding remarks on the use of

the FLM for estimating the 85

percentile speed to

set the speed limit are provided in the last section.

2 DATA COLLECTION

Spot speed survey were conducted on selected four

sites for five different time periods of the day, for a

typical weekday and weekend and for both

directions. The five time periods include both peak

(AM, MD, PM) and off-peak periods (15 minutes

within each time period). Only passenger vehicles

(excluding trucks and busses) were selected

randomly for the survey, keeping in mind that a

minimum of 50 vehicles should be observed for spot

speed study (Ewing, 1999) on each selected road

segments. The 85

percentile speed of the spot speed

data was calculated for 40 different cases (4

sites*2directions*5 time periods) for two days (one

typical weekday and one weekend).

The detailed road attribute data including the

length of the road segment, number of access

points/intersecting links, number of pedestrian

crossings, number of lanes, traffic count and

pedestrian count data (15 minutes count), and the

current posted speed limit for each road were

collected. The length of Site 1 is 2.78 km, has 8

access points and 3 pedestrian crossings on each

direction. The traffic volume is relatively high, but

number of pedestrian is low on both weekday and

weekend. Site 2 is 0.46 km long with 4 access points

and 3 pedestrian crossings on each direction. This

site has the highest pedestrian volume with the

lowest traffic volume among the four sites. The

length of Site 3 is 2.15 km. It has 11 and 8 access

points on direction 1 and direction 2, respectively.

The site has the highest traffic volume (among the

four sites) on both weekday and weekend.

Pedestrian volume is also high at this site. Site 4 is

FUZZY LOGIC APPROACH FOR ESTIMATING 85TH PERCENTILE SPEED BASED ON ROAD ATTRIBUTE

DATA

2.94 km long, 4 access points on both directions

with no pedestrian crossing. The traffic volume is

moderate with very little pedestrian activity. The

traffic and pedestrian count data were converted to

hourly volume data prior to developing the FLM. It

is to be noted that all road attribute data are fixed for

each road segments for different time periods and

for weekday and weekend except the traffic volume

and pedestrian data. The current posted speed limits

for site1, site 2, site 3 and site 4 are 40, 60, 80 and

80 km/hr, respectively.

3 DEVELOPMENT OF FLM FOR

PERCENTILE SPEED

ESTIMATION

The development of the FLM starts with preparing

the data sets for both weekday and weekend. The

road attribute data collected from the fields were

used as the input variables. The estimated 85

percentile of the operating speed was used as the

output variable. The input and output variables and

their corresponding modified name used in the FLM

are shown in Table 1. Two separate models were

developed (for weekday and weekend). It is to be

noted that volume to capacity ratio was also

calculated from the hourly traffic volume to

incorporate in the FLM development.

Table 1: Input and output variables and their

corresponding modified name in fuzzy logic.

Variable

category

Variable name Denoted in

FLM

Input

variables

Length Length

Number of access

points/intersecting links

IntLnks

Number of pedestrian

crossings

PedCros

Volume to capacity (V/C)

ratio

VCRat

Hourly pedestrian volume PedVol

Posted speed limit PostSp

Output

variable

percentile speed SpEF

The FLM development was done in two stages

using the tool FuzzyTech (INFORM, 2001)- first,

initial models were developed for both weekday and

weekend by setting the memberships (fuzzy sets’

parameters) and the knowledge base (rules)

intuitively (using some correlation analysis).

Secondly, to overcome the limitations of intuitive

setting of knowledge base, the neuro-fuzzy logic

(integrated fuzzy and neural nets) (Hawas, 2004)

was used.

3.1 Development of Initial Fuzzy Logic

Model

The development of initial models involves three

major steps- fuzzification (converting numeric

variables into linguistic terms), fuzzy inference

(knowledge base- ‘IF-THEN’ logics) and de-

fuzzification (converting linguistic terms into

numeric output values) (Figure 1).

Figure 1: Conceptual block diagram of the proposed FLM.

3.1.1 Fuzzification

The input and output variables are numeric in nature.

The drivers mostly perceive these as linguistic

terms. For example, the traffic volume may be

perceived as high or medium or low rather than its

actual numeric values. As such, the numeric values

of each input variables were converted into three

linguistic terms and the values of the output variable

has been converted into five linguistic terms (Table

2). The minimum and maximum values of each

variable were determined from the survey results. It

is to be noted that the variability of data for the

output variable is high and grouping these data into

more linguistic terms might result in more accurate

estimation of the output variable. On the other hand,

three terms have been selected for the input

variables due to low variability of the data. It will

also reduce the number of rule bases and neuro-

fuzzy training time.

The ‘L-shape’ membership function (MBF) was

used for all variables. The MBFs were generated

using the “Compute MBF” fuzzification method.

Figure 2 shows the MBF for the Hourly Pedestrian

Volume input variable for weekday. For this

particular variable, the ranges of linguistic terms

were set as (0, 92), (42.465, 138) and (92, 184) for

the low, medium and high terms, respectively. The

possibility that a numeric level belongs to a

linguistic term’s range is denoted by the membership

degree, µ (Y axis in Figure 2). A µ of 0.0 indicates

zero possibility, while µ of 1.0 indicates full

membership.

ICAART 2012 - International Conference on Agents and Artificial Intelligence

Table 2: The proposed FLM variables term definitions.

Variable

name

Day of the

Week

Min Max

Linguistic

terms

Length

Weekday,

Weekend

0.46 2.94

Low,

medium,

high

IntLnks

Weekday,

Weekend

4 11

Low,

medium,

high

PedCros

Weekday,

Weekend

0 3

Low,

medium,

high

VCRat

Weekday 0.08 1.03

Low,

medium,

high

Weekend 0.07 1.13

PedVol

Weekday 0 184 Low,

medium,

high

Weekend 0 156

PostSp

Weekday,

Weekend

40 80

Low,

medium,

high

SpEF

Weekday 13.9 109.9

Very low,

low,

medium,

high, very

high

Weekend 22.36 124.89

Figure 2: Membership function for ‘hourly pedestrian

volume’ input variable.

3.1.2 Fuzzy Inference (knowledge base- ‘IF-

THEN’ logics)

The rules (IF-THEN logics) were generated to

describe the logical relationship between the input

variables (IF part) and the output variable (THEN

part). The degree of support (DoS) was used to

weigh each rule according to its importance. A

‘DoS’ value of ‘0’ means non-valid rules. Initially,

all the DoS’s were set to a fixed value of ‘1’. The IF-

THEN rules were formed exhaustively based on the

correlation of the input and output variables

considering all possible combinations of input and

output terms. The neuro-fuzzy training capability

was activated in later stage to eliminate non-valid

rules (the ones with DoS approaching zero value).

Two correlation matrices were developed for

both weekday and weekend to define the

relationship between the input and output variables

(Table 3) in the fuzzy inference system..

Table 3: Correlation values between input and output

variables for both weekday and weekend.

percentile speed

Weekday Weekend

Length 0.87 0.82

Number of access

points/intersecting

links

0.15 0.11

Number of

pedestrian crossings

-0.64 -0.35

Volume to capacity

(V/C) ratio

0.27 0.08

Hourly pedestrian

volume

-0.84 -0.57

Posted speed limit 0.77 0.53

It is to be noted that some of the correlation

values is showing unexpected signs (e.g. V/C ratio

to 85

percentile speed shows positive relation).

This is because of Site 2 (a local road), which has

very low 85

percentile speed (low posted speed

limit of 40 km/hr) and very low traffic volume.

Including the data of this particular road segment in

calculating the correlation values affects the overall

results, particularly because of the limited data (only

four segments). Site 2 data were kept for calculating

the correlation values to have representation of both

road categories in the devised FLM, keeping in mind

that increasing the sample road segments may result

in better correlation values.

The used operator type for generating the fuzzy

rules has been the ‘MIN-MAX’. The ‘MIN-MAX’

method tests the magnitude of each rule and selects

the highest one.

The fuzzy composition eventually combines the

different rules to one conclusion. The ‘BSUM’

(Bounded Sum) method was used as it evaluates all

rules. A total of 729 rules were generated for both

weekday and weekend models. Table 4 shows six

rules as an example with the final adjusted DoS’s

after the neuro-fuzzy training. Detail of the neuro-

fuzzy training will be discussed later.

The bold row indicates that for a road segment

with low length, low number of intersecting links,

low number of pedestrian crossings, medium hourly

traffic volume, medium hourly pedestrian volume

and low posted speed limit, the estimated 85

percentile speed is medium and the strength for this

rule (DoS) is 0.90.

FUZZY LOGIC APPROACH FOR ESTIMATING 85TH PERCENTILE SPEED BASED ON ROAD ATTRIBUTE

DATA

Table 4: Examples of (IF-THEN) rules.

IF THEN

Length

IntLnks

PedCros

VCRat

PedVol

PostSp

DoS

SpEF

low low low low low low 0.90 med.

low low low low med. low 1.00 med.

low low low low high low 1.00 med.

low low low med. low low 1.00 low

low low low med. med. low 0.90 med.

low low low med. high low 0.90 med.

3.1.3 Defuzzification

The results of the inference process are the linguistic

terms describing the 85

percentile speed. As

mentioned above, five linguistic terms were used for

the output results- very low through very high 85

percentile speed). In the defuzzification process, all

output linguistic terms are transformed into crisp

numeric values. This is done by aggregating

(combining) the results of the inference process and

then by computing the fuzzy centroid of the

combined area. The ‘Center-of-Maximum (CoM)

method (Ross, 1995) is used for estimating the

output numeric value, Y, as follows:

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

∑

sult

)(

*)(

(1)

Where Y= numeric value representing the 85

percentile speed; µ

Result

(j) = membership value of

consequence (linguistic terms) j. Y

is referred to as

the base value of the consequence j. It is the

consequence’s numeric value corresponding to a µ

value of 1.

Figure 3 illustrates MBF for the output variable

(85

percentile speed) for weekday using the CoM

de-fuzzification procedure. The thick arrows

indicate the 85

percentile speed base values, Yj on

the horizontal axis and the height of the thick black

arrows indicate µ

Result

(j). The base values of the five

percentile terms are 29.9, 45.9, 61.9, 77.9 and

93.9 respectively. µ

Result

(medium), µ

Result

(high) are 1

and 0.95, respectively. The µ

Result

values of all other

terms are zeros. The 85

percentile speed of 69.68

km/hr (indicated by the thin black arrow) was

calculated using the Eq. (1).

Figure 3: Membership function for the ‘85

percentile

speed’ output variable.

3.2 Neuro-fuzzy Data Training

The initial fuzzy logic models for both weekday and

weekend were trained in neuro-fuzzy technique.

Neuro-fuzzy technique is the combination of neural

nets and fuzzy logic. It is comprised of the three

fuzzy logic steps (fuzzification, fuzzy inference and

de-fuzzification) with a layer of hidden neurons in

each process (Hawas, 2004). Fuzzy Associative

Maps (FAMs) approach is commonly used in neuro-

fuzzy technique to train the data. A FAM is a fuzzy

logic rule with an associated weight. This enables

the use of a modified error back propagation

algorithm with fuzzy logic. The neuro-fuzzy training

have been conducted in three steps- defining the

MBFs, rules and DoS for training, selection of

training parameters, and carrying out training

(INFORM, 2001).

Initially the default setting of the FuzzyTech tool

was used to define range of the numeric values for

each term. The rules were formed exhaustively with

all DoS values of 1. Therefore in the first step, all

MBFs and rules were selected for the neuro-fuzzy

training to find the optimized fuzzy logic model.

Then the parameters (step width for DoS and terms)

were selected for the training. The whole neuro-

fuzzy training was carried out for five cycles with

each cycle for 1000 iterations.

The step width for the DoS values has been set

to 0.1 for each cycle. The step width for the terms

has been set to 5% in the first cycle, which was

increased by 5% in later cycles. The maximum and

average deviations were observed after completion

of each cycle. The cycle, for which the deviation

values are less, was selected as the final FLM. The

process was run for both weekday and weekend

models. After the training phase, the MBFs and the

DoS values were determined as shown in Table 4

and Figure 4. It can be seen from the Figure 4 that

the initial 85

percentile speed terms were set

uniformly over the variable’s range [Figure 4(a)].

The base value for high 85

percentile speed is 77.9

km/hr (indicated by black arrow). The training

algorithm examines the effect of introducing a pre-

specified shift to the term’s base value (+5% in this

ICAART 2012 - International Conference on Agents and Artificial Intelligence

case). If the base shift results in a reduction in the

deviation, a new base is identified [71.5 in this case

as shown with black arrow in Figure 4(b) for

weekday model].

Figure 4: Membership function of ‘85

percentile speed’

(a) before and (b) after neuro-fuzzy training.

4 MODEL VALIDATION AND

RESULT ANALYSIS

After completing the training phase, the 85

percentile speeds were estimated (for both weekday

and weekend) with the same set of input data which

were used to develop the models. As the notion of

fuzzy sets are completely non statistical in nature

(Zadeh, 1965), the residual values (Figure 5) were

used to compare both weekday and weekend model

results. The x axis of the figure represents a specific

road segment and a time period. It can be seen from

the figure that the number of positive and negative

deviations are almost same for both weekday and

weekend models. The maximum deviations for

weekday and weekend are 57.63% and 81.44%,

respectively. This results in higher average deviation

for weekend (19.65% for weekend compared to

14.90% for weekday).

Figure 5 also shows that the number of residuals

with values of 15% or less represent 62.5% and 75%

of all the residuals for weekday and weekend,

respectively. It can be said that both models estimate

the 85

percentile speed to a reasonable level for

such limited number of sample size.

The estimated values of the 85

percentile speed

were classified according to their corresponding

current posted speed limits. A comparative

descriptive analysis of the estimated (model results)

and actual (field data) values of the grouped data for

both weekday and weekend models are presented in

Table 5.

It is evident in Table 5 that the mean, median,

minimum, maximum and standard deviations of the

estimated model results are very close to those of the

actual data in case of lower posted speed limit (40

km/hr) for both weekday and weekend models. On

the other hand, some variations on these values can

be observed in both models’ results for road

segments with higher posted speed limits (60 km/hr

and 80 km/hr).

Figures 6 through 8 illustrate the combined

effects of two input variables on the 85

percentile

speed data.

Figure 6 shows the effects of ‘number of

pedestrian crossings’ and ‘length’ on the 85

percentile speed for weekday model. As indicated in

the figure, the ‘length’ variable is positively

correlated with the 85

percentile speed. On the

other hand, the ‘number of pedestrian crossings’ is

negatively correlated with the 85

percentile speed.

The highest 85

percentile speed (71.50 km/hr) is

found for highest ‘length’ (2.9 km) and least

‘number of pedestrian crossings’ (0-1).

Similarly, Figure 7 illustrates the effects of the

‘Posted Speed Limit’ and the ‘Hourly Pedestrian

Volume’ (as input variables) on the ‘85

Percentile

Speed’ for weekday. As shown, the posted speed

limit is positively correlated and hourly pedestrian

volume is negatively correlated with the 85

percentile speed. As can also be seen, the effect of

the posted speed is not quite noticeable if it exceeds

60 km/hr in cases of high pedestrian volumes.

As shown, the posted speed limit is positively

correlated and hourly pedestrian volume is

negatively correlated with the 85

percentile speed.

As can also be seen, the effect of the posted speed is

not quite noticeable if it exceeds 60 km/hr in cases

of high pedestrian volumes.

FUZZY LOGIC APPROACH FOR ESTIMATING 85TH PERCENTILE SPEED BASED ON ROAD ATTRIBUTE

DATA

-90

-80

-70

-60

-50

-40

-30

-20

-10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Percentage of deviation

Weekday Weekend

Figure 5: Percentages of deviations for both weekday and weekend FLMs.

Table 5: Comparison of descriptive statistics between the actual field data and the estimated FLM results for both weekday

and weekend.

Weekday Weekend

40 km/hr 60 km/hr 80 km/hr 40 km/hr 60 km/hr 80 km/hr

Data*

Data**

Data*

Data**

Data*

Data**

Data*

Data**

Data*

Data**

Data*

Mean 38.2 38.94 67.82 69.77 68.7 75.89 44.79 50.55 84.71 80.89 70.1 83.74

Median 36.55 38.94 66 69.97 73 73.99 45.1 51.16 87.1 80.41 71.5 84.18

Min 29.9 29.9 55 68.78 48 71.5 39.45 40.48 52.2 79.69 47 81.61

Max 50 45.9 82 70.66 93.9 81.14 51.5 56.54 107.8 84.18 93 84.18

S.D.

***

6.37 6.07 9.6 0.93 11.36 4.12 4.49 6.32 18.66 1.48 13.61 0.91

*S. Data= Survey Data ;**E. Data= Estimated Data;***S.D.= Standard Deviation

Figure 6: Effects of ‘Length and Number of Pedestrian

Crossings’ on the ‘85

Percentile Speed’ (weekday

model).

Figure 7: Effects of ‘Posted Speed Limit and Hourly

Pedestrian Volume’ on the ‘85

Percentile Speed’

(weekday model).

ICAART 2012 - International Conference on Agents and Artificial Intelligence

Figure 8 illustrates the relationship between the

‘Length’ and ‘Posted Speed Limit’ (as input

variables), and the ‘85

Percentile Speed’ for

weekday. The two input variables are positively

correlated with the 85

percentile speed. The higher

the length and/or the posted speed limit, the higher is

the 85

percentile speed.

Figure 8: Effects of ‘Length’ and ‘Posted Speed Limit’ on

the ‘85

Percentile Speed’ (weekday model).

It can be said that regardless limited number of

data, fuzzy logic shows the relationship between the

input and output variables realistically. As fuzzy

logic handles linguistic terms (for a range of

numeric values), it is less sensitive to each

individual numeric value. This replicates true human

nature about perceiving factors on the roads. For

example, it is clear from Figure 6 that drivers’

choice of operating speed (represented by 85

percentile speed) is influenced by the length of the

road segment or pedestrian volume. With larger

length, the operating speed tends to be higher. such

changes do not occur for every one km change of

length. In reality, the decision of choosing any

particular range of operating speed tend to be stable

for range of length (say between 0 to 1 km). Fuzzy

logic predicts such relationship very realistically.

5 CONCLUSIONS

This paper discussed the development of the FLM

for estimating the 85

percentile speed based on six

road attributes data. The advantage of fuzzy logic is

its ability to address the uncertain nature of human

thinking (perception). The same road (road attribute

data) can be perceived differently by different

drivers and choose their operating speed

accordingly. The other advantage is the using the

neuro-fuzzy which can be utilized to automate the

development of the knowledge base.

The FLMs are widely known for describing the

vagueness and nonlinearity in the human behaviour

relationships between inputs and output. However,

such models are generally only valid in situations for

which data are available to calibrate the model. If

the FLM is to be used to assess the choice behaviour

that is not covered in the data for calibration, the

applicability of the model for estimating the 85

percentile speed might be questionable. As such, the

data for calibration should thoroughly cover the

entire range of (input and output) variables for better

and more accurate estimation.

Identifying and setting appropriate posted speed

limit for a given road segment is a complex task

which involves studying the speed behaviour pattern

of the drivers, the characteristics of road

environment, road geometry, etc. This study focused

on only one aspect; the drivers’ speeding behaviour

based on the basic road characteristics, the traffic

intensity and pedestrian activities for a very limited

number of road segments.

One may argue the necessity to develop such

models while such 85

percentile speed can be

actually measured in the field. In response to such

argument is that tremendous savings in the resources

(that would be needed to carry on actual field survey

measures over an entire network) can be

materialized. It is envisioned that these models can

be developed with a reasonable representative

sample of road segments in a typical network. The

derived models can then be validated and

subsequently applied to the entire network.

Keeping in mind the limited data set used in the

study (due to the resources constraints), that likely

contributes to deficiencies in representing the

various road characteristics and environmental

factors (with only few data points); it is legitimate to

assume that the richness in data collection will

ultimately lead to better more statistically significant

models. Along this line, it is suggested that a

systematic sampling approach should be adopted in

selecting the road segments to include in the data set

to use for models’ calibration. The principles of the

minimum sample size should be observed. It is

suggested that a stratified sampling procedure to be

used in selecting the road segments for spot speed

field observations. All the network roadway

segments may be stratified based on their intrinsic

characteristics of posted speed, length, traffic

volume, pedestrian intensity, etc. A representative

stratified sampling procedure with a minimum

FUZZY LOGIC APPROACH FOR ESTIMATING 85TH PERCENTILE SPEED BASED ON ROAD ATTRIBUTE

DATA

sample size according to a pre-specified confidence

level and interval should be observed in generalizing

the fuzzy logic modeling approach.

ACKNOWLEDGEMENTS

This research is part of M.Sc. thesis entitled

‘Assessing the Methodology of Setting Posted Speed

Limit in Al Ain-UAE’ funded by Roadway,

Transportation and Traffic Safety Research Center,

United Arab Emirates University.

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