TransportaTion

DEVELOPMENT OF AN INFRASTRUCTURE
COEFFICIENT BY AN ANALYTIC HIERARCHY
PROCESS AND ITS RELATIONSHIP TO SAFETY
Haneen FARAH

Ph.D. Candidate, Department of Civil and Environmental Engineering
Technion – Israel Institute of Technology
Haifa, Israel

Abishai POLUS

Moshe A. COHEN

Professor, Department of Civil and Environmental Engineering 	
Technion	Haifa, Israel

Professor, Department of Industrial Engineering and Management
Jerusalem College of Engineering
Jerusalem, Israel(Received December 12, 2006)

The study has four main objectives: (1) to test the correlation between different infrastructure characteristics and crash-rates,
and trends; (2) to develop an Infrastructure Coefficient (IC) that represents the overall infrastructure characteristics of two-lane rural
highways; (3) to develop a crash-prediction model for two-lane rural highways in which the IC developed is the independent variable;and (4) to estimate and quantify the contribution of the infrastructure as a whole to highway crashes.
Infrastructure is defined in this study as the highway and its geometric features: alignment, road-side elements, sight-distances,
presence of guardrails, access-points, roadway consistency, and additional variables that all together measure the overall infrastructure quality of a highway. The first phase in the development of the IC involves an examination of the correlation between different
infrastructure characteristics and crash-rates. In the second phase, the Analytic Hierarchy Process (AHP) is utilized to develop the IC.
Finally, a crash-rate prediction model that relates crash-rates to IC for two-lane rural highways is developed.
The IC that was developed consists of a linear combination of five infrastructure characteristics: road consistency, lane width,
road-side score, percentage of highway with a no-passing zone, and number of access points per unit length. These five characteristics were found to have the most significant contribution to safety among all the characteristics included in this study. A model for theprediction of crash rates based on the proposed IC is calibrated and presented.
It is suggested that this model be used to evaluate the safety level of existing or planned highways. This study also found that,at a 99% confidence level, a highway with good infrastructure quality reduces crash-rates by 44% on average compared with a highway with poor infrastructure quality.
Key Words: Crash-prediction, Infrastructure characteristics, Analytic Hierarchy Process (AHP), Crash-rate, Two-lane rural highway

1. INTRODUCTION
Crashes usually result from a combination of four
contributing elements – the driver, the road, the vehicle,
and the environment. Drivers are often involved in crashes because of their own errors, but also because they areaffected by a combination of highway and/or vehicle elements. It is certainly not only the driver who bears responsibility for the occurrence of crashes. Henderson1
concluded that focusing too much on the driver as thecause of a crash often masks the ability to see other causes
whose amelioratization could reduce crash rates, as wellas crash severity. The approach that attributes crashes
solely to drivers is promulgated by many transportation
professionals, particularly in law-enforcement agencies,
who continue to consider human factors as major con-

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IATSS Research Vol.31 No.1, 2007

tributors to road crashes. One possible reason for this lineof thinking is that the relative contribution of highway
infrastructure as a whole to the occurrence of crashes,
unlike the contribution of other elements, has not yet
been fully quantified.
This paper has four objectives: (1) to test the correlation between the different infrastructure characteristics and crash-rates, and their trends; (2) to develop a
numerical coefficient to rate highway infrastructures; (3)to develop a crash-rate prediction model for two-lane rural highways; and (4) to estimate and quantify the contribution of the infrastructure as a whole to highway crashes.
The investigation approach chosen is the Analytic Hierarchy Process (AHP), a decision-making method developed by Saaty 2 that reduces complex decisions to a seriesof pair-wise comparisons and synthesizes the results.

DEVELOPMENT OF AN INFRASTRUCTURE COEFFICIENT BY AN ANALYTIC HIERARCHY PROCESS AND ITS RELATIONSHIP TO SAFETY

AHP was chosen for this study in order to develop an
Infrastructure Coefficient (IC) by attributing a specificweight to each infrastructure characteristic to reflect its
relative importance to road safety compared with theother characteristics considered in the study. Multiplying
each of the weights by its appropriate infrastructure value
and summing up all the results yields the IC value for the
specific roadway segment.
The uniqueness of the proposed approach and of
the IC developed is that they incorporate most features –although not all of them – of a highway’s infrastructure.
This study defines Infrastructure as the highway and its
geometric features, which include alignment, road-side
elements, sight-distances, presence of guardrails, accesspoints, design consistency, and additional variables that,
all together, measure the overall quality of the highwayalignment and its elements.
Developing an IC has likely significant benefits inassessing whether specific highways are potentially dangerous because of their infrastructure characteristics alone.
Transportation agencies could also use the proposed coefficient when evaluating several design alternatives inorder to select an alternative that potentially will havelower crash-rates.
Rural highway infrastructure has different tangible
components, such as lane and shoulder widths, sight-distance availability and no-passing zone lengths, road-side
characteristics and their proximity to obstacles, and anumber of access points/kilometer. Another importantfeature of rural highways is the consistency of the alignment design, both vertical and horizontal. A key objective of this study is to include the various infrastructurecomponents (as defined in this study) in an aggregatedcoefficient and, based on this coefficient, to predict futurecrash-rates on two-lane rural highways.

2. LITERATURE REVIEWThis section contains two parts. The first part willconcentrate on studies that have dealt with individual
roadway elements and their relationship to safety. The
second part will concentrate on crash-prediction models.
The first part presents a review of a large group of studies
on the impact of specific highway elements on safety.
Zegeer and Council 3 conducted a study of the impact of cross-sectional roadway elements on safety. Suchelements included lane width, shoulder width, roadsidefeatures, and others. They found that improving roadsides can contribute to a 44% reduction in crashes whileshoulder widening can reduce crashes by up to 49%.

H. FARAH, A. POLUS, M. A. COHEN

Elvik 4 found that guardrails reduce both crash rates andcrash severity. Fink and Krammes 5 proposed that thedegree of curvature was a good predictor of crash rate on
horizontal curves. Ogden 6 studied the effect of paved
shoulders on crashes on two-lane rural highways in Australia and found that shoulder-paving was associated witha statistically significant reduction in accident frequency
with casualties. An extensive literature review conductedby Hauer 7 on shoulder width and shoulder type concluded that roads with paved shoulders were associated withfewer accidents than were similar roads with soil (unsealed) shoulders and that wider shoulders were associated with fewer run-off-the-road and opposite-direction
accidents, which accounted for some 40%-60% of allaccidents. However, wider shoulders may also be associated with more of the ”other” accidents. Papayannoulis
et al.8 who conducted a study on access spacing, observedthat doubling the access density from 10 to 20 accesspoints/mile increased accident rates by 40%. They foundthat the greater the frequency of access points (driveways and intersections), the greater was the number ofcrashes. Polus and Mattar-Habib 9 developed a model toestimate road consistency and showed that crash rate
decreased as design consistency on two-lane rural highways improved.
The literature provides a long list of studies on theimpact of individual infrastructure elements on crashes.
Elvik and Vaa’s10 handbook of road safety measures contains an extensive review of studies worldwide on thevarious types of infrastructure features and their relationship to crash rates.
Much literature addresses the problem of accidentrate estimation and the identification of the various factors affecting this rate. Most of the previous work doneon developing crash-prediction models concentrated on
different regression methods, such as linear, Poisson,and negative binomial regressions. Joshua and Garber 11
used multiple linear and Poisson regressions to estimate
truck accident rates, using traffic and geometric characteristics as independent variables. Miaou et al.12 proposeda Poisson regression model to establish empirical relationships between truck crash-rates and highway geometric and traffic data for 8,779 miles of rural interstate
highways in the U.S. Hadi et al.13 using data from theFlorida Department of Transportation’s Roadway Characteristics Inventory (RCI) system, estimated a negative
binomial (NB) regression for accident rates on various
types of rural and urban highways with different trafficlevels. Vogt and Bared14 employed both a Poisson and anegative binomial regression to develop a crash-predicIATSS Research Vol.31 No.1, 2007121

TransportaTion

tion model for both two-lane road segments and threelegged and four-legged intersections. Later, Daniel etal.15 developed Poisson and negative binomial accidentprediction models for truck crashes on Route 1 in New
Jersey; using a database developed in New Jersey for1998 and 1999, they included signalized intersections.
Karlaftis and Golias16 on the other hand, examined therelationship among rural (two-lane and multi-lane) roadgeometric characteristics, accident rates, and their prediction, using a rigorous non-parametric statistical method known as a hierarchical tree-based regression (HTBR).
Mayora and Rubio17 developed a negative binomial
multivariate crash-prediction model for the Spanish national network’s two-lane rural roads. The data set contained 3,450 kms of rural roads having several road andtraffic characteristics. The R-square of the model was
found to be 0.87. Zhang and Ivan18 employed negative
binomial generalized linear models (GLIM) to evaluate
the effects of a roadway’s geometric features on the incidence of head-on crashes on two-lane rural roads inConnecticut. They defined three models, which they
estimated on the basis of all valid combinations of thesignificant variables. The researchers used Akaike’s Information Criterion (AIC) to select the best of the threemodels, which was the one that included the sum of absolute change rates of horizontal curvature. Polus et al.19
developed a crash-prediction model that related crashrates to an IC by using smallest space analysis. This IC
was a linear weighted combination of several infrastructure characteristics.
From the first part of the literature review, it can beconcluded that most previous studies dealt with one infrastructure characteristic and its impact on safety. Noneof these studies dealt with the impact of the entire infrastructure as a whole on crash rates. The second part of theliterature review leads to the conclusion that none of theprevious models, except for Polus et al.19, developed an
IC that summarized and incorporated various infrastructure characteristics and then used it as an independent
variable in the models. All previous crash-prediction
models offered several infrastructure characteristics as
independent variables.
Therefore, the significance of the present study is
twofold: (1) its quantitative estimation of the contributionof the infrastructure as a whole to crash rates; (2) its inclusion of various infrastructure characteristics in a representative aggregated IC, which is then used as anindependent variable in the crash-prediction model.

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3. DATA COLLECTION
The data collection consisted of three parts:
a. Selection of highway segments: This study focused on two-lane rural highways in northern Israel. Most
rural roads in Israel are undivided two-lane highways.
Twenty-five different segments were randomly selected; most were several kilometers long, the average length
being 7.4 km. All segments selected connect two majorintersections although typically there were several minor
intersections in between them. It was not possible tobreak each road segment into smaller segments because
many small segments did not have any crashes. An increase in the crash-history data-base by collecting accident data from previous years was considered, but deemed
not a desirable approach because of the very real likelihood of geometric changes and/or changes in flow (suchas speeds, volumes) and vehicle characteristics (such as
new ABS equipment, second generation airbags, etc.).
b. Collecting infrastructure characteristics: For eachhighway, 12 infrastructure parameters were measured(detailed in Table 1); these included, among others, topography, lane and shoulder widths, degree of road-side
hazards (depending on the proximity of adjacent trees,
rigid obstacles like rocks, steep ditches), shoulder dropoff at the end of the shoulder (i.e., difference in height
elevation between the paved shoulder and the unpaved
road-side), number of access points per unit length, number of access points with acceleration and deceleration
lanes, length of no-passing zones (considered a surrogate
variable for sight-distance), length of road segment wherea guardrail was required according to existing guidelines
vs. length of the highway where a guardrail was actuallyprovided, and road consistency (which will be discussed
later in this section). The horizontal and vertical alignment parameters were obtained from “as-built” plans,
and those parameters were used to calculate the consistency measure. All other infrastructure characteristics
were obtained directly from field measurements.
c. Crash data for the same highway segments: Thisdata was obtained from files of the Israel Central Bureauof Statistics for five consecutive years, 1997 through2001. Highway segments that had significant infrastructure changes (e.g., widening and paving of shoulders,construction of long guardrails, or intersection control
and channelization changes) during the five years forwhich the crash data were collected were eliminated fromthe data set.
The data included crash numbers and traffic volumes, from which rates could be determined. All crashes

DEVELOPMENT OF AN INFRASTRUCTURE COEFFICIENT BY AN ANALYTIC HIERARCHY PROCESS AND ITS RELATIONSHIP TO SAFETY

H. FARAH, A. POLUS, M. A. COHEN

Road No.

Length (km.)

Lane Width (m.)

Shoulder Width (m.)

Mean Access Points
per Km. (Points/km.)

Percentage ofIntersection with
Speed Change Lane(%)

Percentage of Hwy
with No-Passing
Zone (%)

Percentage of Hwy
with G-R (%) *Percentage G-R
Required vs.
Existing G-R (%)

Shoulder Drop-off(cm.)

Topography **Road-Side Score ***Consistency ****

Table 1 Main infrastructure characteristics of 25 highway segments

1

13.76

3.75

2.65

2.00

18%

9%

38%

55%

17.50

3

4

2.48

2

9.89

3.85

2.60

2.12

7%

27%

24%

0%

7.50

3

2

2.13

3

5.92

3.80

2.75

0.51

33%

15%

100%

0%

0.00

1+2

5

2.38

4

7.39

3.80

2.90

0.68

7%

23%

74%

0%

5.00

1

5

2.66

5

7.07

3.75

2.65

1.98

11%

28%

57%

M.D.

22.50

3

4

1.17

6

6.61

3.75

2.65

1.13

19%

20%

88%

M.D.

22.50

3

5

2.41

7

6.32

3.75

2.40

2.53

6%

8%

38%

0%

0.00

3

6

2.10

8

5.12

3.60

2.50

1.07

47%

23%

33%

0%

0.00

3

7

0.99

9

10.72

3.70

2.60

0.42

10%

7%

44%

0%

2.00

3

6

2.57

10

7.43

3.65

2.50

0.87

23%

35%

63%

0%

2.00

2+3

6

2.60

11

10.20

3.70

2.75

0.88

17%

33%

58%

0%

4.00

2+3

6

0.98

12

7.30

3.85

2.75

0.55

17%

16%

81%

4%

0.00

1

5

2.68

13

8.85

3.35

1.20

3.62

3%

15%

27%

9%

17.50

2+3

2

0.01

14

12.77

3.45

1.00

1.10

25%

53%

40%

0%

0.00

1

3

0.00

15

6.96

3.80

2.35

1.51

6%

40%

34%

44%

11.00

1

4

0.57

16

6.72

3.40

0.70

1.93

7%

30%

17%

237%

2.50

3

1

0.75

17

5.27

3.20

1.20

0.76

0%

25%

29%

M.D

6.00

1

2

0.00

18

5.17

3.45

2.00

1.26

14%

15%

27%

94%

0.00

2

2

1.50

19

6.00

3.65

1.20

1.58

0%

33%

25%

17%

17.50

1

2

0.44

20

3.93

3.45

2.20

2.16

6%

42%

26%

46%

0.00

1

2

0.47

21

9.35

3.20

0.60

1.07

0%

53%

21%

12%

0.00

1

1

0.00

22

10.00

3.25

1.20

1.85

11%

9%

27%

M.D.

0.00

1+3

1

0.02

23

9.00

3.65

2.65

1.94

15%

53%

77%

0%

0.00

1

5

0.19

24

4.19

3.10

1.10

1.43

8%

73%

35%

127%

2.50

1

3

0.04

25

6.70

3.40

1.70

1.94

19%

19%

31%

66%

5.50

1

2

0.81

+ M.D. – Missing Data
* G-R – Guardrail** Topography – Mountainous (1), Hilly (2), Level (3)*** Road-Side Score – Note Table 3.
**** Consistency – Poor (RC 1.0), Moderate (1 RC 2), Good (RC 2.0)
Note: Scores of Infrastructure features are presented in Tables 2 and 3.

in the data set involved human casualties (i.e., damageonly crashes were not included). In other words, light,
serious, and fatal crashes were included in this study. It
was not possible to conduct the different statistical analyses for each severity level or for each type of accident
separately, since the number of crashes over a period offive years would not be sufficient for attaining statistically significant results. An increase in the crash- history
data through collecting accident data from previous years
was considered, but deemed not a desirable approach be-cause of the very real likelihood of geometric changes
and/or of major significant flow (speeds, volumes) andvehicle characteristics (ABS, airbags). The data set, atthe end, consisted of 1,035 crashes that occurred on the
25 highway segments for which data were collected forthe five-year period.
For the purpose of this analysis and the statisticalmethod used, it was preferred to convert the actual physical dimension of each element (e.g., lane width, percentage of intersections with speed-change lanes, etc.) to
IATSS Research Vol.31 No.1, 2007123

TransportaTion

categorical variables. The physical dimensions weregrouped into ranges, separated by thresholds, and thevalues were substituted with a score for each range. Low
score values (such as 1) represented a poorly designed,
seemingly dangerous infrastructure, and higher score values (up to 7 for the road-side characteristics) represented
an apparently safe and well-designed infrastructure. Theseelements received a surrogate nominal numerical scorethat represented the attributes of the infrastructure and its
relative risk to drivers. Scores for 10 of the 12 infrastructure elements are presented in Table 2, while Table 3 presents the road-side scores.
Some thresholds that were established in order toallocate the different infrastructure characteristics to representative ranges were based on engineering judgment.
Others were set by dividing the whole domain into an
equal number of ranges. For example, shoulder width
was categorized into four ranges. The first range-category
included all highway segments with a shoulder width ofless than or equal to 0.9 m; this threshold was set, sincein this case when a driver decides to stop on the shoulder,for example in emergency situations, part of the car will
intrude into the through lane because this shoulder widthis less than the average width of a car. The second category contains shoulder widths between 0.9 m and 1.8 m; inthis case, most of the car’s width will be away from thelane, but the shoulder width is still not enough to give adriver sufficient space to remain on the shoulder for a
repair if needed. The third category (1.8 m – 2.4 m) gives
enough space for both the car and the driver’s movement
around the car; however, it is not enough for trucks.

Lastly, category four (2.4 m – 3.0 m) provides sufficient
shoulder width for trucks. Shoulder drop-off, on the other
hand, was categorized into two levels. The first category
includes highway segments with shoulder drop-offs ofless than 5 cm. In this case, run-off-the-road instances
will not cause loss of control. When the shoulder drop-off
is greater than 5 cm, running off the shoulders onto aroad-side area will in most cases result in a serious crash.
A similar approach was used to set the thresholds of roadconsistency, topography, and lane width. As noted, thethresholds of the remaining infrastructure characteristics
were set by dividing the whole range into an equal number of spans.
The consistency-parameter value, which was calculated by a model (developed in a separate study by Polusand Mattar-Habib 9) that provides the actual consistency
values for a given highway design, showed that this value
was moderately (R-square = 0.55) related to crash-rates
on two-lane rural highways (Fig. 1). The consistency wasdetermined by the amount of variability in operating
speed along a two-lane highway and was measured by
two independent variables: (1) the area bounded by thelongitudinal speed-profile and the average operating
speed and (2) the standard deviation of speeds. Speedprediction models for curves and tangent segments wereused to estimate speeds, based on the geometry, during
the calibration of the consistency model. As the variability in speed increased, the consistency of the highway
segment decreased. Consistency was classified by three
thresholds–poor, acceptable, and good–and its scores
ranged accordingly from 1 to 3. For more details on the

Table 2 Scores for infrastructure, topography, and consistency features
Score

Shoulder Width(m.)% of Highwaywith G-R* (%)

Number of Access
Points/km.

Percentage of G-R* Required vs.
Existing G-R* (%)

Shoulder Drop-off
(cm.)

1

0.9

0% – 20%

3.00 – 3.65

100%

0.05

2

0.9 – 1.8

20% – 40%

2.35 – 3.00

50% – 100%

0.00 – 0.05

3

1.8 – 2.4

40% – 60%

1.70 – 2.35

0% – 50%

4

2.4 – 3.0

60% – 80%

1.05 – 1.70

80% – 100%

0.40 – 1.05

5
Score

Lane Width (m.)

Topography% of Highway with
No-Passing Zone

% of Access Points withAcceleration/Deceleration Lanes

Consistency

13.00 – 3.30

Mountainous

60%

0% – 9%RC 1 (Poor)2

3.30 – 3.60

Hilly

45% – 60%

9% – 18%

1 RC 2(Moderate)

33.60 – 3.90

Level

RC 2 (Good)

30% – 45%

18% – 27%415% – 30%

27% – 36%

50% – 15%36% – 45%

* G-R – Guardrail

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DEVELOPMENT OF AN INFRASTRUCTURE COEFFICIENT BY AN ANALYTIC HIERARCHY PROCESS AND ITS RELATIONSHIP TO SAFETY

Table 3 Road-side criteria score
Score

Road-Side Features

1• No guardrail along most of the segment length(LGR <30%)• Shoulder width less than 0.9 m.
• Shoulder drop-off greater than 0.05 m.
• Rigid obstacles within 9.0 m. or less from thepavement edge
• Slope of ditch steeper than 4:1; ditch more than
0.40 m. deep, no guardrail• No recovery area beyond shoulder

2• Features as for Score 1, except that theshoulder width is more than 0.9 meter3• Guardrail length between 30% and 70% of thesegment length• Shoulder width from 0.9-1.8 m.
• Dangerous roadside features, such as rocks or
cuts, cliffs, but with guardrail• Portion of road without guardrail has rigid
obstacles within 9.0 m. of pavement edge or ashoulder drop-off of 0.05 m. or more or norecovery area beyond shoulder

4• Features as for Score 3 except that theshoulder width is more than 2.4 meters

5• Guardrail length greater than 70% of thesegment length• Shoulders wider than 2.4 m.
• Dangerous roadside features, such as rocks or
cuts, cliffs, but with guardrail• No shoulder drop-off and recoverable road side6

• Guardrail length is between 30% and 70% of
the segment length• Shoulders wider than 2.4 m.
• Moderate roadside compared to Score 5• No shoulder drop-off and no rigid obstacles
closer than 9.0 m. from pavement edge

7

• Shoulder wider than 2.4 m.
• No shoulders drop-off• Rigid obstacles at a distance greater than 9.0 m.
from pavement edge
• Wide recovery area beyond shoulders• Side slope flatter than 4:1• Length of guardrail 30% or less of segment
lengthdevelopment of the road consistency model, see Polusand Mattar-Habib 9.
The Road-Side Score (RSS) that was developed in
the present work (Table 3) is based on the most pertinent
features of the road side, such as shoulder width, slope atthe edge of the shoulders, presence of rigid obstacles, andthe existence of a drop-off at the edge of the shoulder.
RSS ranged from 1 for very dangerous road sides (narrow shoulders, no recovery area beyond the shoulders,rigid obstacles near the pavement) to 7 for very safe road

H. FARAH, A. POLUS, M. A. COHEN

sides (shoulder wider than 2.4 m, no shoulder drop-off,side slopes flatter than 4:1, and a wide recovery area beyond the shoulders). The shoulder drop-off criterion refers to the drop between the far edge of the shoulder andthe road-side area. This measure was adopted from very
similar roadside-hazard ratings developed by Zegeer etal.20 to characterize the accident potential for roadsidedesigns found on two-lane highways. It was later incorporated into the crash-prediction model developed as apart of the Interactive Highway Safety Design Model 21.

4. PRELIMINARY ANALYSIS
Several regression analyses of the correlation between crash-rates and each infrastructure parameter wereconducted prior to the main analysis. The purpose of thepreliminary analyses was to investigate the trend of therelationships between individual parameters and crashes
in order to identify whether they behaved according to
expected engineering judgment and whether they were inagreement with previous findings.
Some of the most significant regression analyses areillustrated in Figures 1- 3. These figures also present themathematical relationships and R-square values. The regression results showed the following:a. The trend of the impact of each individual parameteron crash-rates was as would be expected by engineering judgment and as was found in most previous
studies. In regard to the impact of shoulder width on
crash-rates, the literature review revealed different results. Some authors found that as shoulder width increases, crash-rates decrease 22,23; others found thatcrash-rates increase as shoulder width increases beyonda certain width 24. In this study, crash-rates on ruralroads were found to decrease monotonically as shoulder widths in the range of 0.45 m -3.00 m increased.
b. The infrastructure characteristics with the highest Rsquares and those with the most significant relationship to crash-rates were road consistency, lane width,shoulder width, road-side score, percentage of highways with guardrails, no-passing zone percentage, andaccess points.
c. As can be noticed in Figures 1- 3, the correlations are
relatively low, because there is a relatively high dispersion of the data. This was expected, since crashes
happen as a result of numerous and different factors,
with each factor contributing differently to the occurrence of a crash. Moreover, these factors and theirrelative con­tribution typically change from one crashto another.
IATSS Research Vol.31 No.1, 2007

125

Crash Rates (Crashes per million vehicle Kms.)

TransportaTion

0.7
0.6-0.38*RC-0.38*R CCR
C R==0.49*e
0.49*eR2 = 0.55
R 2 = 0.55

0.5
0.4
0.3
0.2
0.1
Crash
0.0 Rates (Crashes per Million Vehicle Km.)
0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.75

3.90

R oad Consistency
C ons is tency
Road

Crash Rates (Crashes per million vehicle kms.)

Fig. 1 Crash-rates vs. road consistency

0.7
0.6
0.5
0.4
0.3
0.2

W
-1.73*LW
CR= 130.07*e
130.07*e-1.73*LCR =2R2 = 0.41
R = 0.41

0.1

Crash0.0
Rates (Crashes per Million Vehicle Kms.)
3.00
3.15
3.30

3.45

3.60

L ane Width (m.)
Lane
(m.)

Crash Rates (Crashes per million vehicle kms.)

Fig. 2 Crash-rates vs. lane width

0.7

CR+ 0.48C R==-0.15Ln(RSS)-0.15L n(R S S ) + 0.48
R2 = 0.25R 2 = 0.25

0.6
0.5
0.4

5. DEVELOPMENT OF AN INFRASTRUCTURE
COEFFICIENT (IC) BY THE ANALYTICHIERARCHY PROCESS (AHP)

0.3
0.2
0.1
0.0
Crash Rates (Crashes per Million Vehicle Kms.)
0
1
2
3

4

5

R oa d-S ide SScorec ore
Road-Side

Fig. 3 Crash-rates vs. road-side score126

Since the variables for the road-side score (RSS)
developed in this study (see Table 3) were already accounted for in the road-side score variable, there was noneed to consider them again as independent variables.
The main analyses were conducted with five infrastructure characteristics: road consistency, lane width, percentage of highway with a no-passing zone, number ofaccess points/km., and road-side score. These were chosen from the total of 12 variables for four main reasons:(1) they show the most significant relationship to crashrates, (2) together they provide a description of both thehorizontal and vertical alignment of the roadway, (3)some of these characteristics are included indirectly
through the RSS measure, and (4) the remaining infrastructure characteristics showed weak relationships tocrash-rates.
Another examination that was conducted during
the preliminary analysis evaluated the relationship between the number of crashes and the average daily traffic volumes on the roads studied. This relationship was
expected to be non-linear as some researchers have suggested 25,26. However, this study assumed that the relationship between crash numbers and traffic volume waslinear, for two reasons: (1) after testing, no significant
difference was found between the linear and parabolic
relationships; (2) the Average Daily Traffic (ADT) on
most segments was below 10,000. Other studies haveshown that a non-linear relationship starts at higher traffic volumes. Therefore, the volumes in this study wereassumed to be on the linear portion of the otherwise generally non-linear relationship.
As a result of this linearity, further analyses wereconducted with crash-rate data without the need for any
additional adjustments to the impact of traffic volume. Ina linear relationship, each traffic volume has a single
crash-rate value that is proportional to the traffic volume
itself (but this is not true in a parabolic relationship).
Figure 4 presents the linear and parabolic relationships
between crash numbers and traffic volumes.

IATSS Research Vol.31 No.1, 2007

6

7

8

The main purpose of using the AHP was to rank theroad infrastructure characteristics according to their contribution to safety. This was done by attributing a specificweight to each characteristic. These weights were thencomputed and determined by the AHP method. The IC
for a specific road segment can be computed by multiply-

DEVELOPMENT OF AN INFRASTRUCTURE COEFFICIENT BY AN ANALYTIC HIERARCHY PROCESS AND ITS RELATIONSHIP TO SAFETY

28
2
2
LinearModel:
L inearModel:R =R0.34= 0.34y =y4.88E-04x= 4.88E -04x++2.52E+00
2.52E +00

Number of Crashes

24

70

2

20

ParabolicModel:
Model:R2 = 0.37
R
= 0.37
Parabolic2-2.23E -08x2 ++9.91E-04x+4.96E-01
9.91E -04x + 4.96E -01-2.23E-08x
y =y =

79-2

16
89-2

12

77-2

4
672-3
805
8
Numberof Crashes
89-1
79-1
866
767 672-2
73
721
4
91-1
65-2
886
65-3
672-1
806
91-2
0
0

2500

5000

7500

75

90

10000 12500

85
77-1

15000

66-2

65-1

66-1

17500 20000

22500

25000

AverageDaily
DailyT Traffic
Volume(ADT(ADT)
Averageraffic V olume)

Fig. 4 Relationship between number of crashes and
ADT volumes on all 25 highway segments (thenumber next to each data point is the roadnumber)ing the weight of each infrastructure characteristic by its
appropriate infrastructure-characteristic value for the
specific road segment and adding up the products. The
importance of the IC coefficient lies in its enabling roadway engineers and practitioners to rank the different
roadway segments according to their IC, which represents the overall infrastructure characteristics of a segment and is not based on a single infrastructure measure.
Roadway segments with high IC values represent a relatively good quality of roadway design (with low crashrates), and segments with low IC values represent a
relatively poor quality design (with high crash-rates).
5.1

AHP - background
The AHP, first developed by Thomas Saaty 2, is amathematical decision-making technique that incorporates both qualitative and quantitative factors. The AHP
has increased in use and popularity because the process
reflects the way people think and make decisions, whichis by simplifying complex decisions to a series of one-onone comparisons and synthesizing the results. Moreover,
the AHP method has many applications in the transportation field in general. For example: the evaluation of different transportation projects that include the decision
making process. Saaty 27 introduced five examples of applications of the AHP in order to illustrate the different
uses of this approach in multicriteria decision methods intransportation analyses. These examples included a commuter route selection hierarchy, a best mix of routes toPittsburgh’s new International Airport, a benefits/costs
hierarchy to choose the best mode to cross a river, a plan-

H. FARAH, A. POLUS, M. A. COHEN

ning hierarchy for a transport system and a simple dependence with feedback cycle to choose a car when criteria
depend on the alternatives. Hu and Shi 28 used the AHP
method for ITS projects evaluation. Trevor 29 used the
AHP method as a tool for infrastructure management.
Sangjin 30 used the AHP method for prioritization of international highway network development. Other examples and studies can be found in the literature.
The purpose of the present study was to rate the five
infrastructure characteristics (defined above) according
to their relative importance and contribution to safety.
Rating the relative contribution to safety of all five infrastructure characteristics simultaneously is a complex task.
However, because the AHP method is a technique that
simplifies decision-making, it was deemed a very appropriate and highly efficient method for use in the present
case. Also it was selected during this study to analyze theinfrastructure impact on safety because it is actually the
only method that does not assume linearity as other multivariate analyses do and it fits most goals of the study,
particularly the objective of developing a single measure(IC) for roads’ infrastructure. Further justifications andlimitations of using the AHP method are discussed in
section 5.3 below.
The AHP method includes four basic axioms:
Reciprocal Axiom: When any two objectives, Oi, Oj (i, jindices), are given to a decision-maker, that person is able
to compare them under any criterion Ci, so that: aij =1/aji(where aij is the relative importance of Oi compared with
Oj under criterion Ci, and aji is the inverse of aij).
Homogeneity Axiom: The elements being comparedshould not differ by more than an order of magnitude in
any cluster.
Synthesis Axiom: Judgments about or the priorities of theelements in a hierarchy do not depend on lower-level elements; this axiom will not be needed in the case underdiscussion.
Expectation Axiom: Individuals who have reasons fortheir beliefs make sure that their ideas are adequately represented for the outcome to match their expectations.
The first major task in the AHP method involves theestimation of a normalized set of weights of the different
objectives. These weights assist the decision-maker incomparing various alternatives. (In our analysis, the objectives are the different infrastructure characteristics,
and the alternatives are the various road segments.) The
weights are mapped from a matrix of pairwise comparisons, A = (aij), which are positive and reciprocal. Thus,
IATSS Research Vol.31 No.1, 2007127

TransportaTion

given matrix “A”, (1):

A

a12
 1

1
1 / a12 .
 .
1 / a 1n 1 / a 2 n

the pairwise comparisons.

.. .. a1n .. .. a 2 n .  . ........................ (1). .. .. 1 

Where:
A = pairwise comparison matrix, in which the number in the ith row and jth column gives the relative
importance of Oi compared with Oj;
n = number of objectives;
aij = 1/aji for all i, j=1, 2, . . ., n.
The problem that remains is to map a set of weights,
W1,. . ., Wn, from matrix “A” for the objectives O1, O2,. . ,On (infrastructure characteristics) through an understanding of how the pairwise comparisons aij convert to weights
Wn.
In an ideal situation, the pairwise judgment is madeby computing the following ratio: aij = Wi / Wj (i, j=1, 2, . . .,n), where Wi is the weight of objective i and Wj is theweight of objective j. This means that the judgment matrix (matrix “A” - pairwise comparison matrix) is actually
the ratio of the relative weight attributed to objective Oi to
the relative weight attributed to objective Oj, Therefore,
matrix “A” can be rewritten as a set of weight ratios:

 w1

 w1
 w2

A' =  w.1

 .
 wn

 w1

w1
.. ..
w2
w2
.. ..
w2
wn
.. ..
w2

w1 

wn 
w2 
wn  ................................
(2)
. 

. 
wn 

wn 

The weights are the eigenvector corresponding to
the largest eigenvalue of matrix “A”, denoted by max. In
the ideal case, the value of the largest eigenvalue is n,
whereas non-consistency of matrix “A” yields higher
values. Therefore, Saaty 2 suggested that the consistencyof matrix “A” be measured by the consistency index C.
I. = ( max-n)/ (n - 1).
The closer this index is to 0, the more consistent are

128

IATSS Research Vol.31 No.1, 2007

5.2

Application of the AHP for weighting infrastructure characteristics
The matrix cells for the pairwise comparisons describe the relative safety importance of each two infrastructure characteristics. This means that a comparison for
its importance to safety of each infrastructure characteristic with all other infrastructure characteristics accounted for in the study will be included in the matrix (5 5).
Table 4 describes the infrastructure characteristics thatwere chosen for the construction of the IC in descendingorder of their importance to safety.
It was difficult to identify a sufficiently large poolof experts in highway safety design in order to achieve a
reliable grading of the relative contribution to safety ofeach infrastructure characteristic. Therefore, the approach adopted in this study was to determine importancebased on the R-square and t-test results of the regression
relationships found in the preliminary analysis of the relationship of each infrastructure characteristic to the crashrate. For example, because road consistency explains
about 55% of the crash-rate variance, which was the highest among the infrastructure characteristics selected andthe most significant according to the t-stat result (-5.34),
it was considered to be the most important road characteristic for safety and given a grade of 5 (Table 4). In
contrast, access points are the least important to safety,
since this characteristic had the lowest R-square in thesame analysis and the lowest t-stat result (1.69); it therefore received a grade of 1 (Table 4).
In order to construct the matrix of pairwise comparisons of the infrastructure characteristics, Saaty’s
scale (Table 5) was used to help in determining the pairwise judgments 2.
For example, according to Saaty’s scale 2, if objective “i” is more important than objective “j” under achosen criterion, then aij equals 4 in the pairwise com­
Table 4 Grading, according to R-square, of the in­fra­
structure characteristics chosen
Infrastructure
Characteristic

R- Squaret-statGrade

Road Consistency

0.55

-5.34

5

Mean Lane Width

0.41

-3.98

4

Road-Side Score

0.25

-2.75

3

% of Highway with
No-Passing Zone

0.14

1.94

2

Access Points/km.

0.04

1.69

1

DEVELOPMENT OF AN INFRASTRUCTURE COEFFICIENT BY AN ANALYTIC HIERARCHY PROCESS AND ITS RELATIONSHIP TO SAFETY

par­i­son matrix. In our analysis, the objectives are the different infrastructure characteristics, and the criterion
according to which the objectives are compared is roadsafety. For example, when comparing road consistency
and access points/km., there is a difference of 4 grades
between these two characteristics (which is the maximum
difference between any two infrastructure characteristic
grades – Table 4) because road consistency (Grade = 5) is
more important to safety than are access points/km.
(Grade=1). When judged according to Saaty’s scale2(Table 5), road consistency is much more important tosafety than are access points/km.; therefore, aij = 8 (seeTable 6).
Based on Table 5 and Table 6, the matrix of pairwise comparisons of infrastructure characteristics – Matrix “A” – was constructed and is presented in Table 6.
In Matrix “A,” the number in the ith row and jth
column gives the relative importance of the infrastructurefeature in the ith row compared with the infrastructurefeature in the jth column. The problem that remains is tomap a set of weights, W1,. . ., Wn, from Matrix “A” forthe objectives O1, O2,. . , On (infrastructure characteristics) through an understanding of how the pairwise comparisons aij convert to weights Wn.
In this case, the largest eigenvalue of Matrix “A,”
Table 5 Saaty’s (1980) pairwise judgment scale2
Pairwise Comparison

aij

Objective i is much more important than Objective j

8

Objective i is more important than Objective j

4

Objective i is slightly more important than Objective j

2

Objective i is of equal importance as Objective j

1

Objective i is slightly more unimportant than Objective j 0.5
Objective i is more unimportant than Objective j

0.25

Objective i is much more unimportant than Objective j

0.125

Table 6 Judgment values according to relative impor­tance to safety

H. FARAH, A. POLUS, M. A. COHEN

shown in Table 6, is 5.0966, resulting in a consistency
index of 0.024, which is considered to be sufficiently
close to 0. The corresponding eigenvector of the weights(normalized so that they add up to 1) is presented in Table 7. Now, the IC can be computed for each roadway
segment and the 25 roadway segments ranked by multiplying each of the weights from Table 7 by the appropriate infrastructure-characteristic value for each roadway
segment and summing up the results. This is done using
Equation 3:
IC=0.26·LW-0.09·NPZ+0.45·RC+0.15·RSS+0.05·AP .... (3)Where:
LW - lane width (m.);
NPZ - percentage of highway with a no-passingzone (%);
RC - road consistency;
RSS - road-side score (note Table 3);
AP - number of access points/km. (points/km.);
The coefficients of Equation 3 are, of course, thecalculated weights, taken from Table 7.
It is important to remember that for the purpose ofthis analysis and the statistical method used, it was preferable to convert the actual physical dimension of eachelement (lane width, percentage of intersections withspeed-change lanes, etc.) to categorical variables. Furthermore, since the coefficients of Equation 3 are actuallynormalized weights, it was necessary to present the infrastructure characteristics in terms of the nominal variables of an equal number of categories (in our case, fivecategories) in each scale. Low scores on these scales
indicate poor infrastructure quality (e.g., narrow lane
width, bad consistency, etc.), and high scores a good
infrastructure quality. If IC is calibrated versus crashTable 7 Weighting infrastructure characteristics
according to AHP method
Infrastructure Characteristics

Weight

%NPZ

AP

RC

0.45

4

4

8

LW

0.26

2

4

4

RSS

0.15

0.5

1

2

4

%NPZ

0.09

0.25

0.25

0.5

1

2

AP

0.05

0.125

0.25

0.25

0.5

1

Σ

1.0

RC

LW

RSS

RC

1

2

LW

0.5

1

RSS

0.25

%NPZ
AP

RC = Road consistency
LW = Lane width (m.)
RSS = Road-Side Score (note Table 3)%NPZ = Percentage of highway with a no-passing zone (%)
AP = Number of access points/km. (points/km.)

RC = Road consistency
LW = Lane width (m.)
RSS = Road-Side Score (note Table 3)%NPZ = Percentage of highway with a no-passing zone (%)
AP = Number of access points/km. (points/km.)

IATSS Research Vol.31 No.1, 2007

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TransportaTion

5.3

Advantages and possible limitations of using the
AHP method
The AHP method was found to be a very appropriate and highly efficient method for determining the relative contribution to safety of each infrastructure element.
This results from the following advantages of this method: (a) It enables obtaining the relative weights of various
elements–the infrastructure, in this study–by “one-onone” comparisons conducted by a pool of experts. In thisstudy, it was difficult to find a sufficiently large pool ofhighway design and safety experts, and therefore it wasnecessary to resort to a unique approach whereby weights
were determined by the R-square and t-test results of theregression relationships found in the preliminary analysis(b) It is among the simplest of multi-attribute decisionmaking methods, which bypass the potential pitfalls ofasking vague questions in long surveys; (c) It permits acertain degree of inconsistency and can be measured andquantified. AHP is the only method that can tolerate inconsistencies and, unlike neural networks, it allows theresults to be interpreted.
On the other hand, this method has some possible
limitations: (a) Each pair of attributes must be checked,
which may be a tedious task because of the large attributesets. In the present study, only a handful of attributes existed, and therefore this was not a limitation; (b) If theimportance of attributes differs by more than an order ofmagnitude, AHP cannot be used. In this study, however,
two-lane rural highways are, in general, not much different from one another, and therefore this limitation did notexist; (c) The addition of a new attribute can change theorder of importance of the old attributes. However, thisstudy had a fixed (5 elements), pre-determined number of
attributes, and so this concern was not an issue.

6. CRASH PREDICTION BY THE
INFRASTRUCTURE COEFFICIENT (IC)The IC represents the overall infrastructure characteristic of the highway. Based on the data collected andthe relative weights of each variable as determined by

130

IATSS Research Vol.31 No.1, 2007

AHP, the relationship between crash-rate (CR, in crashes/million vehicle-km.) and the IC was calibrated and isgiven in Eq. (4):CR = 1.004·exp-0.401· (IC) ............................................. (4)R2 = 0.56
This relationship, which is presented in Figure 5,
can be used to predict crash-rates on new or existing twolane highways, based on their infrastructure elements.
Note that one of the infrastructure elements is road consistency; this needs to be calculated separately according
to the Polus and Mattar-Habib 9 model.
The linear correlation coefficients between each
two infrastructure features were examined. Some infrastructure features were strongly correlated; for example,
lane widths with road consistency (0.75), shoulder widths
with road-side score (0.77) and shoulder widths with lane
widths (0.85). Some of these correlations were expected
because they conform to common engineering judgment
and are due to reasonable design practice. For example,
more use would be made of guardrails in an area withmountainous terrain, which also has less design consistency and more no-passing zones. Furthermore, often,
although not always, roads with high-standard design elements have quality elements in all their geometric features, and these are correlated. These strong correlations,however, may prevent the use of the models presented(Eqs. 3 and 4) to identify the exact contribution of eachindividual element to expected crash-rates. This issue
can be investigated in future research.

Crash Rates (Crashes per million vehicle kms.)

rates, therefore, it may be possible to estimate the safetylevel of a new or existing roadway based on its infrastructure components. This is of tremendous importance whenassessing various alternatives and conducting an economic evaluation, when it is necessary to allocate funds
to the most cost and safety-efficient projects. Alignment
characteristics, then, could be converted to safety levels
by using the IC coefficient.

1.0

C R≤0.25≤0.25 Lower
L ower C
ras h-R ate RRoads
oads
CR
Crash-Rate

0.9

C R>0.25>0.25 Higher
ras h-R ate R oads
CR
Higher CCrash-Rate
Roadsx x-0.401*IC

0.8

1.004*e-0.401*ICCRC R= =1.004*e
R 2 = 0.56
R2 = 0.56

0.7
0.6

767

886

91-2

0.5

672-2

672-3

866

90

721
0.4
0.3
0.2
0.1

89-1
91-1

89-2

79-2

75

77-2

805
66-1
672-1

66-2
73
4
85
65-1 65-2
77-1
65-3

0.0 Rates (Crashes per Million Vehicle Kms.)
Crash

1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25

Infras tructureCoefficientC oefficient by AHPInfrastructure
AHP

Fig. 5 Relationship between crash-rates and IC cal­culated by Eq. (4)DEVELOPMENT OF AN INFRASTRUCTURE COEFFICIENT BY AN ANALYTIC HIERARCHY PROCESS AND ITS RELATIONSHIP TO SAFETY

7. FURTHER TESTSAn additional purpose of this study was to examine
the extent of the impact of poor infrastructure quality on
crash-rates. The sample of 25 roadway segments included in developing the crash-rate prediction model was divided into two samples (good quality and poor quality),
based only on each segment’s IC as given in Eq. (3). The
first sample consisted of those roadway segments that
had an IC above 3, and the second sample those with an
IC below 3. The threshold of IC = 3 that separates presumably good from supposedly poor quality road designs
was found to be the threshold that yields the highest ratio
between crash rates on poor quality road segments andcrash rates on good quality road segments. As shown in
Figure 5, roadway segments with a higher IC have lower
crash-rates. In order to ascertain whether the averagecrash-rate for each of the two samples of roadways in the
study (lower crash-rate roadways and higher crash-rate
roadways) was significantly different from each other, at-test was conducted. The null hypothesis is that the two
samples have the same average crash-rates, and the alternative hypothesis is that they have different crash-rate
averages. Based on the t-test, it was found that, at a 99%
confidence level, a highway with a good quality of infrastructure reduces crash-rates by 44% compared with ahighway with poor quality infrastructure.

8. CONCLUSIONS AND FURTHER RESEARCH
The purpose of this research was to develop an IC
that represents the overall characteristic of a highway andto develop a model that correlates this IC with crash-rates
on two-lane rural highways. The research approach that
was adopted is called the AHP. The IC developed enables
highway planners and safety auditors to predict crashrates based on the infrastructure features of a highway.
This coefficient can be used when evaluating several alternatives for a new highway and even when rehabilitating existing highways so as to improve their overall
safety features.
The literature repeatedly indicates the major contribution of the human factor to crashes. However, thisstudy found that bad infrastructure contributes significantly to crashes. This study also shows that it is possible
to distinguish between lower crash-rate roads and higher
crash-rate roads by means of their overall infrastructure
characteristics. Well-built and maintained highways can
reduce crashes by 44%, compared with highways with
bad infrastructure, and this finding is at a 99% confidence

H. FARAH, A. POLUS, M. A. COHEN

level. As a result of this very significant finding, more
focus should be placed on upgrading the infrastructure
characteristics of roadways; for example, investing in theelimination of road hazards by improving alignment consistency, upgrading such roadside features as paving
shoulders, building guardrails where necessary, and fencing steep side-slopes.
Further research could concentrate on the following: (1) validation of the models developed by increasing
the data set of rural two-lane highways; (2) the development of crash-prediction models based on ICs for othertypes of highway facilities (e.g., freeways, intersections);(3) use of the AHP approach to validate and test proposedcrash-prediction models for two-lane rural highways inother countries; (4) further evaluation of potential correlations between ICs and their impact on crash prediction;and (5) developing crash-prediction models that accountfor vehicle and human features besides the infrastructurefeatures.

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