SAFETY ASSESSMENT OF FREEWAY MERGING AND DIVERGING
INFLUENCE AREAS BASED ON CONFLICT ANALYSIS
OF SIMULATED TRAFFIC
By
Markos Alito Atamo
B.Sc., Addis Ababa University, Ethiopia, 2002
M.Sc., Addis Ababa University, Ethiopia, 2005
A thesis submitted to the
University of Colorado Denver
in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Civil Engineering
2012
2012 by Markos Alito Atamo
All rights reserved
This thesis for the Doctor of Philosophy degree by
Markos Alito Atamo
has been approved for the
College of Engineering and Applied Science
by
UP, 2 o l Z-
Date
Atamo, Markos Alito (Ph.D., Civil Engineering)
Safety Assessment of Freeway Merging and Diverging Influence Areas Based
on Conflict Analysis of Simulated Traffic
Thesis directed by Professor Bruce N. Janson.
ABSTRACT
The safety of merging and diverging influence areas, intersections,
interchanges, and other traffic facilities is assessed by tracking and analyzing
police-reported motor vehicle crash records. Since the nature of road crashes
is random and infrequent, this process is slow to reveal the need for
remediation of the roadway design and traffic control strategy. Moreover, this
process is not applicable to assess new designs that have not yet been built,
or deployed in the real world.
This study summarizes a technique combining micro-simulation and
automated conflict analysis to assess the safety of traffic facilities without
waiting for a statistically above-normal number of crashes to occur. The
technique is also valuable in assessing the relative performance of one
design versus another. Traffic Conflict Technique (TCT) is among the most
common surrogate measures to study the safety of roadway facilities. The
software referred to as Surrogate Safety Assessment Model (SSAM) was
developed by FHWA and was used in this study. The SSAM software
application was designed to perform statistical analysis of vehicle trajectory
data. Trajectory data is the output from microscopic traffic simulation models.
Among the various traffic simulation modeling tools, VISSIM was chosen
because of its compatibility with SSAM, its versatility for analyzing networks of
big sizes and its ability to provide users with the capability to model any type
of geometric configurations.
Forty-two merging and forty-two diverging influence areas in Colorado, USA,
were modeled in VISSM and conflict analysis was performed using SSAM
under AM-peak traffic conditions. Five field validation tests were conducted.
Conflicts predicted by SSAM approach were compared with actual crash
records at merging and diverging influence areas in all statistical validation
tests. The results of the validation effort of safety assessment based on
conflict analysis of simulated traffic suggested that this technique is
recommended for safety assessment at merging and diverging locations.
This abstract accurately represents the content of the candidates
dissertation. I recommend its publication.
Signed
Bruce N. Janson
DEDICATION
I dedicate this thesis to my loving and devoted wife, Azeb, for her unfaltering
support and understanding while I was completing it. I also dedicate this to
my daughters Yohana, Heldana, and Yosabet and to my parents who gave
me an appreciation of learning and taught me the value of perseverance and
resolve.
ACKNOWLEDGEMENT
My thanks to each of the members of my doctoral committee for their support
during the completion of this thesis.
Very special thanks to my advisor, Professor Janson, for his wise guidance,
instruction and unlimited support. I am very grateful for having the opportunity
to learn from him.
TABLE OF CONTENTS
Figures xiii
Tables xv
Chapter
1. Introduction................................................... 1
1.1 Background..................................................... 1
1.2 Traffic Safety Overview........................................ 2
1.3 Statement of the Problem....................................... 4
1.4 Research Objectives and Contributions to the
Transportation Industry........................................ 5
1.5 Glossary of Terms- Quick Reference Guide....................... 7
1.6 Study Flow Structure...................................... 11
2. Review of the Literature...................................... 13
2.1 Traffic Conflict Technique.................................... 13
2.2 Merging and Diverging Movements on Freeways................... 15
2.3 Survey of Modeling Data....................................... 16
2.4 Interchanges and Ramps........................................ 17
viii
22
23
25
27
29
32
35
36
38
42
42
43
44
49
51
51
51
51
55
Background of Safety on Freeway Ramps.............
Log-linear Regression Models......................
Poisson Regression Model..........................
Negative Binomial Regression Model................
Goodness of Fit Measure...........................
Traffic Crash Prediction Model....................
Empirical Bayes Technique.........................
Empirical Bayes Safety Estimate...................
Bayesian Identification of Accident-Prone Locations
Simulation Modeling...............................
Choice of a Simulation Tool.......................
VISSIM Micro-Simulation Tool......................
SSAM Conflict Analysis Tool.......................
SAS/STAT Software and the GENMOD Procedure..
Research Approach and Methodology.................
Field Validation..................................
Purpose...........................................
Data Assembly and Geometric Definition............
Simulation Modeling of Interchanges and
Modeling Assumptions..............................
IX
3.5 Identification and Removal of Outliers.................... 59
3.6 Methodology............................................... 60
3.6.1 Field Validation Test 1: Merging and Diverging
Location Ranking by Total Incidents....................... 60
3.6.1.1 Conflict Ranking.............................................. 61
3.6.1.2 Crash Ranking................................................. 61
3.6.1.3 Ranking Comparison............................................ 62
3.6.2 Field Validation Test 2: Merging and Diverging
Location Ranking by Specific Incident Types............... 63
3.6.3 Field Validation Test 3: Crash and Conflict
Prediction Regression Model Paired Comparison............. 64
3.6.4 Field Validation Test 4: Crash and Conflict
Prediction Regression Model Comparative
Analysis For Total Incidents.................................. 65
3.6.5 Field Validation Test 4: Crash and Conflict
Prediction Regression Model Comparative
Analysis For Specific Incident Types...................... 69
3.7 Goodness of Fit Measure....................................... 69
4. Test Results and Discussion................................... 72
X
4.1 Field Validation Test 1: Merging and Diverging
Location Ranking by Total Incidents............................ 75
4.2 Field Validation Test 2: Merging and Diverging Location
Ranking by Specific Incident Types............................. 76
4.3 Field Validation Test 3: Crash and Conflict
Prediction Regression Model Paired Comparison.................. 80
4.3.1 Illustration................................................... 91
4.4 Field Validation Test 4: Crash and Conflict Prediction
Regression Model Comparative Analysis
for Total Incidents........................................... 93
4.4.1 Development of Conflict Prediction Regression
Models for Total Incidents.................................... 93
4.4.2 Identification of Accident Prone Locations (APL).............. 95
4.4.3 Illustration.................................................. 96
4.4.4 Ranking Locations............................................. 97
4.5 Field Validation Test 5: Crash and Conflict
Prediction Regression Model Comparative
Analysis For Specific Incident Types....................... 101
4.5.1 Development of Conflict Prediction Regression
Models for Specific Incident Types......................... 101
XI
4.5.2 Identification of Accident Prone Locations (APL) to
Rear End Incidents.......................................... 104
4.5.3 Ranking Locations........................................... 104
5. Summary, Conclusions, and Recommendations................... 108
5.1 Summary and Conclusions..................................... 102
5.2 Recommendations............................................. 113
Appendix
A Interchange traffic flow information............................. 116
B Average 3 year crashes recorded at
merge and diverge locations......................... 117
C Average yearly crashes recorded at
merge and diverge locations......................... 118
D Conflicts of five replications at merge and diverge
locations recorded by SSAM software....................... 119
E Average hourly conflicts at merge and diverge
locations recorded by SSAM software....................... 120
Bibliography......................................................... 121
xii
LIST OF FIGURES
Figure
1.1 STUDY WORKFLOW STRUCTURE........................ 12
2.1 TYPICAL INTERCHANGE CONFIGURATIONS.............. 19
2.2 TYPICAL RAMP CONFIGURATIONS..................... 21
2.3 EVENT-FILE BASED INFORMATION
FLOW DIAGRAM................................... 45
2.4 ILLUSTRATION OF CONFLICT ANGLE DIAGRAM.......... 49
3.1 ILLUSTRATION OF MERGE INFLUENCE AREA............ 54
3.2 ILLUSTRATION OF DIVERGE INFLUENCE AREA.......... 54
3.3 SCREEN CAPTURE. VISSIM GEOMETRIC
MODEL OF I-25&E HAMPDEN AVE.................. 57
3.4 SCREEN CAPTURE. VISSIM TRAFFIC
MODEL OF I-25&E HAMPDEN AVE.................. 58
4.1 SCREEN CAPTURE. SSAM SCREEN-
xiii
CONFIGURATION TAB
73
4.2 SCREEN CAPTURE. SSAM SCREEN MAP TAB
VIEW AT 1-25 & E HAMPDEN AVE................... 74
4.3 SCREEN CAPTURE. VISSIM CONFLICT SCENARIO
RESULTING FROM LANE CHANGE MANEUVER............ 77
4.4 TOTAL CRASH AS A FUNCTION OF MAINLINE ADT
AND MERGING ADT................................ 83
4.5 TOTAL CRASH AS A FUNCTION OF MAINLINE ADT
AND DIVERGING ADT.............................. 84
4.6 TOTAL CRASH AS A FUNCTION OF TOTAL
CONFLICT AT MERGE.............................. 88
4.7 TOTAL CRASH AS A FUNCTION OF TOTAL
CONFLICT AT DIVERGE............................ 89
XIV
LIST OF TABLES
Table
4.1 Distribution of crashes and conflicts by incident type.......... 79
4.2 Correlation coefficients by incident type....................... 80
4.3 Prediction model of total crashes as a function of
mainline ADT and merging ADT.................................... 82
4.4 Prediction model of total crashes as a function of
mainline ADT and diverging ADT.................................. 82
4.5 Prediction model of total crashes as a function of
conflicts at merge................................................... 86
4.6 Prediction model of total crashes as a function of
conflicts at diverge................................................. 86
4.7 Prediction model of conflicts as a function of
mainline PHV and merging PHV......................................... g4
4.8 Prediction model of conflicts as a function of
mainline PHV and diverging PHV................................... 94
XV
4.9 Comparison between total crash and total conflict
prone locations at merge..................................... 98
4.10 Comparison between total crash and total conflict
prone locations at diverge................................... 99
4.11 Summary of APLs of total incidents........................... 100
4.12 Average total crashes and total conflicts
based on incident proneness of locations..................... 100
4.13 Prediction model of rear-end crashes as a
function of mainline ADT and merging ADT..................... 102
4.14 Prediction model of rear-end crashes as a
function of mainline PHV and merging PHV..................... 102
4.15 Prediction model of rear-end crashes as a
function of mainline ADT and diverging ADT................... 103
4.16 Prediction model of rear-end crashes as a
function of mainline PHV and diverging PHV................... 103
4.17 Comparison between rear-end crash and rear-end
conflict prone locations at merge............................ 105
4.18 Comparison between rear-end crash and rear-end
conflict prone locations at diverge.......................... 106
XVI
4.19 Summary of APLs of rear-end incidents........................ 107
4.20 Average rear-end crashes and rear-end conflicts
based on incident proneness of locations..................... 107
xvii
1. Introduction
1.1 Background
According to the National Highway Traffic Safety Administration (NHTSA
2006) report, motor vehicle travel is the primary means of transportation in the
United States, providing an unprecedented degree of mobility. Despite all its
advantages, deaths and injuries resulting from motor vehicle crashes are the
leading cause of death for people of every age from 2 through 34. Traffic
fatalities accounted for more than 90 percent of transportation-related
fatalities.
National Highway Traffic Safety Administration (NHTSA 2009) stated that in
the United States more than 5.5million police-reported motor vehicle crashes
occurred. Of these 1.5million (28%) crashes resulted in an injury, 30,797
(fewer than 1%) resulted in a death and 3.4million (73%) involved in property
damage only. The fatality rate per 100 million VMT was 1.03.
There were 8.6million vehicles involved in single and two-vehicle crashes.
The number of vehicles involved in a merging/lane changing maneuver were
312,000 (3.6%). Resulting from these maneuvers were 769 fatalities, 48,000
injury, and 263,000 property damage only crashes. Similarly, the number of
vehicles involved in a going straight maneuver was 4.3million (50.4%).
Resulting from these were 27, 124 fatalities 1.25million injury, and 3.0million
property damage only.
l
The World Health Organization (2004) projected that between 2004 and 2030
global deaths increase by 28% which is predominantly due to the increasing
number of road traffic accident deaths. Road traffic accident deaths are
projected to increase from 1.3 million in 2004 to 2.4 million in 2030, primarily
due to the increased motor vehicle ownership and use associated with
economic growth in low- and middle-income countries. Road traffic accidents
are projected to rise from the ninth leading cause of death globally in 2004 to
the fifth in 2030. According to the United Nations General Assembly (2008),
by 2020 road traffic deaths and injuries will exceed HIV/AIDS as a burden of
death and disability.
1.2 Traffic Safety Overview
A traffic accident occurs when a road vehicle collides with any physical object
and results in injury, property damage, and death. Factors contribute to the
risk of collision include; vehicle design, speed of operation, road design, and
driver impairment. Worldwide motor vehicle collisions lead to significant death
and disability as well as significant financial costs to both society and the
individual.
For the last two decades, several legislations have been making safety a
central, explicit, comprehensive, and integrated part of transportation
planning. As a result of this, safety management systems have advanced to a
great extent. Traffic safety data and analytical tools have been improved and
refined, and the effects of countermeasures have become better understood.
2
Since 1991 there have been three major Acts announced in the Unites States
of America: (1) the 1991 Intermodal Surface Transportation Efficiency Act
(ISTEA); (2) the 1998 Transportation Equity Act for the 21st Century (TEA-21),
and (3) the 2005 Safe, Accountable, Flexible, Efficient Transportation Equity
Act (SAFETEA-LU.)
The Intermodal Surface Transportation Efficiency Act (ISTEA) of 1991 moved
the historical focus of highway and transit programs away from construction,
capacity, and congestion. The Act changed the emphasis towards mobility
and access, system performance, and consideration for the environment and
quality of life.
The Act did not specifically mention safety as part of the planning process but
mandated six comprehensive management systems including a Safety
Management System (SMS) as a prerequisite for funding. The SMS was part
of the strategy to improve the management, operations, and safety of the
highway system through improved data analysis and collection, through
improved coordination, cooperation, and communication among agencies,
and through the development of collaborative strategic plans (Depue 2003).
In 1998, the Transportation Equity Act for the 21st Century (TEA-21) called
for comprehensive safety consciousness. The Act required state DOTs (and
MPOs) to increase the safety and security of the transportation system for
motorized and non-motorized users. This was the first time that safety
became an explicit part of transportation plans. Prior to TEA-21, safety was
sometimes a prominent factor in project development and design, but this
legislation calls for safety consciousness in a more comprehensive, system-
wide, multimodal context, (FHWA 2001a).
3
The Safe, Accountable, Flexible, Efficient Transportation Equity Act
(SAFETEA-LU) became law in 2005. SAFETEA-LU has a strong focus on
integrated and comprehensive safety planning. It was built on previous
legislation in giving specific and increasing recognition to safety issues.
The Act establishes the Flighway Safety Improvement Program (HSIP) as a
core program and nearly doubles the funds available for infrastructure safety
and comprehensive strategic highway safety planning. The purpose of the
HSIP is to reduce fatal and serious/life changing crashes. The program
includes planning, implementation, and evaluation of safety programs and
projects. (Bahar, G., and Morris, N. (2007)).
Generally, these legislations have encouraged or insisted on giving safety
priority through better data, better analysis, better reporting systems, and the
adoption of a structured comprehensive approach. A detailed study of the
safety of highways would help to understand safety and help to make safety
legislation a success.
1.3 Statement of the Problem
Until recently the safety of merging and diverging influence areas,
intersections, interchanges, and other traffic facilities is most often
assessed by tracking and analyzing police-reported motor vehicle crashes
over time. Since the nature of crashes is random and infrequent, the
process of analysis of safety based on the police report is slow to reveal
the need for remediation of either the roadway design or the flow-control
strategy. This process is also not applicable to assess new designs that
4
have yet to be built, or to assess new flow control strategies before they
are employed on-site.
This study summarizes a technique combining micro-simulation and
automated conflict analysis to assess the safety of traffic facilities without
waiting for a statistically above-normal number of crashes to occur. The
technique is also valuable in assessing the relative performance of one
design versus another in comparing alternative designs.
1.4 Research Objectives and Contributions to the Transportation
Industry
The objective of this research was to assess the safety of freeway merging
and diverging influence areas using conflict analysis technique and compare
the results with the actual crash experience. SSAM conflict analysis software
was used for predicting safety performances at the predefined locations. The
Surrogate Safety Assessment Model (SSAM) is a software application
designed to perform statistical analysis of vehicle trajectory data output from
microscopic traffic simulation model, in this study VISSIM.
VISSIM is a traffic simulation modeling tool which was chosen because of its
compatibility with SSAM, its versatility for analyzing networks of big sizes and
its ability to provide users with the capability to model any type of geometric
configurations or unique operation/driver behavior encountered within the
transportation system. It is a time-based microscopic simulation tool that uses
various driver behavior and vehicle performance models to accurately
5
represent urban traffic and public transport operations. This study identified
areas in need of further research.
The study will make the following contributions to the industry:
Helps in assessing the relative safety performance of one design versus
another.
Provide transportation agencies, planners, engineers, researchers with
information about the type, frequency and relative location of conflicts.
Provide solution that improves safety, access, and mobility of the
merge/diverge influence area.
Provide the safety analyst with a fast report to reveal the need for
remediation of the roadway design.
6
1.5 Glossary of Terms Quick Reference Guide
Accident (traffic): Event between road-users that results in injury, fatality
or property damage.
Accident causation: Underlying reasons that pre-empt a traffic accident,
most usually involving an unforeseen chain-of-events. Accident causation is
often attributed to one of the three main components of the traffic system:
road-user, vehicle or roadway, or a combination of thereof.
Accident outcome: Result of an accident in terms of injury severity, fatality
and in some cases also property damage.
Accident rate: Number of accidents in accordance with a measure of
exposure.
Accident severity: Level of injury sustained in a traffic accident: usually
categorized as minor, serious or fatal.
Calibration: Process used in Traffic Simulation to (statistically) ensure that
the functioning and behavior of a particular model and/or sub-model
corresponds with observed empirical measurements or predetermined values.
Car-following: Term used to describe the status of a vehicle that has a
time/distance gap or headway less than a predetermined maximum value.
Collision: Impact event between two or more road-users/vehicles, or a road-
user (vehicle) and stationary object.
7
Collision course: Existence of a common projected conflict point in time and
space for two (or more) road-users/vehicles, usually based on momentary
measures of trajectory, speed and distance.
Conflict: An observable situation in which two or more road users approach
each other in time and space to such an extent that there is risk of collision if
their movements remain unchanged.
Conflict distance: A momentary measurement of (spatial) distance to a
common conflict point for a road-user/vehicle in a conflict situation.
Conflict point: Common spatial location of projected trajectories given
momentary measures of speed and distance for two or more road-
users/vehicles.
Conflict severity: Seriousness of a potential collision or near-accident
measured by temporal or spatial proximity.
Conflict speed: Momentary measurement of velocity for a road-user (vehicle)
in a conflict situation.
Conflict zone: Common area used by road-users/vehicles approaching from
different trajectories.
Crash: Term that is sometimes preferred to (traffic) accident due to the fact
that it implies an element of causality rather than an unforeseen random
occurrence.
8
Driver behavior: Largely misused and over-simplified term used in traffic
engineering that is used to describe the actions and/or variability of drivers in
different driving situations. It should relate to the study of individual behavioral
processes that underlie driver actions (performance).
Exposure: Measure of spatial or temporal duration in the traffic system in
relation to the number of dynamic system objects road-users, vehicles
(axles), etc.
Fatality: Death resulting from a traffic accident (usually within a 30 day period
after the accident occurrence).
Gap-acceptance: Process that describes and measures interaction between
prioritized and non-prioritized road-users. Generally involves spatial or
temporal measurement of gaps or lags in prioritized streams that are
accepted or rejected in relation to a particular yielding maneuver.
Incident: the term used in a more abstract sense to refer to either crashes or
conflicts.
Injury accidents: Traffic accidents that result in minor or serious injury to one
or more parties.
Macroscopic (macro-) simulation: Simulation at a less detailed
(aggregated, macroscopic) level.
Microscopic (micro-) simulation: Simulation at a very detailed (microscopic)
level.
9
PET: It is the minimum post-encroachment time observed during the conflict.
Post encroachment time is the time between when the first vehicle last
occupied a position and the time when the second vehicle subsequently
arrived to the same position. A value of zero indicates a collision. A post-
encroachment time is associated with each time step during a conflict. A
conflict event is concluded when the final PET value is recorded at the last
location where a time-to-collision value was still below the critical threshold
value. This value is recorded in seconds.
Police reported accidents: Accidents that are reported by the police and are
recorded in the accident database of accident.
Safety: Freedom from accident or loss.
Simulation (traffic): Abstract imitation of the operation of a real-world
process or system over time and event occurrence. Traffic simulation is
concerned with the modeling of processes in the traffic system and can be
conducted at different levels of abstraction depending on the purpose of the
study.
TTC: It is the minimum time-to-collision value observed during the conflict.
This estimate is based on the current location, speed, and future trajectory of
two vehicles at a given instant. A TTC value is defined for each time step
during the conflict event. A conflict event is concluded after the TTC value
rises back above the critical threshold value. This value is recorded in
seconds.
10
1.6 Study Workflow Structure
Figure 1.1 illustrates Study Workflow Structure. Accordingly, this research is
divided into three Parts. Part 1 included introduction, information and data
search. It consists of Chapter 1 and Chapter 2. Chapter 1: Introduction, it
provided an introduction to the study by presenting the background
information, traffic safety overview, statement of the problem, study objectives
and contributions to the transportation industry; and glossary of terms.
Chapter 2: Literature Review: a comprehensive literature review on the safety
performance of merging and diverging influence areas from published
information was provided. It presented the overview of the merging and
diverging movements on freeways, the survey and collection of available
modeling data, background of safety on freeway speed change locations,
regression models, Bayesian accident-prone locations, and simulation and
conflict analysis tools. Also preliminary qualitative analysis of the data was
carried out to identify the general validity of the selected variables. Part 2
included data analysis. It consists of Chapter 3: Research approach and
methodology, this section described the study methodology used in the field
validation test and the steps taken to complete the study. Part 3 consists of
Chapter 4 and Chapter 5. Chapter 4: Test results and discussion, this section
validated the actual crash data and discussed the results of the analysis.
Chapter 5: Presented the summary, conclusions and recommendations
drawn from the results of the study.
li
FIGURE 1.1 STUDY WORKFLOW STRUCTURE
12
2. Review of the Literature
2.1 Traffic Conflict Technique
According to Amundsen and Hyden (1977), a conflict is defined as an
observable situation in which two or more road users approach each other in
time and space to such an extent that there is risk of collision if their
movements remain unchanged.
The traffic conflict technique method initially developed at the Detroit General
Motors laboratory in the late 1960s for identifying safety problems (Perkins
and Harris, 1968). It was based on observer judgments using time-lapse
filming, and proves a costly and time consuming technique. They correlated
conflict patterns to accident types. Spicer (1973) studied about the safety of
six intersections and concluded that there was good correlation between
serious conflicts and reported injury accidents. Sayed (1997) conducted a
study to estimate the safety of un- signalized intersections using traffic safety
technique. A computer simulation model was used to study traffic conflicts
with time-to-collision as the critical traffic event in simulating driver behavior.
Using the data collected from 30 conflict surveys, he established traffic
conflict frequency and severity standards for un-signalized intersections.
These standards allow the relative comparison of the conflict risk at various
intersections. Miglez et al. (1985) developed a methodology to predict traffic
accidents from observed conflicts. Also, statistical procedures were
developed to determine conflict rate values that could be considered
"abnormally" high. The study concluded that traffic conflicts are good
13
surrogates of accidents in that they produce estimates of average accident
rates nearly as accurate as those produced from historical accident data.
Gettman, Pu, Sayed, and Shelby (2008), studied a method of safety
assessment utilizing a traffic conflicts analysis technique applied to simulation
models of intersections, interchanges, and roundabouts. They developed a
software application to automate the task of traffic conflicts analysis and
conducted validation testing to gauge the efficacy of the assessment method.
Several surrogate traffic conflict measures have been developed to assess
the safety of highway facility. The common surrogate conflict measures are
gap time, encroachment time, deceleration rate, proportion of stopping
distance, post-encroachment time, initially attempted post-encroachment
time, and time-to-collision.
There is general consensus that higher rates of traffic conflicts can indicate
lower levels of safety for a particular facility, given the fact that conflicts
generally result from a lack or misunderstanding of communication between
the different road users (Risser 1985 and Archer 2000)
In this study, traffic conflicts occur with adequate frequency to overcome the
statistical challenges posed by infrequent crashes. Also, since adequate
conflict data can be collected in a relatively short time, conflict analysis is not
subject to the problem of changing of the underlying conditions (e.g., traffic
volumes, geometry) that affect long-term crash records.
14
2.2 Merging and Diverging Movements on Freeways
According to Roess, R., Prassas, E., and McShane W. (2004), merging
occurs when two separate traffic streams join to form a single stream.
Merging can occur at on-ramps to freeways or multi-lane highways, or when
two significant facilities join to form a single traffic stream. Merging vehicles
often make lane changes to align themselves in lanes appropriate to their
desired movement. Diverging occurs when one traffic stream separates to
form two separate traffic streams. This occurs at off-ramps from freeways and
multilane highways, but can also occur when a major facility splits to form two
separate facilities. Again, diverging vehicles must properly align themselves in
appropriate lanes, thus indicating lane-changing; non-diverging vehicles also
make lane changes to avoid the turbulence created by diverge maneuvers.
Therefore, a merge area would always follow an on-ramp whereas a diverge
area would always precede an off-ramp. Road users in such areas are
required to select and adjust speeds without causing undue hazards to
themselves or to other road users. Such hazards would normally increase in
terms of frequency and intensity with increasing volumes of vehicles entering
and exiting a specific segment on the freeway. This increase may result from
the combination of increasing number of required lane changes and
decreasing probability of a suitable gap between moving vehicles to perform a
merge or diverge operation (Sarhan, M.; Hassan, Y.; and Abd El Halim, A.O.
2008).
15
2.3 Survey of Modeling Data
Since the nature of road crashes is random, the choice of the analysis period
has a significant impact on the accuracy and reliability of the safety
assessment. Accident counts that are recorded for overly extended time
period may introduce biases in the analysis when current traffic and
geometric conditions differ from those prevailing when the crashes occurred.
Similarly, an overly short period reduces the number of crashes considered
and hence the statistical accuracy of the model would be affected. According
to the Permanent International Association of Road Congresses PIARC
(2003) Road Safety Manual, the minimum accepted analysis period is 3
years. For this study, a three year data from year 2008 through 2010 was
used which was obtained from the Colorado Department of Transportation
(CDOT) accident database.
The greatest statistical challenge of the safety assessment of a facility in
accurately pinpointing an underlying crash rate is the nature of motor vehicle
crashes. Crashes are so infrequent and exhibiting variable hourly and yearly
crash counts. The problem is increasingly difficult for areas with lower (more
infrequent) crash rates. There is possible bias in comparing peak-hour
conflicts to annual crashes. The statistical models that correlate the peak-
hour crash with the peak hour conflict on the merging and diverging locations
may not converge as there are too few peak-hour crashes (which are less
than 25% of the total crashes). Field validation through estimation with a
larger data set would result in a more significant parameters estimates and
more accurate crash prediction.
16
Twenty-one interchanges, forty-two merging and forty-two diverging influence
areas were selected. A preliminary assessment was made of the types of
interchange elements that were in sufficient numbers and had sufficient data
available for statistical modeling of accidents to be conducted. Accordingly
diamond interchange configurations were selected.
Using each interchanges milepost as a common identifier, modeling data was
collected for each interchange taking the following into consideration:
1. Interchange layout: number of lanes on mainline and ramps, ramp
length, and ramp configuration.
2. Traffic volumes: average daily traffic (ADT), design hourly volume
(DHV), percent trucks, and on-ramp hourly traffic volume recorded by
ramp meters.
3. Data on crash frequency on mainline and ramps.
4. Location of crash occurred on the highway. Only crashes at the merge
and diverge influence areas of the interchange were considered.
5. Accident Type: accidents were regrouped into three: rear-end, crossing
and lane-changing. Only vehicle-to-vehicle accidents were considered.
6. Direction: the direction of traffic flow at the time of crash: North,
Northeast, Northwest, East, West, South, Southeast, Southwest.
2.4 Interchanges and Ramps
Grade separation of intersecting roadways reduces crashes caused by
crossing and turning movements. An interchange is a system of
interconnecting roadways in conjunction with one or more grade separations
that provides for the movement of traffic between two or more roadways or
highways on different levels. Access control is a highly desirable feature
17
along the crossroad at an interchange to provide efficient traffic operations
and safety. The most common roadways connections at an interchange
consist of freeway-to-freeway (access-controlled freeways), freeway-to-
arterial and arterial-to-arterial. Freeway-to-arterial and arterial-to-arterial
connections are non-access-controlled highways. This research focused
exclusively on a freeway-to-arterial interchanges.
There are several basic interchange configurations to accommodate turning
movements at a grade separation and it is determined by number of
intersection legs, expected volumes of through and turning movements,
composition and type of traffic, topography, design control, proper signing,
and physical constraints such as existing rivers, railroads, and roadways.
All freeway interchanges with non-access-controlled highways should provide
ramps to serve all basic directions to prevent wrong-way movements.
According to AASHTO 2004, the term ramp includes all types,
arrangements, and sizes of turning roadways that connect two or more legs at
an interchange. The different ramp patterns of an interchange (i.e. the
different types of interchange configurations) are made up of various
combinations of ramps. Figure 2.1 illustrates typical interchange
configurations: from the simplest full-diamond interchange to complex, multi-
level directional interchanges. Many variations of each of these basic
interchange configurations are possible.
18
(4-Quad)
i / \ t
\
Full Diamond
with Slip Ramps
ZL
Partial Cloverleaf (Parclo)
h\
'
Full Cloverleaf with
Collector/Distributor
Roads
A U
\ r
Directional
FIGURE 2.1 TYPICAL INTERCHANGE CONFIGURATIONS (BAUER, M.
AND HARWOOD, W 1998)
19
A one way road that leaves a mainline highway facility is called an off-ramp or
exit ramp. A one way road that joins a mainline highway facility is called as an
on-ramp or entrance ramp. This distinction is important because according to
Cirillo (1967) & Lundy (1966), the accident rate of on-ramps was consistently
lower than off-ramp accident rates. Accordingly an on-ramp accident of 0.59
accident per MVMT and off-ramp accident of 0.95 accident per MVTM have
been confirmed. Vehicles typically travel along off-ramps at higher speeds
than along on-ramps, so that accidents are more likely to occur on off-ramps.
Figure 2.2, illustrates a number of typical ramp configurations. Each of the
ramps of the ramp configurations illustrated traffic exiting from a mainline
freeway, but an analogous ramp configuration for traffic entering the mainline
freeway also exists.
20
Direct Connection*
Semi-Direct
Connection*
(to two-way
frontage road)
(to two-way
frontage road)
(to one-way
frontage road)
* When used in directional Interchanges
b Scissors connection
FIGURE 2.2 TYPICAL RAMP CONFIGURATIONS (BAUER, M. AND
HARWOOD, W 1998)
21
2.5 Background of Safety on Freeway Ramps
Numerous studies have studied the safety performance of freeway ramps
during the past several decades. Bared, J., Giering G., Warren, D., (1999)
developed the statistical model of accidents to estimate accident frequencies
for entire ramps as a function of speed change lane length among other
variables. According to the accident model developed in that study, the longer
speed change lane showed the less accident frequency.
The result of the study by Lord, D., Bonneson, J., (2005), showed that the exit
ramps are more dangerous and the non-free-flow type ramp experience twice
as many accidents as other types of ramps. Previous researchers have
developed several crash prediction models to relate crash frequency at ramp
sections to different explanatory variables such as traffic volumes and ramp
design elements.
Bauer, M, Harwood, W. (1998), studied the relationship between traffic
crashes and highway geometric design elements and traffic volumes for
interchange ramps and speed change lanes. The statistical modeling
approaches used in that research included Poisson and negative binomial
regression. Several models were developed to predict crashes on ramp
sections and speed change lanes. The variables that were included in crash
models included mainline freeway AADT, ramp AADT, area type
(rural/urban), and ramp type (on/off), ramp configuration, right shoulder width,
and lengths of ramp and speed-change lane. The regression model is
presented in Section 2.6 of this study.
Accident rates decrease as length of weaving area, or acceleration and
deceleration lane increases (Cirillo 1967, 1968, 1970). Cirillo developed
statistical model and provided a relationship between the length of weaving
22
and acceleration and deceleration lanes and traffic volume levels and
percentage of merging and diverging traffic. Increase in traffic volume was
associated with an increase in crash. The effect of acceleration lane length on
accident rate was significant when merging traffic percentage exceeded 6%
of the main line traffic volume. As the percentage of merging traffic increase
beyond this volume, the additional length of acceleration lane provides a
significant reduction in accidents. The effect was not as great for deceleration
lanes compared to acceleration lanes.
Studies suggested that a good portion of the accidents associated with ramps
occur at the entrance and exit of ramps. Mullins and Keese (1961) found that
23% of all through-lane accidents occur near entrance terminals. 52% of the
on-ramp accidents according to Lundy (1966) occur at entrance terminal.
McCartt, A., Northrup, V., Retting, R. (2004) studied about the types and
characteristics of ramp-related motor vehicle crashes on urban interstate
roadways in Northern Virginia. The study found that 48% accidents occurred
in the process of exiting freeway, 36% occurred when the traffic entering and
16% occurred in the midpoint.
2.6 Log-linear Regression Models
Bauer, M. and Harwood, W. (1998) developed statistical model for
interchange. These models are Log-linear regression models. They included
Poisson and negative binomial regression models. Statistical background on
both the Poisson and negative binomial models is provided next.
23
The following notations are used:
n = interchange elements (e.g., ramp proper segments, entire ramps),
i = is a set of q parameters (xn ,Xi2,...,Xiq ) (e.g. the geometric design,
traffic volume, and other related characteristics of that element.
Yt= the number of accidents occurring at the ith element during a specific
period (say 3-year): where i = 1,2, ...,n.
yj= the actual observation of y{ during the 3-year period, where
Yi = 0,1,2,... and i = 1,2,..., n.
E(Yi) = |ii = the expected number of accidents at the ith element and the
q parameters,
Note: In section 2.5 of this study all logarithms are natural logarithms and
are denoted by log.
The main objective of a statistical model is to develop a relationship E(Yi) =
|ii and q parameters, X{1 ,Xi2, ....,Xiq.
This relationship can be formulated through a general linear model (GLM) of
the form:
Function (^) = (B0 + Mil + + (3qXiq
(2.1)
24
where:
(B0, Pi, p2 -Pq, are the regression coefficients and estimated from the
data.
The estimation procedure used to obtain the regression coefficients is
dependent on the assumption made about the distribution of the Yj,
2.6.1 Poisson Regression Model
The assumption of a log-normal distribution [i.e., the assumption that log(Yi)
follows a normal distribution] is not valid when the average number of
accidents at a ramp is small. The Poisson model then becomes a natural
choice as it models the occurrence of rare discrete events well. The Poisson
distribution has a mean and variance, a2 both equal to |.
According to the model formulated by Bauer and Harwood (1998):
Assuming the number of accidents,^, follows a Poisson distribution with
mean |, the probability that a ramp with y} accidents can be expressed as
q
(2.2)
25
P(Y; = y;; w) =
(2.3)
where: yp denotes the factorial of yi.
Maximum likelihood estimation method is used to estimate the Poisson
regression coefficients (B0 P!,...,pq. Maximization of the likelihood function is
performed by taking the derivative of the likelihood function with respect to the
parameter value. However, it is convenient to take the natural log of the
likelihood function before differentiating. Since the natural log is a monotonic
function, maximizing the log-likelihood is equivalent to maximizing the
likelihood.
So, the likelihood is:
The log-likelihood over all n interchange elements in the category of elements
is therefore:
n
(2.4)
log(L) = -n\i + (y1 + + yn) log(g) log^! x ... x xn!)
(2.5)
26
Which is equivalent to:
log(L) = ^[y; logOO |ii log(yi!)]
i=l
(2.6)
2.6.2 Negative Binomial Regression Model
As it has been discussed in Section 2.5.1, in Poisson distribution the mean
and the variance of the distribution are equal. However, previous traffic
accident research has shown that this is not always the case.
Paternoster and Brame, (1997); Osgood, (2000) suggested the negative
binomial distribution as an alternative to the Poisson when there is evidence
of overdisperson.
Overdispersion is a phenomenon that implies there is more variability around
the model's fitted values than is consistent with a Poisson formulation.
Suppose a Poisson model is used for modeling accidents and if the variance
(or dispersion) of the data exceeds the estimated mean of the accident data
distribution, then the data are said to be overdispersed, and the underlying
assumption of the variance being equal to the mean for the Poisson
distribution is violated (Bauer, M. and Harwood, W. (1998)). The negative
binomial is proposed as a means to correct for this problem (Osgood, 2000).
Negative binomial distribution has two parameters, unlike the Poisson
distribution.
27
For negative binomial distribution the relationship between the expected
number of accidents occurring at the ith element and the q parameters is
same as Equation (2.1). The probability that a ramp Y; = y} accidents can be
expressed as:
PM = yd =
r(y+E> ftuF
rry + ijr(i)n + iqly*i
Vi = 0,1,2,...
(2.7)
The mean and variance of the negative binomial distribution of accident
frequency are given by:
Mean = E(Y) = (2.8)
Variance = Var(Y) = \i[ + k[i2 (2.9)
where:
k = the negative binomial dispersion parameter
The model regression coefficients (B0 are estimated by the method
of maximum likelihood minimizing the negative of the log likelihood.
Bauer, M. and Harwood, W (1998) developed the log likelihood for the
negative binomial distribution and is given by:
28
n
log(L)
^ Yi log
i=l
a
(a + 1).
nk log(a + a) + function of yj, k
(2.10)
Modifying Equation (2.10):
log(L) = ^ yi log
i=l
gk
.(gk + 1)J k
n
log(a + gk) + function of yj, k
(2.11)
Which is equivalent to:
log
- Po + PlXil + P2Xi2 1------h PqXiq
(2.12)
2.6.3 Goodness of Fit Measure
The scaled deviance and Pearsons chi-square statistic are helpful in
assessing the goodness of fit of a given generalized linear model. According
to Nelder and Wedderburn (1972), for a fixed value of the dispersion
parameter , scaled deviance is defined to be twice the difference between
the maximum achievable log likelihood and the log likelihood at the maximum
likelihood estimates of the regression parameters.
29
Let Z(x,ju) the log-likelihood function,
where:
/1 = the mean of the distribution
y = the response values,
Then the scaled deviance is defined by:
SD(y,ii) = 2l{l(y,y) - (2.13)
SD(y,ii) =
D(y. M)
0
where:
(2.14)
D(y,n) =model (residual) deviance
0= the generalized linear model dispersion parameter
Accordingly, scaled deviance for the Poisson distribution is given by Equation
(2.15):
D = 2
Zy'ln-Z(y'-,)
i=l i=l
(2.15)
30
Also, scaled deviance for the negative binomial distribution is given as:
D = 2I
i i
where:
ylog(f)-(y+v)hB
k = the negative binomial dispersion parameter
(2.16)
Since
distributions the scaled deviance is equal to the deviance.
Pearsons chi-square statistics is given by:
2 v 2
*
i=i
and the scaled Pearsons chi-square is defined as:
where:
fi = the mean of y
V(yd = the variance function of the distribution.
(2.17)
(2.18)
31
In both Equation (2.16) and (2.17) the weight to each interchange is to be
one.
Since 0 is one for both Poisson distribution and negative binomial
distributions the scaled Pearsons chi-square is equal to the Pearsons chi-
square statistics.
2.7 Traffic Crash Prediction Model
Bauer, M. and Harwood, W. (1998) developed models to predict accidents.
Initially accidents on ramps and speed-change lanes were modeled
separately with the thought that accident predictions from the separate
models could be added together to determine the combined safety
performance of a ramp and its adjacent speed-change lane. The study proved
that the separate models, by themselves, didn't provide an adequate fit to the
data. Therefore, they developed the best models of the safety performance of
interchange ramps and speed-change lanes by combining the accident
experience of ramps and their adjacent speed-change lanes into a single
model.
Independent variables included in the model include:
Ramp AADT
Mainline freeway AADT
Area type (rural/urban)
Ramp type (off/on)
Ramp configuration
Length of speed-change lane
Ramp length
32
It was determined that these seven independent variables are all statistically
significant at the 20-percent significance level in the model for total accidents,
and all of these independent variables, except ramp configuration, are
significant in the model for fatal and injury accidents.
To predict the average accident frequency for a ramp including the adjacent
speed-change lane, the regression coefficients .Pq are replaced in
equation (2.19) by the estimated values of the coefficients and the variables
X1X2, ->Xq are replaced by their appropriate values or levels.
function(p*) = exp{fQ){AADTramp)Plexp{f2Xi2) ... exp(fqXiq) (2.19)
For example, the expected 3-year total accident frequency can be estimated
as
Y = e-7-27(X1)-78(X2)013exp(0.45X3)exp(0.78X4)exp(-0.02X5)
exp(0.69X6)exp(-0.37X7)exp(0.37X8)
exp(-2.59X9)exp(1.62X10) (2.20)
where:
Y = expected number of total accidents in a 3-year period on entire ramp
plus adjacent speed-change lane
X = ramp AADT (veh/day)
X2 =mainline freeway AADT for the direction of travel in which the ramp is
located (veh/day)
33
X3 = 1 if the ramp is a diamond ramp; 0 otherwise
X4 = 1 if the ramp is a parclo loop ramp; 0 otherwise
X5 = 1 if the ramp is a tree-flow loop ramp; 0 otherwise
X6 = 1 if the ramp is an outer connection ramp; 0 otherwise
X7 = 1 if the area type is rural; 0 otherwise
X8 = 1 if the ramp is an off-ramp; 0 otherwise
*9 = speed-change lane length (mi)
X10 = ramp length (mi)
The estimate of dispersion after fitting, as measured by the deviance and
Pearsons chi-square divided by the degrees of freedom, are 1.0 and 0.95
respectively for total accidents which are well within the acceptable range.
Also the Ft2 goodness of fit is approximately 0.38.
Among these variables, it was found that mainline and ramp AADT to be the
most important predictor of accident on ramps. The increase in crash
frequency was associated with higher accidents. The effect of acceleration
length was more complicated since on one hand longer lengths provide safer
traffic maneuvering and on the other hand corresponding increased length
may provide longer exposure and more accidents.
It was noted that the 3-year accident prediction models were divided by 3 to
obtain the corresponding accidents per ramp per year.
34
2.8 Empirical Bayes Technique
Bayes theorem is a probability theory that shows how new information can be
used to update or revise an existing set of probability. The prior probability
may have to be estimated based on very little information. These probabilities
would be improved as more information becomes available.
When it comes to traffic safety, Empirical Bayes (EB) is a theoretical
framework that combines the actual crash count of a location with an
estimated crash frequency determined from the safety performance function
of the same location. Sayed (1995) stated that the expected number of
accidents at a location is a random variable that fluctuates around some
unknown mean. This randomness is reason that historical accident data at a
location does not always accurately reflect its long-term accident
characteristics. Higle and Witkowski, (1988) stated that a location that has
low accident frequency during long periods of time may have had high
accident rates during portions of this period and vice versa and confirmed that
Empirical Bayes approach accounts for random variations of accident rate.
The technique is based on Bayes theorem which can be mathematically
described as:
P(0|x) =
P(x|0) X P(0)
ZP(x|0)xP(0)
(2.21)
35
Where:
0 = a parameter such as the number of accidents at a location,
P(0) = the prior distribution of 0,
P(x|0) = the probability of making x observation for a specific value of
0 (observation distribution), and
P(0|x) = the posterior distribution of 0 which represents the resolution of the
prior distribution given the observations.
According to Calvin (1990) the distribution of the observation is assumed to
be a Poisson or Binomial distribution and the prior distribution will be a
gamma or beta distribution. In the Empirical Bayes approach, the parameters
are estimated using a sample of observations from population of similar
locations.
2.8.1 Empirical Bayes Safety Estimate
Hauer (1992), Brude and Larsson (1988) stated that the safety of a location
provide clues about its traffic and road characteristics, and its historical
accident data. The Empirical Bayes (EB) approach makes use of both kinds
of clues and is used to refine the estimate of the expected number of
accidents at a location by combining the observed number of accidents at the
location with the predicted number of accidents obtained from the GLM model
to yield a more accurate, location-specific safety estimated. Equation 2.31
confirmed this. Brude and Larsson, (1988) showed that EB method
significantly reduces the regression to the mean effects that are inherent in
observed accidents count. Regression to the mean is a statistical
phenomenon that refers to the tendency of extreme events (high number of
36
accidents) to be followed by less extreme values (a lower number of
accidents) even if no treatment is applied to the field configuration that
generates the accidents at that location.
According to Hauer (1992), the EB safety estimate can be calculates by.
EBSafety estimate OC.pved + (1 Cc). COUTlt, (2.22)
where,
1
11 ~ i+var(pd>
pred
where,
count = observed number of accidents at the location
pred= predicted number of accidents as estimated from the GLIM model
var(pred) = the variance of the GLM estimates
According to (Sayed et.al., 1998),
var(pred) =
(pred)2
K
37
Where:
k = shape parameter
Then, Equation (2.22) can be rearranged as:
EBsafety estimate
k \ / pred
count
(2.23)
In addition, the variance of the EB estimate can be calculated using (Kulmala,
1995):
2.8.2 Bayesian Identification of Accident-Prone Locations
Higle and Witkowski (1988) described that Empirical Bayes procedure is a
useful technique to identify accident-prone locations.
The following notations are used:
1; = accident rate at a location i (treated as a random variable),
Nt = number of accidents at location i during the period of time in question,
Vt = number of vehicles passing through location i during the period of time in
question,
f t (A|Ni.Vj) = probability density function associated with the accident rate at
(2.24)
location i given the observations Nt and Vt (Posterior
distribution) ,
38
fR (A) = probability density function associated with the accident rate across
the region (Posterior distribution) ,and
a,p = parameters of gamma distribution.
Two assumptions were made:
1. At any given location, the actual number of accidents (JVÂ£) follows a
Poisson distribution such that at any given location, where the accident rate
is known (AÂ£ = A) and the expected value is given by XVt then the
observation probability distribution is given by the following:
The parameters a and p of the prior distribution are estimated using the
method of moments estimates (MME), and are chosen so that the mean and
variance associated with the gamma distribution are equal to the mean (x)
and variance (s2) of the sample.
(2.25)
2. The probability distribution of the regional accident rate (the prior
distribution), fR(X), follows a gamma distribution and is given by:
(2.26)
39
If (x) and (s2) are the sample mean and variance of the observed accident
rates respectively, and m is the number of locations under observations, then:
m
X m 2., Vt
i=1
T(N ^
m
i=1
(2.27)
(2.28)
Morris (1988) and Berger (1985) modified the parameters of gamma
distribution to avoid the bias and improve the estimation. Accordingly, the
probability density function associated with the accident rate at a location i is
given by:
fMNuVd
J-l__wn-lp-PiX
r fo)
(2.29)
And thus, location i will be identified as accident-prone if there is a significant
probability that the locations accident rate,If, exceeds the observed regional
accident rate, XR.
40
Thus, location i is identified as accident prone if:
P{Ai>XR\Ni,Vi}>8
(2.30)
or equivalently if:
at
1- I ^-Aa_1e_^dA
-I
o
rfe)
> s
(2.31)
where:
S = the confidence level desired, such as 0.95 or 0.99, and
The value of the regional accident rate, XR, is calculated using:
JT-iNt
(2.32)
Sayed (1995) modified the Higle and Witkowskis method by substituting
a + Ac.Vi for at in Equation (2.31) and is given by:
xR
-I
p{a+)ic.Vj)
r {a + Ac.Vi)
1(+Ac.Vi-l)e(.-ptX)
dA
(2.33)
41
2.9 Simulation Modeling
2.9.1 Choice of a Simulation Tool
A need for simulation modeling has been increasing to understand the
behavior of traffic as transportation systems have become more complex.
Many researches in the past have studied different similarities and differences
of simulation tools and their capacity to model different combinations of traffic,
highway type, geometric configuration, etc. of the system.
Gettman D., and Head L., (2003) conducted a study to evaluate the various
simulation models capabilities for producing measures of intersection safety
and specify algorithms for calculating the measures. The nine multipurpose
micro simulation software includes CORSIM, SIMTRAFFIC, VISSIM,
HUTSIM, PARAMICS, TEXAS, AIMSUN, WATSIM, and INTEGRATION. It
was noted that VISSIM, AIMSUN, PARAMICS, and TEXAS outputs the
proper TRJ files required by SSAM. It was concluded that there are a number
of advantages that VISSIM possesses over other micro-simulation tools.
VISSIM appears to be a full-featured microscopic simulation model with the
ability to obtain detailed state variable information on each vehicle on time
scales with better than second-by-second accuracy. Moreover it has been
interfaced to other external codes such as hardware signal controllers, thus
the developers have experience in development collaboration. The priority
rules feature of VISSIM appears to allow complex modeling of junction
behavior, including friendly merging (situations where following vehicles will
slow for merging vehicles to create a gap), as it occurs in the real world. It is
not apparent that other simulation models are able to represent such
behavior. VISSIM allows multilane merging behavior; it is typical for vehicles
entering the mainline flow to cross the path of an oncoming vehicle traveling
42
in the same direction as the intended direction of travel of the entering vehicle
and start accelerating in the adjacent lane. In this way, the oncoming vehicle
can continue at its current speed without having to break for the turning
vehicle. VISSIM appears to support most of the modeling features required
for obtaining surrogate measures at a reasonable level of fidelity.
Because of its competitive advantages, combined with its capability to
analyze networks of all sizes, VISSIM was chosen to perform the simulation
modeling of traffic.
2.9.2 VISSIM Micro-Simulation Tool
According to VISSM User Manual (2009), VISSIM is a microscopic, time step
and behavior-based simulation model developed to model urban traffic and
public transport operations. The program can analyze private and public
transport operations under constraints such as lane configuration, traffic
composition, traffic signals, etc., thus making it a useful tool for the evaluation
of various alternatives based on transportation engineering and planning
measures of effectiveness.
The model was developed at the University of Karlsruhe, Germany during the
early 1979. PTV America, Inc., a subsidiary of PTV AG located in Karlsruhe,
Germany, is the North American distributor and developer of PTV Vision
software products. VISSIM version 5.20 was used in this study.
Unlike many other simulation tools, it is not strictly node-link based, it is based
on link-connector geometry. In VISSIM the user builds a network based on
43
aerial photographs at the exact point where they are needed to have the
desired effect on road-users.
Traffic flow in VISSIM is simulated by moving driver-vehicle-units through a
network. Every driver is stochastically assigned to a specific vehicle.
Consequently, the drivers behavior will be adapted to the vehicle
performance characteristics. Attributes characterizing each driver-vehicle-unit
can be classified in to three components: (1) technical specification of the
vehicle (e.g. length, engine power, weight, maximum speed, potential
acceleration actual position in the network, and actual speed and
acceleration), (2) behavior of driver-vehide units (e.g acceleration based on
current speed and drivers desired speed, (3) interdependence of driver-
vehicle units (e.g. reference to leading and following vehicles on own and
adjacent travel lanes)
2.10 SSAM Conflict Analysis Tool
The Surrogate Safety Assessment Model (SSAM) is owned by FHWA.
According to Lili Pu and Rahul Joshi (2008), SSAM operates by processing
data describing the trajectories of vehicles driving through a traffic facility and
identifying conflicts. The vehicle trajectory input data for SSAM are generated
by traffic simulation software in a trajectory file format (where files are labeled
with a .trj file extension), specially designed for SSAM. SSAM calculates
surrogate measures of safety corresponding to each vehicle-to-vehicle
interaction and determines whether or not each interaction satisfies the
criteria to be deemed an official conflict. A table of all identified conflicts and
their corresponding surrogate safety measures is then presented to the user.
44
Figure 2.3 illustrates the workflow for using SSAM. It was reported that the
users of the SSAM software would include traffic safety engineers, traffic
simulation analysts, and traffic researchers.
FIGURE 2.3 EVENT-FILE BASED INFORMATION FLOW DIAGRAM
(Gettman D., and Head L., (2003)).
Surrogate Safety Assessment (SSAM) software uses two threshold values for
surrogate measures of safety to delineate which vehicle-to-vehicle
interactions are identified as conflicts. These two thresholds are Time-to-
Collision (TTC) and Post-Encroachment Time (PET). SSAM utilizes a default
maximum TTC value of 1.5 seconds as suggested by (Sayed, Brown, Navis,
1994) and (Hayward, 1972) and the maximum PET value of 5 seconds as
suggested by Hyden (1987).SSAM filters out conflicts that do not fall in the
specified ranges. These default values were used in this study.
45
Gettman, Pu, Sayed, and Shelby (2008) developed conflict identification
algorithm of SSAM and described as follows:
First, SSAM determines the dimensions of the analysis area based on the
TRJ file and constructs a zone grid to cover the entire rectangular analysis
area. By dividing the region into zones, the number of vehicle-to-vehicle
comparisons necessary to identify potential conflicts is reduced considerably.
Second, SSAM analyzes a single time step of a trajectory file. For each
vehicle in the analysis region, it projects that vehicles expected location as a
function of its current speed, if it were to continue traveling along its (future)
path for up to the duration of the configured time-to-collision (TTC) value.
Third, for each vehicle, SSAM calculates the rectangular perimeter
delineating the location and orientation of that vehicle at its projected future
position. Any time a vehicle is added into a zone that currently contains one
or more other vehicles, SSAM checks for overlap of the new vehicle
(rectangle) with each of the other vehicles (rectangles) in that zone. It is
possible that two vehicles may partially occupy the same zone without
overlapping. However, two overlapping rectangles indicate that a future
collision is projected for this pair of vehicles, and therefore, a potential conflict
has been identified. SSAM maintains a list of all conflicting vehicle pairs (all
conflict events) for the current time-step. Each time-step, the list is
prepopulated with all conflicting vehicle-pairs from the prior time-step. If the
current vehicle being added to the zone grid overlaps with any other vehicle,
that vehicle-pair is added to the conflict list for the current time-step (if not
already in the list).
46
Four, SSAM continues to perform a more detailed processing of each
conflicting vehicle-pair in the list for the current time-step as follows:
(a) The TTC of the vehicle-pair is updated by iteratively shortening the future
projection timeline by a tenth of second and re-projecting both vehicles as
before over successively short distances until the pair of vehicles no longer
overlaps in their projected locations. In this way, a more accurate TTC value
is established for this time-step. Instead of the large overlap, the vehicles can
have just barely come into contact. Note that if the projection timeline reduces
to zero seconds and the vehicles still overlap, then this is a crash.
(b) The minimum TTC (taking the minimum of the current TTC value and that
of the prior time-step, if applicable) are calculated and updated. Also, the
current (actual) positions of both vehicles are recorded for post-encroachment
analysis.
(c) If it was found that the vehicle-pair does not overlap over any projection
time between zero and maximum TTC, then this vehicle-pair has made its
way into the conflict event list by virtue of being in the list during the prior
time-step. In this case, the event remains in the list, watching for the one
vehicle (the trailing vehicle) to eventually occupy (or encroach on) on a
position formerly held by the other vehicle (the leading vehicle). The time
differential between when the leading vehicle occupied this location and the
trailing vehicle arrived is the post-encroachment time (PET). If a post-
encroachment was observed, then the minimum PET is updated, and this
conflict event remains in the list, as the post-encroachment could potentially
reduce as the vehicle trajectories progress over time.
47
(d) If a vehicle-pair in the conflict event list is no longer on an imminent
collision course, and it is clear that PET to any prior positions could not further
reduce the minimum PET, or the maximum PET has elapsed, then this
vehicle-pair is identified for removal from the conflict event list. Prior to
removal, all final surrogate measures are computed, including conflict starting
and end points, and conflict angles.
After SSAM identifies the conflicts, it classifies them in to four types: rear end,
lane change, crossing and unclassified conflicts. The link and lane information
is utilized for classification in the case that the vehicles both occupy the same
link at either the start or end of the conflict event. The simulation model
(VISSIM) that produced the vehicle trajectory data can generally provide link
and lane information for both vehicles. If both vehicles occupy the same lane
at the start and end of the event, then it is classified as a rear-end event. If
either vehicle ends the conflict event in a different lane than it started (while
having not changed links), then the event is classified as a lane change. If
either of the vehicles changes links over the course of the event, then the
conflict angle determines the classification using the threshold values
mentioned next.
The event type is classified based on the absolute value of the Conflict Angle.
A conflict is classified as unclassified if the conflict angle is unknown, rear-end
if ||Conflict Angle|| < 30, crossing if ||Conflict Angle|| > 85, lane change if
30 < || conflict angle || < 85. Figure 2.4 illustrates the conflict angle. The
threshold angles (30 and 85) were determined by experimentation.
48
180
o
9 = conflict angle
9, = rear end threshold angle
9j = crossing threshold angle
Refer to User Manual for
more detai
FIGURE 2.4 : ILLUSTRATION OF CONFLICT ANGLE DIAGRAM (SSAM
SOFTWARE)
2.11 SAS/STAT Software and the GENMOD Procedure
According to the SAS/STAT software user manual (2011), the software
provides comprehensive statistical tools for a wide range of statistical
analyses, including analysis of variance, categorical data analysis, cluster
analysis, multiple imputation, multivariate analysis, nonparametric analysis,
power and sample size computations, psychometric analysis, regression,
49
survey data analysis, and survival analysis. A few examples include nonlinear
mixed models, generalized linear models, correspondence analysis, and
robust regression. The current release of SAS software, SAS 9.3 version, was
used for this study.
A component of SAS software called GENMOD procedure was used. The
GENMOD procedure fits generalized linear models, as defined by Nelder and
Wedderburn (1972). The class of generalized linear models is an extension of
traditional linear models that allows the mean of a population to depend on a
linear predictor through a nonlinear link function and allows the response
probability distribution to be any member of an exponential family of
distributions. Many widely used statistical models are generalized linear
models. These include classical linear models with normal errors, logistic and
probit models for binary data, and log-linear models for multinomial data.
Many other useful statistical models can be formulated as generalized linear
models by the selection of an appropriate link function and response
probability distribution.
The GENMOD procedure fits a generalized linear model to the data by
maximum likelihood estimation of the parameter vector. There is, in general,
no closed form solution for the maximum likelihood estimates of the
parameters. The GENMOD procedure estimates the parameters of the model
numerically through an iterative fitting process. The dispersion parameter is
also estimated by maximum likelihood or, optionally, by the residual deviance
or by Pearsons chi-square divided by the degrees of freedom. Covariances,
standard errors, and p-values are computed for the estimated parameters
based on the maximum likelihood estimators.
50
3. Research Approach and Methodology
3.1 Field Validation
The field validation effort for the study sites were assessed with SSAM, and
the results were compared to actual crash histories. Also, surrogate safety
estimates were compared with traditional volume-based models for crash
prediction. The field validation testing was based solely on modeling with the
VISSIM simulation.
3.2 Purpose
The main purpose of the field validation effort was to compare the predictive
safety performance capabilities of the SSAM approach with actual crash
experience of merging and diverging freeway sections. This effort consisted
of a series of statistical tests to assess the correlation between actual crash
frequencies at a series of merge/diverge sections and the corresponding
frequency of conflicts observed in simulation models of these sections.
Traditional volume-based crash prediction models were used as a basis for
comparison.
3.3 Data Assembly and Geometric Definition
Merging and diverging influence areas along freeways at interchanges were
selected based on the following guidelines: (1) a sufficient number of
51
interchanges were needed to obtain the range of parameters necessary to
test the methodology, and to establish statistical measure of significance. (2)
interchanges were not selected based on their crash performance (e.g.,
most dangerous interchanges in an area) as this will lead to the
regression-to-the-mean bias (Hauer, E. 1980). The regression-to-the-mean
bias is the tendency of a randomly high accident frequency occurring at a
location during a specific time period to be followed by a smaller accident
frequency during a consecutive period of equal duration, even if no treatment
is applied to the field configuration that generates the accidents at that
location.
Appendix A provided a summary of the twenty-one interchanges used in this
study. It shows, for each interchange: the highway names, cross street
names, truck percentage, average daily traffic (ADT) and peak hour volume
(PHV) for the mainline, on-ramp and off-ramp movements.
Prior to fitting the model all merge/diverge related accidents were isolated
from the CDOT accident database. This eliminated the influence of non-
merge/diverge accidents from the analysis. Appendix C presents the crash
data in terms of average yearly crash counts for each merge/diverge
locations. The crash counts were derived by filtering through all interchange
crash records to include only two (or more) vehicle crashes. Thus, single-
vehicle crashes, such as run-off-road crashes, fixed-object crashes, and
animal, pedestrian, or bicycle related crashes, were excluded.
In addition to the crash count, properly defining the interchange geometry was
an important part of the modeling process. Traffic exiting a highway is
required to reduce the speed. The speed-change lane that enables the driver
52
to reduce the speed between the highway and the turning roadway in a safe
and comfortable manner is called deceleration lane. On the other hand traffic
entering a highway is required to increase the speed. The speed-change lane
that enables the driver to increase the speed between the highway and the
turning roadway in a safe and comfortable manner is called acceleration lane.
Roess and Ulerio ( 1993) studied the on-ramp and off-ramp junctions and
showed that lane changing and turbulence extend to 1500 feet downstream
from the tip of the merge gore and 1500 feet upstream from the tip of the
diverge gore. Moreover, the mainline traffic starts to change lane upstream of
the gore at merge. Similarly at diverging location it is common to see some
traffic to change lanes downstream of the gore for adjustment. As a result of
these, at both merge/diverge locations crashes at a distance of 1500ft on
either sides of the gore (total 3000ft) were compared with the corresponding
conflicts recorded for the same distance (3000ft). Figure 3.1 and Figure 3.2
illustrates the model geometric configuration of merge and diverge influence
areas respectively. Collection of traffic counts from CDOT crash database
and conflict analysis by SSAM were based on the definition of these Figures.
The model considered only right-hand traffic flow conditions for both
merge/diverge influence areas.
53
traffic movement
gore
=> number of lanes vary
FIGURE 3.1 ILLUSTRATION OF MERGE INFLUENCE AREA
FIGURE 3.2 ILLUSTRATION OF DIVERGE INFLUENCE AREA
54
3.4 Simulation Modeling of Interchanges and Modeling Assumptions
Forty two merging and diverging locations were coded in VISSIM simulation
modeling tool. The process of modeling of interchanges in VISSIM was
started by tracing an aerial photo of the proper geometric configuration by
defining the number, width, and length of lanes. After the geometric
configuration of the interchange was defined, other modeling parameters
such as traffic flow (peak-hour volume), traffic composition, percent truck,
routing decision, etc., were allocated.
Several modeling parameters were defined during the process including:
speed profiles, vehicle type, traffic composition, routing decisions and other
aspects. The traffic composition was assumed to be composed of passenger
cars and trucks. The percentage of trucks was coded at each interchange.
The desired speed profiles were assumed to range from 50mph to 75mph for
mainline traffic and 30mph to 45mph for on-ramp and off-ramp traffic. Car-
following and lane-changing behavior were set to model freeway (free lane
selection) traffic flow using the Wiedemann 99 model with all default
parameters used (VISSIM 5.2 User Manual, 2009). A simulation resolution of
5 time steps per simulation second was used. Among the different types of
routing decisions a static routing option was used which defines the vehicles
routes from a start point to any of the defined destinations using a static
percentage for each destination.
The lane-changing algorithm in VISSIM allows for two types of lane changes:
necessary lane changing and free lane changing. A free lane changing option
was chosen. In a free lane change, VISSIM checks for the desired speed
55
safety distance of the trailing vehicle on the new lane. This safety distance
depends on the vehicle speeds.
Following nominal verification, each interchange was simulated five times for
a period of 3600 simulation seconds (1 hour). Instead of running multiple
simulation runs with different random seeds, a multirun option was used. This
option lets VISSIM automatically run the requested five successive runs at
each location. When run this way, VISSIM automatically uses a new random
seed number at the starts of each run.
The modeled interchanges were tested for realistic and reasonable vehicle
behaviors. The TRJ output files from VISSIM run model were imported into
the SSAM application to identify traffic conflicts and calculate the
corresponding surrogate safety measures. The output from SSAM was
formatted and analyzed by SAS GENMOD statistical software to produce
safety performance functions.
The traffic flow inputs to VISSIM were based on peak hour volumes, as
recorded by the CDOT traffic database. The volumes used for simulation are
included in Appendix A.1. Figure 3.3 and Figure 3.4 are screen captures of
geometric layout and flow of traffic modeled in VISSIM respectively.
56
S?
FIGURE 3.4 SCREEN CAPTURE. VISSIM TRAFFIC MODEL OF 1-25 &
E HAMPDEN AVE
58
3.5 Identification and Removal of Outliers
Before any statistical inferences were applied, the outliers were identified and
removed from the dataset. Outliers are observations or subsets of
observations which appear to be inconsistent with the remainder of the data
(Barnett & Lewis, 1978). There are three ways for outliers to arise in a sample
(Barnett and Lewis (1994, pp. 33-34)): (1) data due to a reading error, a
recording error, or a calculation error in the data; (2) a data value that
incorrectly included in the data set; (3) a correctly recorded data value that
belongs in the data set. Since these causes of outliers are possible to occur in
the data, due attention were given to identify and remove them.
The Standardized Residual Criterion (z-score method) was used to identify
outliers. The standardized residual, the STUDENT statistic, is the residual
expressed in units of standard deviation from the mean value. Thus, a
standardized residual with an absolute value of 3 is 3 standard deviations
above the mean value. Observations with standardized residual with an
absolute value of 3 or greater are potential outliers and were removed from
the analysis.
X; X
z = --------
er
(3.1)
where: Z= It denotes the number of standard deviations a data value xÂ£ is
from the mean, x.
59
3.6 Methodology
The methodology used for the field validation task was based on relating
surrogate safety measures that SSAM derived from simulation models with
actual crash occurrence observed on the field at merging and diverging
locations. The field validation effort involve the analysis of 21 interchanges
(42 merging and 42 diverging) locations, modeled with the VISSIM simulation.
Gettman, Pu, Sayed, and Shelby (2008) provided five statistical field
validation tests for the analysis of intersections. These tests were modified
and used in this study for merging and diverging locations:
1. Field Validation Test 1: Merging and Diverging Section Ranking by Total
Incidents
2. Field Validation Test 2: Merging and Diverging Section Ranking by Specific
Incident Types
3. Field Validation Test 3: Crash and Conflict Prediction Regression Model
Paired Comparison
4. Field Validation Test 4: Crash and Conflict Prediction Regression Model
Comparative Analysis of Total Incidents
5. Field Validation Test 5: Crash and Conflict Prediction Regression Model
Comparative Analysis of Specific Incident Types
3.6.1 Field Validation Test 1: Merging and Diverging Location Ranking
by Total Incidents
In this field validation test the ranking of merging and diverging locations from
SSAM according to predicted total conflicts was compared to the same
60
locations using actual crash frequency. Three steps were performed in this
test:
3.6.1.1 Conflict Ranking
In this step, SSAM was used to predict the expected total number of conflicts
at each merging and diverging locations. Each location was simulated for five
replications, each lasting 3600 simulation seconds (1 hour). Thus, the sum of
all conflicts recorded over all five replications was divided by 5 to determine
the average hourly conflict frequency in terms of conflicts per hour. The
merging and diverging sections were then ranked based on their average
hourly conflict frequency in descending order.
3.6.1.2 Crash Ranking
Crash ranking in this step was performed in such a way that the average
yearly crash frequency for each merging and diverging locations was first
determined by dividing the total number of crashes over the observation
period by the number of years in the observation period. The 3 years
observation period were used for all study locations. Merging and diverging
locations were then ranked based on their average yearly crash frequency in
descending order.
61
3.6.1.3 Ranking Comparison
The ranking derived from SSAMs conflict prediction (section 3.6.1.1) was
compared to the rankings based on average yearly crash frequency (section
3.6.1.2). The Spearman rank correlation coefficient was used to determine
the level of agreement between the two rankings. The Spearman rank
correlation coefficient is often used as a nonparametric alternative to a
traditional coefficient of correlation and can be applied under general
conditions. The Spearman rank correlation coefficient (ps) is calculated as
shown in Equation 3.2. A score of 1.0 represents perfect correlation and a
score of 0 indicates no correlation. An advantage of using (ps) is that when
testing for correlation between two sets of data, it is not necessary to make
assumptions about the nature of the populations sampled.
n(n2 1)
(3.2)
Where:
di =the difference between two rankings for pair i.
n = the number of paired ranked.
For hypothesis test, the Spearman rank correlation coefficient,ps, was
compared with the critical value ,ps (critical)-
For n < 30, ps (critical) can be read from the critical values table.
62
For n > 30, use:
Z
Ps (critical) ~ i /,
VoT^T)
(3-3)
Where:
Z corresponds to the level of significance.
For example, if a = 0.05, then Z = 1.96.If the absolute value of the
test statistics ps exceeds the positive critical value, then reject H0: ps = 0 and
conclude that there is a correlation.
3.6.2 Field Validation Test 2: Merging and Diverging Location Ranking
by Specific Incident Types
Comparative ranking procedures for Rear-end, crossing and lane-changing
crash/conflict types were repeated in Field Validation Test 2 the same as
Field Validation Test 1. These three conflict types were classified and counted
by SSAM for each type. The average hourly conflict frequency for each
conflict type was computed as in Field Validation Test 1, and these results
were used to rank the merging and diverging sections for each conflict type.
To provide type-specific crash frequencies, all crash reports from CDOT
crash database were reviewed to determine whether it was a rear-end
incident, crossing incident, or lane-changing incident. If the classification
based on the crash type was not obvious, engineering judgment was applied
to determine the most representative type. Average yearly crash frequencies
was tabulated for each incident type, rank ordered, and compared using the
63
Spearmans rank correlation test, as in Field Validation Test 1. The results of
this step demonstrated the capability of SSAM to accurately identify and rank
merging and diverging sections .
3.6.3 Field Validation Test 3: Crash and Conflict Prediction
Regression Model Paired Comparison.
In this field validation test, the correlation between conflicts obtained from
SSAM and crashes were developed. Regression equations were established
to estimate the average yearly crash frequencies at merging and diverging
locations as a function of the average hourly conflict frequencies. The R2 ,
Pearson chi-square and scaled deviance goodness-of-fit testing were used to
determine the strength of the relationship between conflicts and crashes.
Regression equations to predict crashes based on volume were developed
and compared with the conflict-based crash prediction model to study the
relative capabilities of surrogate safety assessment. Generalized linear
modeling GLM technique (Hauer, 1997; Sayed and Rodriguez, 1999) were
used to calculate the expected crash frequency at each merging and
diverging location, using the GENMOD procedure in the SAS 9.3 statistical
software package.
64
3.6.4 Field Validation Test 4: Crash and Conflict Prediction Regression
Model Comparative Analysis of Total Incidents
This Field Validation Test consists of four steps and the details of the test are
as follows:
Step A: Conflict prediction models for merging and diverging locations were
developed using standard GLM procedures relating conflicts calculated by
SSAM as a function of hourly traffic volume.
Step B: Crash prediction models for merging and diverging locations were
developed using standard GLM procedures relating actual crash data
obtained from CDOT accident database as a function of daily traffic volume.
Step C: The two prediction models were compared to determine whether or
not the conflict prediction models can predict risk in a manner similar to the
crash prediction model for merging and diverging locations with the same
characteristics. The comparison consists of identification and ranking of
crash/conflict prone locations. A crash/conflict prone location is defined as
any location that exhibits a significantly higher number of crashes/conflicts as
compared to a specific normal value. The normal value was provided by the
volume-based crash/conflict prediction models. As stated previously, the
Empirical Bayes (EB) technique improves the location-specific prediction and
thus was used to identify hazardous locations. The EB refinement method
identifies problem sites according to the following four-step process:
1. Estimate the predicted number of crashes/conflicts and its variance
using the crash/conflict prediction model. This prediction can be
65
assumed to follow a gamma distribution (the prior distribution) with
parameters a and /?, where:
^ Var{ A) E{ A)
E{ A) k
and a = (3.E(A) = zc
(3-4)
Where:
Kar(A) = the variance of the predicted crashes/conflicts.
Â£(A) = predicted accident frequency
zc = shape parameter
2. Determine the appropriate point of comparison based on the mean and
variance values obtained in step 1. Usually the 50th percentile (P50) or the
mean is used as a point of comparison P50 is calculated such that Equation
3.5 is satisfied.
(3.5)
0
3. Calculate the EB safety estimate and the variance by rearranging
Equations 2.23 and 2.24 respectively as shown in Equation 3.6
and Equation 3.7.
66
EBsafety estimate ( K+E(A)) E (A) + (K+E(A)) (.COUTlt)
(3-6)
where:
count = observed accident frequency.
V or (EBsafe fy
estimate
g(A) \2 ( E{A)
k + E(A)/ W U + E(A)
(count)
(3.7)
This is also a gamma distribution (the posterior distribution) with parameters
ax and & defined as follows:
EB
/?i = -------
Var(EB)
K
~e{A)
+ 1 and at = ^.EB = /c + count
(3.8)
Then, the probability density function of the posterior distribution is given by
the following:
/eb W
G(A)
(K+count)
^jK+count-lg
E(k + count)
K
.Â£( A)
+11
(3.9)
4. Identify the location as crash/conflict-prone if there is significant
probability that the locations safety estimate exceeds the ^50 value (or
the mean).
67
The location is prone if:
p (w^+1)(K+C0Unt)^K+count~le (Â£(a)+1)a
rPsoUALJ------------------------------ dX
J0 r(jc+count)
> S
(3.10)
Where:
S is the desired confidence level (usually selected at 0.95).
The merging and diverging locations were then ranked in terms of priority for
treatment once crash/conflict-prone sites were identified. Ranking problem
sites enables the road authority to establish an effective road safety program,
ensuring the efficient use of the limited funding available for road safety. Two
techniques were suggested (Sayed and Rodriguez, 1999) that reflect different
priority objectives for a road authority. The first ranking criterion is to calculate
the ratio between the EB estimate and the predicted frequency as obtained
from the GLM model (a risk-minimization objective). The ratio represents the
level of deviation that the merge/diverge is away from a normal safety
performance value, with the higher ratio representing a more hazardous
location. The second criterion, the cost effectiveness objective, is a potential
for improvement (PFI) criterion, which is calculated as the difference
between the observed crash/conflict frequency and the volume-based
estimate of normal crash/conflict frequency.
Step D: Two comparisons were undertaken. The first compared the locations
identified as crash-prone to merging and diverging locations identified as
conflict-prone. The second compared both the risk ratio and PFI merging
68
and diverging location rankings obtained using crash data to the
corresponding rankings obtained using conflict data.
3.6.5 Field Validation Test 5: Crash and Conflict Prediction
Regression Model Comparative Analysis of Specific Type
Incidents
Field Validation Test 5 repeated the same comparative analysis as Field
Validation Test 4 for the rear end, crossing and lane change crash/conflict
types.
3.7 Goodness of Fit Measure
Three statistical measures were used to assess the goodness-of-fit of the
regression models to the actual crash data to the merging and diverging
locations.
The first measure was the Pearson chi-squared and computed by the
following model:
Where:
E(Ai) = the predicted crash frequency of merging or diverging location i
(3.11)
69
yt = the actual crash frequency of merging or diverging location i
n = the number of merging or diverging location
The second statistical measure used was the scaled deviance. This is the
likelihood ratio test statistic measuring twice the difference between the log-
likelihood of the data under the developed model and its log-likelihood under
the full or saturated model. The scaled deviance is computed by the following
model:
There are several approaches to estimate the shape parameter k of the
negative binomial distribution with the method of maximum likelihood being
the most widely used. The method of maximum likelihood will be used in this
analysis.
The third goodness-of-fit measure is the R-squared which was defined by
Miaou, 1996. It estimates the percentage of variation explained by a
regression model. The model is based explicitly on the overdispersion
parameter
The R-squared goodness-of-fit test was computed as:
n
(3.12)
a
(3.13)
70
Where:
a = the overdispersion parameter estimated in the model
amax = the overdispersion parameter estimated in the negative binomial
model, the model with only a constant term and an
overdispersion parameter.
71
4. Test Results and Discussion
This section presents the results of the field validation testing effort. The
experimental procedure, prior to statistical testing, is summarized as follows.
A set of twenty-one interchanges, selected from field sites in Colorado, North
America, and were modeled in VISSIM. Each merge/diverge model was
simulated for five replications for 1 hour of simulated time. The corresponding
five output files (i.e., TRJ files) from VISSIM were then imported into SSAM
for identification of conflicts and computation of the surrogate measures of
safety for each conflict event. SSAM was configured to use conflict
identification threshold values. The maximum time-to-collision (TTC) and
maximum post-encroachment time (PET) values used were 1.5 seconds and
5.0 seconds, respectively. The results of the SSAM analysis consists of the
number of total conflicts and the number of conflicts of each type of vehicle-
vehicle interaction: crossing, rear end, and lane changing. Before any
statistical inferences were applied, the outliers were identified and removed
from the dataset.
Figure 4.1 shows five files added to the case files section. These files were
obtained from a model simulated for five replications. Note that the files
selected have a .trj extension. The default maximum TTC and maximum PET
values were not changed. Also the threshold angles (30 and 85 ) which
were determined by experimentation were not changed.
72
El SSAM C:\Maricos\CU\RESEARCH COMPONENTS\raSSERTA'nON-INTERCHANGES\E5 Hampden Ave (routing test)\I25 & Hampden Ave--NB(RS-MultiiTO)l
File Window Help
[iaaosnifflSa
0] E Yale Ave 1-2 _*
0} 1225 & 6th Ave-i
QJI22S&E Alameda;
0] 1225&E Alameda:
0] 1225 &E Colfax A
6}I22S&E Colfax I,
Q]l22S8>EMESBSt
[|]I22S&EtAss>S9f
0]I2S&E Arapahoe
0] I2S & E Arapahoe!
0]I25&EBeleview!
0] 125 AEBefeviev/
0]I2S&E County Li,
0]I2S&E County U.
0JI2S&E Dry Creel
0] 125 &E Dry Creel:
0] 125 &E Evans (R.L
0]I25&EttffAve-:"
0]I2S&EHffAve-J
0]I2S&EUncoHA/
0] 125&E Lincoln Av
0] 125&E Lincoln A/
0] 125 &E Orchard /
0] 125 &E Orchard/
0] 125&E Yale Ave-I
01125 & Hampden A1
OHHMHIgHt
0] 125 & Hampden A:
0] 125 AS Colorado I
0] 125&S Colorado I
0] 125&S Parker Re;
0] 125&S Parker Rcj
0]I25&SYosemtel
0]I25&SYosemite
0] 125 & University I
0] 125 & University I
0]I25&ridgegateF
0]I25&rdgegateF
0] 125 & Hampden Ave*-N8(RS-Multirun) | o
Case Information
Case Pile: C:^arkosV^J^ESEARCH COMPONB^TS'piSSERTATION-INTCHANGESy25 Hampden Ave (routing test)\I25 &Hampden Ave-NB^S-Muftrun)
| Comments: [Yotr comments here.
Analyst: |Your name here.
Analysis Date: Fri Feb 0316:56:43 MST 2012
[ Edt Info ~j Apply Change
Case Hies
Trajectory Res: fcWarkosVOJVESEARCH COMPON&ITSÂ¥)ISSStTATION-INTERCHANGES\I2S Hampden Ave (routing test)y25 & Hampden Ave-NB (RS-Multirun).l.trj
____________ C;\Marko$VCU1iRESEARCH COMPONS^TStiISS0tTATION-INTSlCH^IGES\I25 Hampden Ave (routing test)\I25 & Hampden Ave-TC (RS-MJtinjn)_2.trj
| Add | CiV^arkosVCUVtESEARCH COMPONB
I-----------1 ClWarkosVCUVtESEARCH COMPON0n3PISSBLTATlON-INTERCHANGE5\I25 Hampden Ave (routing test)\!25 8. Hampden Ave-NB (RS+UlirunJjUrj
| Delete | C;ysarkosCUVtESEARCH COMPONENT5IDISSERTATION-INTERCHANGES\I25 Hampden Ave (routing test)\I25 & Hampden Ave-N8 (RS-Multinjn)_5.trj
Conflict Thresholds
Maximum time-to-colsion (TTC):
Maxrxrn post-encroachment time (PET):
Conflict angle Thresholds:
Rear end angle:
Crossing angle:
1.50-:-
5.00 -fcj
| Edit | | Apply | Analyze Q Check This to ouput frj files in Text Format
FIGURE 4.1. SCREEN CAPTURE. SSAM SCREENCONFIGURATION
TAB
SSAM contains a built-in feature to visualize conflicts. The conflicts can be
visualized within a Map tab or imported to SSAM as VISSIM .inp file.
Typically, the Map file is the graphic file of the simulated network for the case
document. The VISSIM .inp file is the VISSIM network file that has been
simulated and has generated the vehicle trajectory file that was used for
73
SSAM analysis. Figure 4.2 shows the display of conflicts in the Map view
section. The average hourly conflict counts for each merge/diverge locations
is provided in Appendix E.
f 0 SSAM C:\PemACIARESEARCH COMPONENTSDfS5ERTAT10N-tNTERCHANGES'\I25 Hampden Ave (routing test)\E5 & Hampden Ave~NB routing test
Â£4e fflindow Â£jetp
6] 122546th/
1225 46th/
122S 4 E 41;
1225 4 E At;
|]I22S4ECo
SI 1225 IE Co
1225 4 E Me
1225 4 E Mb
125 4 E A;*
0125 4EM
SI I254EBefc
1254EBe*
125 4 E Cry
I2S & E Evai
S]I254EEvai
I2S&E0fF
I25 4EIHf
125 4ELTO
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FIGURE 4.2 SCREEN CAPTURE. SSAM SCREEN MAP TAB VIEW AT
1-25 & E HAMPDEN AVE
74
4.1 Field Validation Test 1: Merging and Diverging Location Ranking
by Total Incidents
Validation Test 1 is a comparison of the ranking of merge/diverge locations
based on average hourly total conflict frequency versus the ranking of
merge/diverge locations based on average yearly total crash frequency. The
Spearman rank correlation coefficient (ps) values of ranking based on total
conflict comparison were 0.486 and 0.551 for merging and diverging
movements respectively, these values are significant at 95 percent level of
confidence.
As a basis of comparison, the merge/diverge locations were also ranked in
terms of total ADT values, and these were also compared with the ranking
based on average yearly total crash frequency. The Spearman rank
correlation coefficient (ps) values of this ranking comparison were 0.419
(significant at a 95 percent level of confidence) and 0.309 ( not significant at a
95 percent level of confidence) for merging and diverging movements
respectively, these values are shown in Table 4.2.
In general, the Spearman rank correlation tests showed that a higher
correlation was found for both merge and diverge movements with
merge/diverge locations rankings based on conflicts than ADT.
75
4.2 Field Validation Test 2: Merging and Diverging Location Ranking
by Specific Incident Types
Validation Test 2 repeats the same comparative ranking procedures as for
validation test 1 for the subsets of crash/conflict types: rear end and lane
changing. There were no crossing conflicts recorded to perform the ranking
comparison for crossing type incidents. Table 4.1 displays the distribution of
conflicts and crashes by incident type. There were 1 percent merging and 4
percent diverging lane changing conflicts were recorded, while the remaining
portion were rear end conflicts. However the proportion of crashes of the lane
changing and rear end maneuvers at merge and diverge, was 26 percent and
23 percent respectively.
There were significant differences between conflict distributions by type and
actual crash distributions by type. The ratios of conflicts-per-hour to crashes-
per-year for total incidents at merge and diverge were 117 and 137
respectively. The ratios of conflicts-per-hour to crashes-per-year for rear-end
and lane-change incidents at merge were 156 and 5 respectively. However
the ratios of conflicts-per-hour to crashes-per-year for rear-end and lane-
change incidents at diverge are 169 and 26 respectively. It seems plausible
that conflicts-to-crashes ratios are higher for less dangerous incidents. That
is, accepting that rear-ends are generally less severe than lane-change, there
is an abundance of these lower risk conflicts. In all the simulation scenarios,
rear-end conflict events made up the bulk of the total conflicts.
It was also observed that the total number of diverging conflicts were 42%
higher than that of the merging conflicts. Similarly, the total number of
diverging crashes are 22% higher than that of merging crashes This was
76
consistent with the study by Cillo (1967) and Lundy (1966) which showed that
the accident rates of off-ramps are higher than the accident rates of on-
ramps.
Figure 4.3 illustrates an example of a conflict, where some vehicles are
angling across lanes and have abruptly cut in front of other vehicles that must
decelerate to avoid collision.
%
i
%
FIGURE 4.3 SCREEN CAPTURE. VISSIM CONFLICT SCENARIO
RESULTING FROM LANE CHANGE MANEUVER
77
A higher proportion of rear-end conflict obtained from SSAM was consistent
with the study reported on crash prediction models on urban signalized
intersections. Guttman, Pu, Sayed, and Shelby (2008) modeled signalized
intersections in VISSIM and simulated under AM peak hour traffic conditions.
The conflict analysis was done using SSAM and found that the proportion of
crossing, rear-end, and lane-change conflicts were 1.7 percent, 91.0 percent,
and 7.3 percent respectively.
Moving on to the results of the ranking tests and looking into Table 4.2, there
is a significant correlation between conflicts and crashes when considered by
conflict type. The Spearman rank correlation coefficient (ps) value at merge
for rear end incident ranking comparison was 0.403, which is significant at a
95 percent level of confidence. Whereas, the Spearman rank correlation
coefficient (ps) value at diverge for rear end incident ranking comparison was
0.456, which is also significant at a 95 percent level of confidence. Moreover,
the Spearman rank correlation coefficient (ps) value at merge and diverge for
the lane changing incident ranking comparison were 0.540 (significant at a 95
percent level of confidence) and 0.550 (significant at a 95 percent level of
confidence) respectively.
For comparison, the merge/diverge locations were ranked on the basis of
total ADT values, and this was also compared with the rankings based on
rear-end and lane-change crashes. Rear-end ranking comparisons at merge
was not significant at 95 percent level of confidence. Moreover, the Spearman
rank correlation coefficient (ps) at diverge for rear-end incident ranking
comparison was not significant at a 95 percent level of confidence. However,
the Spearman rank correlation coefficient (ps) at both merge and diverge for
78
lane-changing ranking comparison were significant at a 95 percent level of
confidence.
In general, rank correlation testing showed a significant correlation between
rear-end conflicts and rear-end crashes and between lane-change conflicts
and lane-change crashes. Also, the rank correlation tests have shown that
stronger correlation was observed based on conflict than ADT.
Table 4.1 Distribution of crashes and conflicts by incident type
Incident Type
Merge Diverge
Rear Lane All Rear Lane All
End Change Type End Change Type
Average Hourly Conflicts 36,572 370 36,942 50,358 2,219 52,577
Percentage of Conflicts by Type 99% 1% 100% 96% 4% 100%
Average Yearly Crashes by Type 234 82 315 298 87 385
Percentage of Crashes by Type 74% 26% 100% 77% 23% 100%
Conflict-to-crash ratio 156 5 117 169 26 137
79
Table 4.2 Correlation coefficients by incident type
Incident Type
Ranking based on Merge Diverge
Rear Lane All Rear Lane All
End Change Type End Change Type
Crashes and Conflicts 0.403 0.540 0.486 0.456 0.550 0.551
Crashes and ADT 0.318 0.533 0.419 0.217 0.551 0.309
4.3 Field Validation Test 3: Crash and Conflict Prediction Regression
Model Paired Comparison
Validation Test 3 assessed the correlation between conflicts and crashes by
using regression to construct a conflicts-based model to predict crash
frequencies at merging and diverging locations. Additionally, the capabilities
of conflict-based crash-prediction were compared to a traditional volume-
based crash-prediction model.
A standard generalized linear modeling (GLM) approach was used to
establish a model of the expected crashes as a function of mainline, merging,
and diverging ADT. Crashes in these models are expressed in terms of
average yearly crash frequency, as a function of the model variables which
are the ADT volumes of the mainline, merging, and diverging (in vehicles per
80
day) or ADTma\n\\ne, ADTmerge, and ,4D7diVerge, respectively. The estimates of
parameters for these models are shown in Table 4.3 and Table 4.4. However,
conflicts are expressed in terms of average hourly conflicts (conflicts per
hour).
Table 4.3 and Table 4.4 show the estimates of the parameters of the total
crash model at merging and diverging locations respectively. Furthermore,
the table shows that both the Pearson chi-squared and the scaled deviance
values were not significant at the 90- percent confidence level, indicating a
good fit. Moreover, these models were compared using the R-squared
goodness-of-fit test (Miao, 1996), and the results conform to those of the
Pearson chi-squared and the scaled deviance. Moreover, graphs
corresponding to Model (1) and Model (2) were provided in Figure 4.4 and
Figure 4.5 respectively.
81
Table 4.3 Prediction model of total crashes as a function of mainline ADT
and merging ADT
Model (1) Total Crash/yr merge= 2.1 2E-04 X ADTmainline 1773 y ADT -209 a r\\-j i merge
Degree of R-Squared Scaled Pearson y2 x 0.1,30 Shape
Freedom R2 Deviance X2 Parameter
30 0.54 32.24 33.61 40.26 5.08
Variable Coefficient
Constant 2.12E-04
ADT mainline 0.773
ADT merge 0.209
Table 4.4 Prediction model of total crashes as a function of mainline ADT
and diverging ADT
Model (2)
Total Crash/yr diverge = 0.061 X ADT mainline X ADTdiverge
Degrees of R-Squared Scaled Pearson x20.i,3i Shape
Freedom R2 Deviance X2 Parameter
31 0.82 34.72 34.39 41.42 30.21
Variable
Constant
ADT mainline
ADT diverge
Coefficient
0.061
0.058
0.478
82
Total Crash per Year
Merging ADT
FIGURE 4.4 TOTAL CRASH AS A FUNCTION OF MAINLINE ADT
AND MERGING ADT
83
Mainline ADT