Evaluation of the City of Scottsdale Loop 101 photo enforcement demonstration program

              Evaluation of the City of Scottsdale Loop 101
Photo Enforcement Demonstration Program
Final Report AZ-684
Prepared by:
Simon Washington, Ph.D.
Kangwon Shin
Ida van Schalkwyk
Arizona State University
Department of Civil & Environmental Engineering
Tempe, AZ
November 2007
Prepared for:
Arizona Department of Transportation
206 South 17th Avenue
Phoenix, Arizona 85007
in cooperation with
U.S. Department of Transportation
Federal Highway Administration
The contents of the report reflect the views of the authors who are responsible for the
facts and the accuracy of the data presented herein. The contents do not necessarily
reflect the official views or policies of the Arizona Department of Transportation or the
Federal Highway Administration. This report does not constitute a standard, specification,
or regulation. Trade or manufacturers’ names which may appear herein are cited only
because they are considered essential to the objectives of the report. The U.S.
Government and the State of Arizona do not endorse products or manufacturers.
Technical Report Documentation Page
1. Report No.
AZ-07-684
2. Government Accession No.
3. Recipient’s Catalog No.
5. Report Date
November 2007
4. Title and Subtitle
Evaluation of the City of Scottsdale Loop 101 Photo Enforcement
Demonstration Program
6. Performing Organization Code
7. Authors
Dr. Simon Washington, Kangwon Shin, and Ida van Schalkwyk
8. Performing Organization Report No.
10. Work Unit No.
9. Performing Organization Name and Address
Arizona State University
Department of Civil & Environmental Engineering
Tempe, AZ 85287-5306
11. Contract or Grant No. T0749A0022
13.Type of Report & Period Covered
Final Report
12. Sponsoring Agency Name and Address
Arizona Department Of Transportation
206 S. 17th Avenue, Phoenix, Arizona 85007
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared in cooperation with the U.S. Department of Transportation, Federal Highway Administration
16. Abstract
Speeding is recognized as one of the most important factors causing traffic crashes. In 2005, 30% of all fatal
crashes were speeding-related (National Highway Traffic Safety Administration 2005). According to NHTSA,
the cost of speed-related crashes is estimated to be $40.4 billion per year (National Highway Traffic Safety
Administration 2005). Intelligent Transportation Systems (ITS) now exist to reduce speeding-related crashes by
enforcing speed limits with camera-based technologies. These enforcement technologies are generically called
“speed cameras” and have been effective on municipal streets and arterials in Arizona.
The City of Scottsdale began automated enforcement efforts in December of 1996. On October 25, 2005,
the Scottsdale City Council approved the nine-month speed enforcement camera demonstration program on a
7.8-mile stretch of the SR 101 segment within Scottsdale. The speed enforcement program (SEP) began on
January 22, 2006 and ended on October 23, 2006. The demonstration program on the SR 101 freeway segment
in Scottsdale is the first use of the fixed-site photo enforcement equipment on a freeway in Arizona and is
believed to be the first in the nation.
This study was conducted to estimate the impact of the SEP on traffic safety, speed, speeding behavior,
and daily travel time uncertainty. More specifically, the objectives were to estimate: the impact of the SEP on
speeding behavior; the changes in mean speed due to the SEP; the impact of the SEP on traffic safety in the
enforcement zone; the total travel time impacts; and the economic impacts of the safety effects.
17. Key Words
Photo enforcement, speeding, safety, red light running,
Empirical Bayes’, before-after study, travel time
savings, motor vehicle crashes
18. Distribution Statement
Document is available to the U.S.
public through the National
Technical Information Service,
Springfield, Virginia 22161
23. Registrant’s Seal
19. Security Classification
Unclassified
20. Security Classification
Unclassified
21. No. of Pages
154
22. Price
SI* (MODERN METRIC) CONVERSION FACTORS
APPROXIMATE CONVERSIONS TO SI UNITS APPROXIMATE CONVERSIONS FROM SI UNITS
Symbol When You Know Multiply By To Find Symbol Symbol When You Know Multiply By To Find Symbol
LENGTH LENGTH
in inches 25.4 millimeters mm mm millimeters 0.039 inches in
ft feet 0.305 meters m m meters 3.28 feet ft
yd yards 0.914 meters m m meters 1.09 yards yd
mi miles 1.61 kilometers km km kilometers 0.621 miles mi
AREA AREA
in2 square inches 645.2 square millimeters mm2 mm2 Square millimeters 0.0016 square inches in2
ft2 square feet 0.093 square meters m2 m2 Square meters 10.764 square feet ft2
yd2 square yards 0.836 square meters m2 m2 Square meters 1.195 square yards yd2
ac acres 0.405 hectares ha ha hectares 2.47 acres ac
mi2 square miles 2.59 square kilometers km2 km2 Square kilometers 0.386 square miles mi2
VOLUME VOLUME
fl oz fluid ounces 29.57 milliliters mL mL milliliters 0.034 fluid ounces fl oz
gal gallons 3.785 liters L L liters 0.264 gallons gal
ft3 cubic feet 0.028 cubic meters m3 m3 Cubic meters 35.315 cubic feet ft3
yd3 cubic yards 0.765 cubic meters m3 m3 Cubic meters 1.308 cubic yards yd3
NOTE: Volumes greater than 1000L shall be shown in m3.
MASS MASS
oz ounces 28.35 grams g g grams 0.035 ounces oz
lb pounds 0.454 kilograms kg kg kilograms 2.205 pounds lb
T short tons (2000lb) 0.907 megagrams
(or “metric ton”)
mg
(or “t”)
mg megagrams
(or “metric ton”)
1.102 short tons (2000lb) T
TEMPERATURE (exact) TEMPERATURE (exact)
ºF Fahrenheit
temperature
5(F-32)/9
or (F-32)/1.8
Celsius temperature ºC ºC Celsius temperature 1.8C + 32 Fahrenheit
temperature
ºF
ILLUMINATION ILLUMINATION
fc foot candles 10.76 lux lx lx lux 0.0929 foot-candles fc
fl foot-Lamberts 3.426 candela/m2 cd/m2 cd/m2 candela/m2 0.2919 foot-Lamberts fl
FORCE AND PRESSURE OR STRESS FORCE AND PRESSURE OR STRESS
lbf poundforce 4.45 newtons N N newtons 0.225 poundforce lbf
lbf/in2 poundforce per
square inch
6.89 kilopascals kPa kPa kilopascals 0.145 poundforce per
square inch
lbf/in2
SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380
Table of Contents
Executive Summary...........................................................................................................1
Chapter 1 Introduction....................................................................................................13
1.1 Background and Objectives ......................................................................................13
1.2 Description of the Demonstration Program ..............................................................14
Chapter 2 Literature Review ..........................................................................................17
2.1 Relationship between Speed and Safety ...................................................................17
2.2 Impact of Speed Enforcement Cameras....................................................................18
2.2.1 Speed Enforcement Cameras on Freeways.........................................................19
2.2.2 Speed Enforcement Cameras on non-Freeways .................................................21
2.3 Summary of Findings................................................................................................23
Chapter 3 Effects of the SEP on Speeding Behavior and Speed..................................25
3.1 Changes in the Detection Frequency ........................................................................25
3.1.1 Data Description .................................................................................................25
3.1.2 Effect of SEP on the Detection Frequency .........................................................32
3.2 Changes in the Mean Speed......................................................................................34
3.2.1 Data Description .................................................................................................34
3.2.2 The Speed-Flow Relationship and Level of Service...........................................35
3.2.3 Effect of the SEP on Mean Speeds .....................................................................41
Chapter 4 Effects of the SEP on Traffic Safety.............................................................45
4.1 Preliminaries: Target Crashes and Data Description ................................................45
4.1.1 Determining Target Crashes ...............................................................................45
4.1.2 Crash Data Description .......................................................................................47
4.2 The Four-Step Procedures for Before-and-After Study............................................49
4.3 Before-and-After Study with a Comparison Group..................................................53
4.3.1 Overview of the Before-and-After Study with a Comparison Group.................53
4.3.2 Estimating Comparison Ratios ...........................................................................56
4.3.3 Results of the Before-and-After Study with a Comparison Group.....................61
4.4 BA Study with Traffic Flow Correction ...................................................................63
4.4.1 Overview of the BA Study with Traffic Flow Correction ..................................63
4.4.2 Change in Traffic Flow in the Enforcement Zone ..............................................65
4.4.3 Developing Safety Performance Functions ........................................................67
4.4.4 Results of the Before-and-After Study with Traffic Flow Correction................74
4.5 Empirical Bayes’ Before-and-After Study................................................................76
4.5.1 Regression-to-the-Mean Phenomenon................................................................76
4.5.2 Overview of Empirical Bayes’ Before-and-After Study ....................................79
4.5.3 Results of the EB Before-and-After Study .........................................................88
4.6 Economic Analysis ...................................................................................................89
4.6.1 Arizona-specific Crash Costs..............................................................................90
4.6.2 Economic Benefits ..............................................................................................91
Chapter 5 Effect of SEP on Travel Times .....................................................................93
5.1 Background...............................................................................................................93
5.1.1 Motivation and Study Objectives........................................................................93
5.1.2 Past Studies .........................................................................................................94
5.2 Data Preparation........................................................................................................96
5.2.1 MAG Transportation Network and Travel Demand Data ..................................96
5.2.2 Multi-Class Sub-area Analysis ...........................................................................99
5.2.3 Additional Input Data .......................................................................................102
5.2.4 Model Validation ..............................................................................................107
5.2.5 Simulation Scenarios ........................................................................................115
5.3 Change in Travel Time Distribution .......................................................................117
5.3.1 Preliminary Analysis.........................................................................................117
5.3.2 Travel Time Variation by Simulation Scenario ................................................123
5.3.3 Daily Travel Time Uncertainty.........................................................................125
5.4 Change in Total Travel Time..................................................................................127
Chapter 6 Conceptual Plan for Long-Term Deployment of Automated Freeway
Speed Photo Enforcement in Arizona....................................................................131
Chapter 7 Conclusions and Recommendations...........................................................135
References......................................................................................................................138
List of Tables
Table 1: Crash benefits in $1,000/year from BA with traffic flow correction
and Empirical Bayes’ BA ..................................................................................7
Table 2: Summary of studies on freeways.........................................................................20
Table 3: Summary of outline of studies on non-freeways .................................................21
Table 4: Summary statistics for daily detection frequency by site and period ..................25
Table 5: Summary statistics for the daily detection frequency per camera
by day of week and period ...............................................................................27
Table 6: A list of holidays in 2006 and 2007.....................................................................27
Table 7: Summary statistics for the daily detection frequency during the 4 periods
by the 2 categories ...........................................................................................28
Table 8: Brown-Forsythe test results for the homogeneity of variance.............................32
Table 9: WLS estimates for the difference in daily speeding detection
frequency per camera.......................................................................................33
Table 10: Relative changes in daily speeding detection frequency per camera ................33
Table 11: Description of the 6 measurement sites for the before period ...........................34
Table 12: Summary of statistics for speed by site .............................................................35
Table 13: LOS criteria for basic freeway sections.............................................................39
Table 14: Summary statistics for the speed at stable condition during the before
and program period ..........................................................................................41
Table 15: WLS estimates for the impact of the SEP on speed (n=1934) ..........................41
Table 16: Estimated speed reduction (mph) due to the SEP..............................................43
Table 17: The four-step procedure for simple before-and-after study...............................52
Table 18: Key notations used in the before and after study with a comparison group......54
Table 19: The four-step procedure for the BA study with a comparison group ................55
Table 20: Estimates for the odds ratios and 95% CI for the estimates ..............................59
Table 21: Estimates of the comparison ratio......................................................................60
Table 22: Results of the BA study with a comparison group ............................................61
Table 23: The four-step procedure for the BA study with traffic flow correction ............64
Table 24: Change in AADT within the enforcement zone ................................................65
Table 25: Summary statistics for AADT in the enforcement and comparison zone .........66
Table 26: Summary statistics for variables in the full model [N=348] .............................72
Table 27: Estimated safety performance functions for BA studies [n=335] .....................73
Table 28: Results of the BA study with traffic flow correction.........................................74
Table 29: Summary statistics for mean crash frequency per mile by year ........................77
Table 30: The four-step procedure for the empirical Bayes’ BA study
(Time-constant κ).............................................................................................83
Table 31: The four-step procedure for the empirical Bayes’ BA study
(Time-varying κ)..............................................................................................87
Table 32: Results of the EB BA study ...............................................................................88
Table 33: Estimated Arizona-specific crash costs per crash..............................................90
Table 34: Changes in safety by severity ............................................................................91
Table 35: Summary of crash benefits per year ($1,000)................................................9298
Table 36: MAG volume-delay function coefficients
during non-peak period (when v/c<2) .............................................................98
Table 37: Description of the eight validation sites for the before period ........................103
Table 38: Summary statistics for speed by reference site (mph) .....................................103
Table 39: Summary statistics for traffic flow rate by reference site (veh/lane/hr) ..........104
Table 40: Summary statistics for the speed (mph)
during the before and program periods..........................................................104
Table 41: Summary statistics for incident duration (minutes).........................................106
Table 42: Simulation output and percent change in output for each feedback run..........109
Table 43: Paired t-test results for comparing simulated and observed data ....................111
Table 44: Speed comparison by feedback run (feedback 1–10) ......................................112
Table 45: Speed comparison by feedback run (feedback 11–20) ....................................112
Table 46: Speed comparison by feedback run (feedback 21–30) ....................................113
Table 47: Traffic flow rate comparison by feedback run (feedback 1–10) .....................113
Table 48: Traffic flow rate comparison by feedback run (feedback 11–20) ...................114
Table 49: Traffic flow rate comparison by feedback run (feedback 21–30) ...................114
Table 50: Summary Statistics for the Travel Time of the Selected Trips (minute).........118
Table 51: Results of the BF and KW Tests......................................................................119
Table 52: Change in travel time distribution by simulation state and direction ..............124
Table 53: Annual daily travel time unreliability (%).......................................................126
Table 54: Summary statistics for total travel time and the results of the BF test ............127
Table 55: GLS estimation results for difference in total travel time
with 95% CIs (veh-hours)..............................................................................128
Table 56: Total travel time savings (veh-hours/year) ......................................................129
List of Figures
Figure 1: Six photo enforcement sites on Loop 101 ............................................................2
Figure 2: Average daily detection frequency (vehicles ≥ 76 mph) by period .....................2
Figure 3: Observed mean speeds by flow rate by period.....................................................3
Figure 4: Estimated impact of SEP on crashes by crash type and crash severity: BA
method using comparison zone..........................................................................5
Figure 5: Estimated impact of SEP on crashes by crash type and crash severity: BA
method using correction for traffic flow............................................................6
Figure 6: Estimated impact of SEP on crashes by crash type and crash severity:
Empirical Bayes’ BA method. ...........................................................................7
Figure 7: Loop 101 sub-area simulated network for travel time impact analysis................8
Figure 8: Location of the speed enforcement zone............................................................15
Figure 9: Location of six enforcement sites.......................................................................16
Figure 10: Average daily detection frequency by period...................................................26
Figure 11: Average daily detection frequency by period and site .....................................26
Figure 12: Average daily detection frequency by periods and day of week......................28
Figure 13: Average daily detection frequency per camera during the four periods ..........29
Figure 14: Average daily detection frequency per camera
during the four periods (weekdays) .................................................................30
Figure 15: Average daily detection frequency per camera during the four periods
(weekends and holidays)..................................................................................31
Figure 16: Speed-flow curve .............................................................................................36
Figure 17: Speed-flow curves and LOS on a basic freeway segment ...............................38
Figure 18: Impact of the SEP on speed by period .............................................................42
Figure 19: Detection frequency by TOD ...........................................................................45
Figure 20: Detection rate by TOD .....................................................................................46
Figure 21: Number of crashes that occurred at the enforcement zone
during the before period...................................................................................47
Figure 22: Percentage of off-peak crashes by crash type (before period) .........................48
Figure 23: Percentage of peak-period crashes by crash type (before period)....................48
Figure 24: Basic concept of the before-and-after study.....................................................50
Figure 25: Basic concept of the before-and-after study with comparison group...............53
Figure 26: Enforcement zone and comparison group ........................................................56
Figure 27: Change in total target crashes by year (comparison group vs.
enforcement zone)............................................................................................58
Figure 28: Change in total PDO crashes by year (comparison group vs.
enforcement zone)............................................................................................58
Figure 29: Results of the BA study with a comparison group...........................................62
Figure 30: Change in AADT in the enforcement zone from the before (2001–2005)
to the program (2006) period (Mean AADT and associated 95% C.I.s) ........65
Figure 31: Change in AADT by year (comparison zone vs. enforcement zone)...............67
Figure 32: Results of the BA study with traffic flow correction .......................................75
Figure 33: Regression-to-the-mean phenomenon on Loop 101 from 2002 to 2003..........77
Figure 34: Regression-to-the-mean phenomenon on Loop 101 from 2005 to 2006..........78
Figure 35: EB before-and-after study results.....................................................................89
Figure 36: 2006 MAG Transportation Network ................................................................97
Figure 37: Trip length distribution of all non-peak trips ...................................................99
Figure 38: Multi-Class sub-area analysis procedure........................................................100
Figure 39: Selected sub-area............................................................................................101
Figure 40: Trip length distribution of non-peak trips within sub-area.............................101
Figure 41: Extracted Sub-area Network (75 TAZs) ........................................................102
Figure 42: Empirical CDF of mean speed during the before and program period ..........105
Figure 43: Enforcement zone and comparison section ....................................................106
Figure 44: Histogram of incident duration (minutes) ......................................................107
Figure 45: Percent change in simulation outputs by feedback run ..................................110
Figure 46: Comparison of observed and simulated speeds at eight reference sites.........111
Figure 47: Comparison of observed and simulated traffic flow
at eight reference sites....................................................................................111
Figure 48: Simulation scenarios.......................................................................................115
Figure 49: Effect reduction by distance ..........................................................................116
Figure 50: Change in travel time distribution (Base vs. SEP) .........................................120
Figure 51: Change in travel time distribution (Base vs. one-lane blockage)...................121
Figure 52: Change in travel time distribution (Base vs. two-lane blockage)...................122
List of Acronyms
AADT Annual Average Daily Traffic
ADOT Arizona Department of Transportation
AZDPS Arizona Department of Public Safety
BA Before-and-After
BF Brown-Forsythe
CBD Central Business District
CDF Cumulative Distribution Function
CI Confidence Interval
DPS Department of Public Safety
EB Empirical Bayes’
FARS Fatality Analysis Reporting System
FF Free Flow
FHWA Federal Highway Administration
FMS Freeway Management System
GIS Geographic Information Systems
GLS Generalized Least Square
HOV High Occupancy Vehicle
HCM Highway Capacity Manual
ITS Intelligent Transportation Systems
KW Kruskal-Wallis
LOS Level of Service
MAG Maricopa Association of Governments
MP Milepost
MVD Motor Vehicle Division
NBRM Negative Binomial Regression Model
NHTSA National Highway Traffic Safety Administration
NR Non-Recurrent Congestion
OD Origin-Destination
PCE Passenger Car Equivalent
PDO Property Damage Only
RTM Regression to the Mean
SEP Speed Enforcement Camera Demonstration Program
TLD Trip Length Distribution
TTS Total Time Savings
TRB Transportation Review Board
VHT Vehicle Hours Traveled
VMT Vehicle Miles Traveled
VPD Vehicles Per Day
WLS Weighted Least Square
1
Executive Summary
This executive summary presents brief results of a comprehensive analysis of the fixed
speed-enforcement camera demonstration program (SEP) that was implemented on
Arizona State Route 101 (Loop 101) from January 2006 through October 2006. The
results reflected in this report are updated and are based on more complete crash and
speed data obtained since the Draft Summary Report was released in January of 2007.
Specifically, additional speed detection data are used, and all crash data from 2006 on the
Loop 101 are used (allowing for a larger comparison site and increasing the sample size
of crashes during the program period). The analysis is focused on estimating the impact
of the SEP regarding:
• Citable speeding behavior (i.e., speeds > 75 mph);
• Average speeds;
• Traffic safety (motor vehicle crashes) within the enforcement zone;
• Total travel time;
• Expected economic factors.
This evaluation, sponsored by the City of Scottsdale, utilizes data from the Arizona
Department of Public Safety (crash reports), Arizona Department of Transportation
(motor vehicle crashes, traffic volumes, traffic speeds), the City of Scottsdale (traffic
volumes and speeds), RedFlex (detections, traffic speeds), the Arizona Crash Outcome
Data Evaluation System (crashes and crash costs), the Maricopa Association Government
(transportation planning data), and the National Highway Safety Administration (crash
costs).
Five time periods are referenced in the analysis.
• Before (2001 – 2005: various period)
• Warning (01/22/06 – 02/21/06)
• Program (02/22/06 – 10/23/06)
• After (10/24/06 – 12/03/06)
• Reactivation (02/22/07 – 06/29/07)
The Scottsdale 101 automated enforcement program consists of six speed detection
stations within a 6.5 mile segment of Loop 101 within the city limits of Scottsdale,
Arizona (see Figure 1). Three cameras are positioned to enforce speeds in each direction
of travel (clockwise and counter-clockwise) on the Scottsdale portion of the Loop 101
freeway. The speed limit on this stretch of the Loop 101 freeway is 65 mph, and the
enforcement equipment is set to photograph and cite drivers when they are traveling
76 mph or faster.
2
Effect on Speeding Detections
The average number of daily speeding detections per camera (speeds ≥ 76 mph) was
162.2 during the warning period, 129.7 during the program period, 1482.4 during the
after period, and 134.68 during the reactivation period, as shown in Figure 2.
Frequencies were higher on weekends than on weekdays. The average detection
frequency for weekdays significantly increased by about 1047% (1006% for weekends
and holidays) from the program to after period.
Figure 1: Six photo enforcement sites on Loop 101
Figure 2: Average daily detection frequency (vehicles ≥ 76 mph) by period
3
Effect on Mean Speeds
The analysis results reveal that mean traffic speeds were reduced by about 9 mph,
indicating that the SEP was an effective deterrent to speeding (see Figure 3). The impact
of the SEP on speed increases as traffic flow decreases due to the well-known
relationship between speed and traffic flow. Reduced speeds lead to decreases in speed
variation, reduced crash impact speeds, and reduced demands on vehicular control
systems (braking, steering, and suspension).
Because peak-hour traffic speeds are constrained by congestion, it is highly unlikely that
speeds in excess of 76-mph are possible during peak-periods. As a result, it is assumed
that the SEP will only affect unconstrained period travel speeds (and associated crashes).
Figure 3: Observed mean speeds by flow rate by period.
Impact on Traffic Safety
The safety effects of the SEP are estimated by comparing the observed number of crashes
during the SEP to the expected number of crashes had the SEP not been implemented.
Thus, the analysis results hinge upon the ability to predict what crash counts would have
been—a state that is unobserved. In the analyses described herein, three general and
substantively independent procedures were applied to predict crashes in the after period
in the absence of the SEP. By applying three different procedures the results are
compared and contrasted, with the intent to check for consistency among the analysis
results.
Only crashes that occurred during the non-peak periods are analyzed because of the
uncertain and questionable expected influence of the SEP on slow moving, peak-period
4
traffic. Crash types affected by the SEP are categorized into four categories: single-vehicle,
side-swipe (same direction), rear-end crashes, and other. These crashes constitute
about 54%, 17%, 17%, and 12% of all crashes respectively.
The safety analysis consists of three different evaluation methodologies: a before-and-after
(BA) analysis with a comparison group (the comparison site is used to estimate
changes in safety from the before to after periods), a BA analysis with a traffic flow
correction (crashes are assumed to be proportional to traffic volumes), and a state-of-the-practice
empirical Bayes’ BA analysis that corrects for traffic volumes, time trends, and
regression-to-the-mean. The details of the three analysis methods and their varying
assumptions are provided in detail in the body of the report. To avoid confusion, it is
important to note that a “Before-After (BA)” analysis is conventional terminology used in
the professional literature; however, in the context of the analysis periods described
previously, the BA analysis in this study actually refers to a comparison of the before
period to the program period (the program period corresponds with the period after the
countermeasure was installed, the convention used in the professional literature).
BA Study with a Comparison Group
The comparison zone consists of 48 miles outside of the SEP enforcement zone on Loop
101. This comparison zone was chosen because its past crash trends are statistically
similar to those within the enforcement zone. Using the BA study with the comparison
zone to account for crash trends on Loop 101, the estimated change in crashes resulting
from the SEP ranges from an increase of 14% (rear-end injury crashes) to a reduction of
64% (single-vehicle property damage only crashes), as shown in Figure 4. The results
reflect the assumption that the prediction is modified using only trend effects (i.e.,
comparison ratios) in the comparison zone. Although the comparison zone resembles the
enforcement zone as a whole, some zone-specific effects—if present—are not captured in
the comparison zone.
5
Figure 4: Estimated impact of SEP on crashes by crash type and crash severity:
BA method using comparison zone.
BA Study with Traffic Flow Correction
The increase in traffic volumes in the enforcement zone from the before to program
periods was not only significant (42% increase on average) but also separate from the
observed time trend safety effects (i.e., safety changed beyond that explained by traffic
volume increases alone). This analysis procedure accounted simultaneously for the
change in traffic flow in the enforcement zone and the time trend safety effects. Ignoring
the significant traffic flow increase from the before to program periods would
significantly underestimate the effectiveness of the SEP, and underscores the importance
of this analysis approach. Using the BA study with traffic flow correction, the estimated
change in crashes resulting from the SEP ranges from a reduction of 18% (rear-end injury
crashes) to a reduction of 67% (single-vehicle, property damage only crashes). All types
of crashes were reduced, but the decrease in the rear-end injury crashes (18%) is not
statistically significant (p-value=0.377).
6
Figure 5: Estimated impact of SEP on crashes by crash type and crash severity:
BA method using correction for traffic flow.
Empirical Bayes’ BA Study
The Empirical Bayes’ (EB) BA analysis accounts for the change in traffic flow over time,
time trends (not captured by traffic flow), and regression to the mean effects. This
analysis approach reflects the current state of the practice for estimating the safety effects
of the SEP. The advantage of the EB BA approach stems from the fact that
countermeasures are often applied at locations with perceived safety problems, and thus
the expected number of crashes in a subsequent observation period regresses toward the
mean. Specifically, a location with a higher than expected crash count in a before period
should reveal a reduction in crash counts in the after period (statistically speaking). This
expected reduction must be taken into account when correctly evaluating the
effectiveness of the countermeasure. This undesirable statistical effect is diminished by
applying the EB BA study.
Applying the EB BA approach yields an estimated reduction in crashes ranging from
23% (rear-end injury crashes) to 67% (single-vehicle, property damage only (PDO)
crashes), as shown in Figure 6. The results from the EB BA study reveal slightly greater
effects than those obtained from the BA study with traffic flow correction, indicating that
the enforcement zone was in fact slightly ‘safer’ than average compared to similar
sections of Loop 101. This finding is important, and suggests that: 1) an increase in
crashes is predicted (in the absence of the SEP) in the after period; and 2) since the SEP
section was safer than similar 101 sections during the before period, applying the SEP to
7
a freeway section that is ‘worse than average’ with respect to safety may reveal greater
safety benefits than observed in this study.
Figure 6: Estimated impact of SEP on crashes by crash type and crash severity:
Empirical Bayes’ BA method.
Economic Benefits
To estimate the economic impact of the safety effects of the SEP, the results from both
the BA study with traffic flow correction and the EB BA study (the two extremes) are
used with Arizona-specific crash cost estimates. Annual estimated benefits of the SEP
program range from $16.5 million (BA study with traffic flow correction) to $17.1
million (EB BA study). These benefits include medical costs, other costs (lost
productivity, wages, long-term care, etc.), and quality of life costs. The overall benefits
appear to be similar in magnitude across categories.
Analysis method and crash severity Fatal
crashes
Disabling
injury
Evident
injury
Possible
injury
Property
damage Total
BA study with traffic flow correction $4,902 -$358 $3,234 $521 $8,204 $16,503
Empirical Bayes’ BA study $5,036 -$364 $3,379 $669 $8,328 $17,048
Table 1: Crash benefits in $1,000/year from BA with traffic flow correction and Empirical Bayes’ BA
8
Impact on Travel Time
The SEP slows drivers down (increases travel times) but reduces incidents (reduces travel
times via non-recurrent congestion effects). The impact of the SEP on travel times and
travel time uncertainty was evaluated by simulating network traffic conditions with and
without the SEP. A microscopic traffic simulation tool, which models the acceleration and
speed choice behavior of individual vehicles in detail, was calibrated for the Loop 101
section and used to capture the effects under numerous traffic conditions (see Figure 7).
Figure 7: Loop 101 sub-area simulated network for travel time impact analysis
The selected sub-area used in the simulation model encompasses the 13-mile stretch on
the Loop 101 segment including the enforcement zone as well as adjacent arterials that
are used as alternative routes for the Loop 101 in Scottsdale. The average results from a
total of 180 simulation runs suggest that total travel time savings from the SEP is statis-tically
significant, with an estimated average of 1,336 vehicle-hours/year saved assuming
one-lane blockage crashes and an average of 45,060 vehicle-hours/year assuming two-
9
lane blockage crashes. Mean estimates (using EB BA study results) of the value of travel
time savings as a result of the SEP range from a low of $20,040 to a high of $26,720 for a
one-lane blockage crash. For a two-lane blockage crash, mean estimates of the value of
travel time savings range from $675,900 to $901,200 per year. The complete details of
the simulation, assumptions, and results are described in detail in the body of the report.
Conclusions and Recommendations
The following conclusions were drawn from a variety of detailed statistical analyses, site
visits, logical reasoning, and simulation analyses:
Impact of the SEP on Speeding Behavior and Speed
1. Speeding detection frequency (speeds ≥ 76 mph) increased by a factor of 10.5
times after the SEP was temporarily terminated. During this termination the
cameras were “bagged” and advertising and news media advertised the end of the
program. The SEP seems to be an effective deterrent to speeding within the
enforcement zone, since removing the deterrent resulted in increased speeding.
2. The detection frequency for the reactivation period in 2007 is not statistically
different than that for the program period in 2006, indicating that the activation of
the SEP contributed to reducing drivers’ speeding behavior. The SEP seems to be
an effective deterrent to speeding within the enforcement zone, since reactivating
the potential deterrent resulted in decreased speeding.
3. The SEP reduced the average speed at the enforcement camera sites by about 9
mph and also contributed to reducing the speed dispersion at the enforcement
camera sites. In agreement with a substantial body of prior national and
international research, reduced speeds and speed dispersion improve safety.
4. The reduction in the mean and variance of speed resulting from the SEP depends
on traffic flow: the reductions increased as traffic flow decreased due to the well-known
relationship between speed and traffic flow. Thus, the magnitude of speed
effects of the SEP is inversely related to traffic flow.
Impact of the SEP on Safety
1. As a result of the SEP, the total number of target crashes decreased by 44% to
54%, depending on the analysis. In addition, the total number of injury crashes
decreased by 28% to 48%, while the total number of PDO crashes decreased by
46% to 56%. The state-of-the-practice analysis method resulted in the highest
estimates of reductions. The SEP appears to be effective in improving the overall
crash risk within the selected area.
10
2. All but rear-end crashes types appear to have been reduced. Although the changes
in safety for rear-end crashes were inconsistent among evaluation methods (and
their assumptions), the decrease in rear-end crashes was not statistically
significant. Moreover, the state-of-the-practice analysis method revealed a non-statistically
significant decrease in rear-end crashes. It is concluded that the effect
of the SEP on rear-end crashes is uncertain, and slight increases or decrease are
possible depending on site-specific conditions.
3. Swapping of crash types is common for safety countermeasures—many
countermeasures exhibit the ‘crash swapping’ phenomenon observed in this study
(left-turn channelization, red-light cameras, conversion of stop signs to signals,
etc.) Thus, it is quite expected to see varying magnitudes of reductions across
crash categories, and even some increases are possible.
4. The total estimated SEP benefits (looking at the costs of crashes only) range from
an estimated $16.5 million to $17.1 million per year, depending on the analysis
type and associated assumptions. This estimate does not reflect a cost-benefit
analysis, merely an estimate of the annual safety benefit of the program.
5. This study revealed that the SEP, in terms of safety impacts, is a promising
countermeasure to reduce crashes in Arizona. This finding is consistent with
findings in other countries and reported in the professional literature.
Impact of the SEP on Travel Time
1. The SEP shifted the distribution of the travel time by significantly reducing the
number of speeding drivers (by at least a 67.5% decrease in the proportion of the
number of faster drivers), while travel time reliability remains the same regardless
of the existence of the SEP.
2. The significant change in the travel time distribution by the reduction in speeding
vehicles was a primary factor in reducing the speed variance and mean speeds. As
is known from prior research and from physics principles, reduced speeds and
speed variance generally translates to improved safety.
3. There is not a statistically significant difference in the total free-flow travel time
with and without the SEP, suggesting that drivers travel in the enforcement zone
in the same amount of travel time regardless of the existence of the SEP. If a
larger enforcement zone was used, the difference in free-flow travel time may
become significant.
4. The insignificant difference in total free-flow travel time with and without the
SEP conditions led to total travel time savings, which resulted from the reduction
in crash frequency. The reduction is estimated to be at least (95% lower bound)
11
569 vehicle-hours/year assuming a one-lane block crash state (as a result of a
crash) and at least (95% lower bound) 37,981 vehicle-hours/year assuming the
two-lane block crash.
5. Speed enforcement on the Scottsdale section of Loop 101 not only improved
safety but also improved mobility through travel time savings, improved travel
time reliability, and reduced travel time uncertainty. The annual benefit of travel
time savings ranges from a low of $20,040 (one-lane-blockage crash assuming
$15/hr value of travel time savings) to a high of $901,200 (two-lane-blockage
crash assuming $20.00/hr of travel time savings).
Recommendations
The following actions are recommended to maximize the impacts of speed enforcement
cameras and to improve the results of this study. These recommendations should be
considered in the implementation and/or consideration of an expanded SEP in Arizona.
Although the SEP is not a panacea for reducing speeding-related crashes and other non-speeding
offenses within the enforcement zone, the SEP may be a promising
countermeasure given the following considerations:
1. An “ideal” site for SEP will reveal relatively high rates of speed and
corresponding severity of crashes prior to implementation. The crash history of a
site should be used to aid in selection, and sites that reveal a ‘worse than average’
safety record should be identified as candidate sites. A statistical model that
predicts the expected safety performance of sites should be developed to help
identify candidate sites, and predictors should include exposure and some
important geometric features.
2. Design of SEP sites should consider the element of surprise to drivers and should
aim to minimize it. For example, the placement of cameras in close proximity to
high information load locations (e.g., on- and off-ramps, under-passes, billboards,
weaving sections, directional signs, etc.) should be avoided. Placement of cameras
in sight restricted locations should be avoided. Efforts should be made to increase
driver expectation of speed enforcement camera locations.
3. Photo enforcement technology that measures average speeds (instead of
instantaneous speeds) over a long section of freeway (e.g., five miles) may offer
some operational advantages over the currently used technology, including
reduced sudden braking (and subsequent rear-end accidents).
4. Spillover effects are more likely in a dispersed system of enforcement zones
compared to a concentrated location.
12
5. Further evaluation (of future programs) is needed to enable the continued
knowledge and improvement of safety performance of SEPs.
6. In future evaluations, additional speed data may enable the assessment of
spillover effects. Currently, the extent and magnitude of spillover effects of the
SEP are uncertain.
13
Chapter 1 Introduction
1.1 Background and Objectives
Speeding is recognized as one of the most important factors causing traffic crashes. In
2005, 30% of all fatal crashes were speeding-related (National Highway Traffic
Safety Administration 2005). According to the National Highway Traffic Safety
Administration (NHTSA), the cost of speeding-related crashes is estimated to be $40.4
billion per year (National Highway Traffic Safety Administration 2005). Intelligent
Transportation Systems (ITS) now exist to reduce speeding-related crashes by enforcing
speed limits with camera-based technologies. These enforcement technologies are
generically called “speed cameras” and have been effective on municipal streets and
arterials in Arizona (Roberts and Brown-Esplain 2005).
The City of Scottsdale began automated enforcement efforts in December of 1996.
Between 1996 and 1998, four wet-film mobile speed units and six wet-film red-light
cameras were deployed for a total of nine intersections on enforcement rotation,
depending on the needs of the city. The cameras on city streets have helped Scottsdale
improve safety (Washington and Shin 2005). Scottsdale expanded these efforts in August
of 2004 with a dual-direction fixed-speed enforcement system at 7700 Frank Lloyd
Wright Blvd. This system covers three lanes of traffic eastbound and three lanes of traffic
westbound on Frank Lloyd Wright Boulevard. The city’s recent experience on Frank
Lloyd Wright Boulevard is that speed violations significantly decreased in a one-year
period after installation of cameras.
With these experiences, the City Council on October 25, 2005, approved the nine-month
speed enforcement camera demonstration program (hereafter SEP) on a 7.8-mile stretch
of the Loop 101 segment within Scottsdale. The SEP began on January 22, 2006, and
ended on October 23, 2006. The demonstration program on the Loop 101 freeway
segment in Scottsdale is the first use of the fixed-site photo-enforcement equipment on a
freeway in Arizona and is believed to be the first in the nation.
Accurately estimating the impacts of the traffic safety countermeasures such as the speed-enforcement
cameras is challenging for several reasons. First, many safety-related factors
such as traffic volume, the crash-reporting threshold (legal requirement to report a crash),
the probability of reporting, and the driving population are uncontrolled during the
periods of observation. Second, ‘spillover’ effects can make the selection of comparison
sites difficult. Third, the sites selected for the treatment may not be selected randomly,
14
and as a result may suffer from the regression-to-the-mean effect. Fourth, a speed-enforcement
program may influence specific types of crashes—called target crashes—
which often may be difficult to define and identify. Fifth, crash severity needs to be
considered to fully understand the safety impact of the treatment. Finally, the cause-and-effect
relationship should be investigated before evaluating the impact of the traffic safety
countermeasure because traffic safety is often indirectly influenced by the treatment.
With these challenges in mind, this study was conducted to estimate the impact of the
SEP on traffic safety, speed, speeding behavior, and daily travel time uncertainty. More
specifically, the objective of the research was to:
• Estimate the impact of the SEP on speeding behavior, which is represented as the
detection frequency;
• Estimate the changes in mean speed due to the SEP;
• Estimate the impact of the SEP on traffic safety in the enforcement zone;
• Estimate total travel time savings as a potential byproduct of the SEP;
• Translate the impacts on crashes into estimated economic costs and/or benefits.
1.2 Description of the Demonstration Program
The photo radar technologies have been used in 75 countries throughout the world to
enforce speed. Until 2006, the United States had not seen an application of photo
enforcement on limited-access freeways. In order to reduce speed-related crashes, the
City of Scottsdale in Arizona implemented the first fixed-photo speed-enforcement
camera demonstration program on a freeway in the United States. The nine-month
demonstration program spanning the period January 2006 to October 2006 was
implemented on a 6.5-mile urban freeway segment of Loop 101 running through
Scottsdale, Arizona.
15
Figure 8: Location of the speed enforcement zone
The speed enforcement zone is located on the northeast side of the Phoenix metropolitan
area as shown in Figure 8. The cameras within the enforcement zone are at six fixed
locations (in contrast to mobile photo enforcement vans) along the Loop 101 freeway
from the Shea Boulevard exit to the Scottsdale Road exit as shown in Figure 9.
Three cameras were positioned to enforce speed for each direction of travel. The speed
limit on this stretch of the Loop 101 freeway is 65 mph, and the enforcement equipment
is set to photograph drivers when they are traveling at 76 mph or faster. Vehicle speed is
determined by measuring the time it takes a vehicle to travel from the first sensor to the
last sensor on the detection zone installed at each enforcement site. The enforcement
system uses the known distance between the sensors and the measured time to calculate
speed. Of course time is measured precisely in order to estimate speeds precisely.
16
Figure 9: Location of six enforcement sites
As discussed, the SEP began on January 22, 2006, and ended on October 23, 2006. For
the first 30 days of the program, the city sent warning notices to drivers who exceeded
the 76-mph threshold. The cameras were operated for a total of 275 days:
• Warning period: 1/22/2006 – 2/21/2006 (31 days)
• Program period: 2/22/2006 –10/23/2006 (244 days)
After the SEP ended in October, the City of Scottsdale continued to collect speed and
traffic flow data at the stations. The cameras were reactivated on February 22, 2007, at
the request of Governor Janet Napolitano, and Scottsdale has been operating the cameras
since that date.
17
Chapter 2 Literature Review
In this chapter, numerous studies that analyzed the relationship between speed and safety
as well as the effect of speed-enforcement cameras are summarized, and the lessons and
issues raised by literature that could affect study consideration are discussed. As of 2005,
at least 75 countries rely on such cameras to enforce speed limits, especially on high-risk
roads, including Australia, Austria, Canada, Germany, Greece, Italy, the Netherlands,
Norway, Singapore, South Africa, South Korea, Spain, Switzerland, and Taiwan.
Although speed enforcement cameras have frequently been used in the United States,
their use has been limited (i.e., not at fixed-site) compared to other countries. Cameras
currently are being used in several states, including Arizona, California, Colorado, North
Carolina, Ohio, Oregon, and the District of Columbia (Roberts and Brown-Esplain 2005).
Out of numerous studies conducted in these countries and the nation, all possible studies
of relevance were initially identified on the basis of internet journal database searches.
Then, a number of “critical studies,”—appropriate in terms of methodological rigor and
frequently cited by other researchers or in discussions of speed enforcement effectiveness,
are examined. Extracted from the critical studies is general information on the effects of
speed enforcement cameras and issues that need to be considered in this study.
2.1 Relationship between Speed and Safety
Numerous studies have been conducted to elucidate the relationship between speed and
safety: a detailed review of which is provided in elsewhere (Kweon and Kockelman
2005; Lave and Lave 1998; Skszek 2004; Stuster et al. 1998). In the 1960s, many studies
found that the variance of speed is one of the most important factors affecting safety,
suggesting a U–shaped relationship between crash rate and variance in speed. The
relationship illustrates that the more the speed of driver deviates from the mean speed of
traffic, the greater the likelihood of a crash (Solomon 1964).
In 1985, Lave revitalized the U–shaped relationship by estimating regression models to
test the relationship between the fatality rate, average speed, and the difference between
the 85th percentile and average speed (as a proxy for speed variance) with cross-sectional
data from 1981 and 1982. Lave concluded that there was no statistical evidence
indicating that average speed affects the fatality rate. Consequently, Lave suggested that
the focus of speed laws should be changed so that they coordinate speed rather than limit
it. Other studies also agreed that crash rates increase with increasing speed variance, but
not with average speed (Garber and Ehrhart 2000; Garber and Gadiraju 1989).
18
Snyder (1989) re-estimated Lave’s model using a fixed effect linear model with two
measures for speed variability: the difference between the 85th percentile and median
speed (for faster drivers) and the difference between the 15th percentile and median
speed (for slower drivers). He concluded that both average speed and speed dispersion
are important factors in highway fatalities, but the speed dispersion for faster drivers is
only significant in explaining fatality rate. Levy and Asch (1989) also concluded that lack
of coordination implies greater risk, but average speed also contributes to increasing the
fatality risk depending on speed variance. The authors suggested that enforcement efforts
would be better directed toward slowing down high speed drivers rather than speeding up
low speed drivers. In addition, it is evident that a driver’s speed is one of the most
important factors affecting crash severity, owing to the relationship between vehicle
velocity and kinetic energy (Joksch 1993; Kloeden et al. 2001; Moore et al. 1995;
Solomon 1964). In summary, the results of previous studies that analyzed the relationship
between speed and safety show that traffic safety can be improved by reducing the
average speed and speed dispersion.
2.2 Impact of Speed Enforcement Cameras
The studies summarized in the previous section imply that speed enforcement—through
reduction of high speeds and resulting speed variance—is a promising countermeasure
for reducing crash frequency and severity. The results of numerous studies that evaluated
the effect of speed enforcement programs on safety and speed have confirmed the
validity of the paradigms discussed above (Champness and Folkman 2005; Chen et al.
2002; Cunningham et al. 2005; Elvik 1997; Goldenbeld and van Schagen 2005; Ha et al.
2003; Hauer et al. 1982; Hess 2004; Hess and Polak 2003; Lamm and Kloeckner 1984;
Retting and Farmer 2003; Sisiopiku and Patel 1999; Vaa 1997).
The studies in general show that speed enforcement programs lead to a significant
reduction in speed and crash frequency. Several studies solely evaluated the effect of
speed enforcement on speed (Champness and Folkman 2005; Hauer et al. 1982; Retting
and Farmer 2003; Sisiopiku and Patel 1999; Vaa 1997) or on traffic safety (Elvik 1997;
Hess 2004), while others evaluated both speed and safety (Chen et al. 2002; Cunningham
et al. 2005; Goldenbeld and van Schagen 2005; Ha et al. 2003; Hess and Polak 2003;
Lamm and Kloeckner 1984). Two studies (Ha et al. 2003; Lamm and Kloeckner 1984)
have an enforcement condition similar to that of Scottsdale (i.e., fixed cameras on
freeway), but differed with respect to traffic conditions, road users (skills and ‘safety
culture’), geometric design standards, and weather compared to the Loop 101 in
Scottsdale. Although all studies suggest that photo enforcement cameras are effective in
19
reducing speed and crash frequency at photo enforcement camera deployment sites, the
estimates of the impact of speed cameras on safety varied considerably.
Elvik and Vaa (2004) conducted a meta analysis that combined the effects of automated
enforcement on safety reported in Australia, England, Germany, the Netherlands, Norway,
Sweden, and the United States (Elvik and Vaa 2004). The results yield a 19% reduction in
total crash frequency and a 17% reduction in injury crash frequency. The reduction in total
crash frequency was greater in urban areas (28%) than in rural areas (4%). A recent meta
analysis also combined the effect of speed enforcement cameras on safety using the
evaluation results from 14 observational studies, which were selected from 92 studies
(Pilkington and Kinra 2005). The results show that the effects varied across studies:
reductions from 5% to 69% in crash frequencies, 12% to 65% in injuries, and 17% to 71%
in fatalities. In the following subsections, the results of each study are summarized in detail.
2.2.1 Speed Enforcement Cameras on Freeways
Several studies have evaluated the impacts of speed enforcement cameras on speed and
safety on freeways. Lamm and Kloeckner (1984) assessed the effects of fixed automated
cameras at the Autobahn in Germany. In addition to a reduction of about 12.4 mph in
speed, the accident frequency decreases from 200 accidents/year to 84 accidents/year,
and the number of fatal and injury accidents is reduced from 80 accidents/year to 30
accidents/year.
Chen et al. (2002) evaluated the effects of mobile cameras on Highway 17 in British
Columbia in Canada. By using the simple before and after study, they reveal that the
mean speed at the deployment locations is reduced to below the posted speed limit.
Overall, the mean speed decreased by approximately 1.74 mph, representing a 3%
reduction, and the standard deviation of speed declined by 0.3 mph (6% reduction).
Some studies on freeways focused on the spillover effects—time or distance halo
effects— rather than the direct effects. The time halo effect is defined as the length of
time during which the effect of enforcement is still present after enforcement activity has
been withdrawn. The distance halo effect is the number of kilometers from the
enforcement site, in which the effect is maintained (Hauer et al. 1982; Vaa 1997).
Sisiopiku and Patel (1999) analyzed both time and distance halo effects of mobile speed
cameras on Interstate 96 in Ionia County, Michigan. The average speed just upstream of
the police car’s location was reduced, but as soon as vehicles passed the patrol car,
drivers accelerate to their normal speeds or more, but no “time halo” effects on the
vehicles at the increased speed zone were observed.
20
Ha et al. (2003) investigated the distance halo effects using speed data collected from
seven measurement sites on urban highway in South Korea. Drivers tended to reduce
their speeds when approaching the speed enforcement camera, but drivers accelerated
back to their original speeds on passing the enforcement camera—thus no evidence of
distance spill-over effects were observed.
Champness and Folkman (2005) also examined the time and distance halo effects of
mobile overt speed cameras in Australia. Time and distance halo effects were analyzed
using numerous measurements: mean speeds, 85th, 90th, and 95th percentile speeds, etc.
Distance halo effects were clearly identifiable, with an observed reduction in speeds one
kilometer downstream, but the magnitude of the reduction diminishes at 500 meters
downstream of the camera site. The effect of the speed camera was completely dissipated
at 1.5 kilometers downstream.
Another study attempted to compare the reduction in speed in terms of enforcement type
and time delay in the case of mailed fines on a 75 mph motorway in the Netherlands
(Waard and Rooijers 1994). Two field experiments were conducted to establish the most
effective method of enforcement in reducing driving speeds. The enforcement intensity
study showed a clear relationship between intensity level of enforcement and the
proportion of speeding drivers. The highest intensity levels led to the largest and longest
lasting reduction in driving speeds, but effects on average driving speeds of the methods
on-view stopping versus photographing of offenders were similar.
Table 2: Summary of studies on freeways
Reference Country Camera
type Enforcement sites Posted speed
limits
Lamm and Kloeckner
(1984) Germany Fixed 2 sites on Autobahn 62 mph
(100kph)
Waard and Rooijers
(1994) Netherlands Mobile 6 sites on motorways 75 mph
(120kph)
Sisiopiku and Patel
(1999) US Mobile 29-mile segment on I 96,
Michigan.
70mph
(113kph)
Chen et al. (2002) Canada Mobile 12 sites on Highway 17 56mph
(90kph)
Ha et al. (2003) South Korea Fixed 1 site on urban highway 50mph
(80kph)
Champness and
Folkman (2005) Australia Mobile 1 site Highway section,
Queensland
62 mph
(100kph)
Table 2 summarized the experimental details of these studies. Only two studies (Ha et al.
2003; Lamm and Kloeckner 1984) are similar to the Scottsdale’s enforcement
environment (i.e., fixed camera). However, highways in Germany and South Korea are
likely to have different traffic conditions, road users (skills and ‘safety culture’),
21
geometric design standards, and weather compared to the Scottsdale Loop 101. In fact,
the cameras on the Autobahn were deployed at steep downgrade sections (5% grade).
2.2.2 Speed Enforcement Cameras on non-Freeways
While there were relatively few studies for the speed enforcement cameras on freeways, a
number of studies analyzed the effects of speed cameras on non-freeway roads. Table 3
shows the summary of outline of these studies.
Table 3: Summary of outline of studies on non-freeways
Reference Country Camera
type Enforcement sites Posted speed limits
Hauer et al. (1982) Canada Fixed 4 sites on suburban two-lane
road
37 mph (60kph) or
50mph (80kph)
Vaa (1997) Norway
Fixed
and
Mobile
Roadway 22 and 170 in
Norway
(suburban two-lane road)
37 mph (60kph) or
50mph (80kph)
Elvik (1997) Norway Fixed 64 sites 31 mph (50kph) to
56mph (90kph)
Retting and Farmer
(2003) US Mobile 7 sites on surface streets in
Washington, D.C. 25 mph or 30 mph
Hess (2004; 2003) UK Fixed 43 sites on rural road Speed limits vary
from sites
Goldenbeld and van
Schagen (2005) Netherlands Mobile 28 sites on rural road 50 mph (80kph) or
62 mph (100kph)
Cunningham et al.
(2005) US Mobile 14 sites in Charlotte, North
Carolina 25 mph to 55mph
Elvik (1997) assessed the effects of 64 fixed speed enforcement cameras in Norway on
safety. The study controlled for general trends in the number of accidents and regression
to the mean bias by using comparison groups and empirical Bayesian estimation
respectively. The injury accidents were significantly reduced by 20%, and the property
damage-only accidents were reduced by 12%. However, the reduction in the PDO
accidents was not statistically significant.
Retting and Farmer (2003) evaluated the effects of mobile speed enforcements on speed
at seven sites in Washington, D.C. With eight comparison sites in Baltimore, Maryland,
speed data collected one year before enforcement and approximately six months after
enforcement began were analyzed. Mean speeds at seven sites declined by 14%, and the
proportion of vehicles exceeding the speed limit by more than 10 mph declined by 82%.
Goldenbeld and Schagen (2005) assessed the impacts of mobile inconspicuous speed
cameras on the speed and safety at 28 enforcement sites in the Netherlands. With 15 sites
22
on 80kph rural roads and all other non-enforced roads outside urban areas as comparison
sites, the evaluation was performed. The results show that the mean speed decreased by
4kph on the enforced roads and by 0.5kph on the non-enforced comparison roads during
the enforcement period. With regard to reduction in safety, the number of road accidents
and casualties decreased by 21%.
Again, there are several studies focusing on the spillover effects. Hauer et al. (1982)
attempted to investigate both spillover effects (i.e., time halo and distance halo effects)
comprehensively. The distance halo effects were measured at four enforcement sites with
upstream and downstream measurement sites, which are located on semi-rural two-lane
roads in Halton and Peel counties west of the Toronto metropolitan area. To investigate
time halo effects, speeds were monitored prior to, during, and after exposure to enforce-ment.
The investigation on aggregate speed distributions suggested that the average speed
of the free flowing vehicles was remarkably reduced at the enforcement site. When
enforcement was in place, the average speed at the site was close to the posted speed
limit. The downstream distance halo effect follows the general form of exponential decay,
representing that the effect of enforcement is reduced by half for approximately every
900 meters. The time halo appeared to be the only phenomenon to be affected by the
intensity of enforcement: the effect of enforcement at single day has disappeared after
three days, while enforcement on several consecutive days had a longer term effect.
Vaa (1997) also investigated the impacts of the intensity level of speed enforcement on
speeds. Speed was measured at 12 sites in Norway consecutively for 16 weeks: two
before weeks, six enforcement weeks, and eight after weeks. Vaa concluded that the
average speeds during the enforcement period were reduced, but durations for time halo
effects were influenced by the intensity of the enforcement, which were consistent with
other results (Hauer et al. 1982; Waard and Rooijers 1994).
Hess (2004) assessed the effects of 49 fixed speed enforcement cameras in Cambridge-shire,
U.K. Two consecutive studies (Hess 2004; Hess and Polak 2003) were conducted
in order to quantify the performance of the cameras in terms of their catchment area (the
effects of cameras for various ranges around the cameras). In the 250-meter range, injury
accident numbers were reduced by 45.74%. However, the reductions in the 500-meter,
1,000-meter, and 2,000-meter ranges decreased by 41.30%, 31.62%, and 20.86%
respectively.
Cunningham et al. (2005) analyzed the impact of mobile automated speed enforcement
on speed and safety, which was implemented on 14 key corridors in North Carolina. They
found that median and 85th percentile speeds respectively decreased by 0.88 mph and
0.99 mph from the before period to the after period. In addition, a reduction of 11% to
23
14% in total crashes resulting from the speed enforcement cameras was estimated, which
was obtained by using the comparison group methodology. However, the authors
concluded that the results should be interpreted with limitations, such as the brief
duration of the after period.
2.3 Summary of Findings
A number of studies have evaluated the effects of speed enforcement cameras on safety
and speed. Some studies evaluated the effects on speed or traffic safety solely, while
others evaluated both. In addition, several studies focused on the spillover effects in
terms of time and space. Not surprisingly, the estimates of the safety effect of speed
cameras vary considerably, even though all studies suggest that photo enforcement
cameras are effective in reducing speed and crash frequency at photo enforcement camera
deployment sites.
However, many studies suffer from one or more non-ideal conditions. For example, the
results of some studies may underestimate or overestimate the effects of the speed
enforcement cameras on traffic safety, since total crashes instead of target crashes
(crashes that are materially affected by the photo enforcement speed cameras) were
analyzed. In addition, failure to account for regression to the mean can overestimate the
effects, while benefits can be underestimated if spillover effects are ignored. From the
literature review several noteworthy observations are relevant:
• Change in violation frequency due to the SEP: Since the direct effect of speed
enforcement cameras is a reduction in speeding, it is expected that the number of
violations will decrease, thereby reducing relevant crashes. However, if this
assumption does not hold, the speed enforcement countermeasure could be invalid.
• Reduction in mean speed and speed dispersion due to the SEP: In addition to the
reduction in violation frequency, it is also expected that the mean speed and speed
dispersion will be reduced, which should be carefully investigated.
• Target crashes: The lack of precise definition for target crashes in past studies
could have led to the under-estimation of the safety effects.
• Comparison group not affected by SEP: If crashes at comparison sites (zone) are
affected by the demonstration program, estimating the program effect at the
treated enforcement zone becomes more difficult.
• Exposure changes between the before and program periods: It is important to
account for changes in traffic exposure between the before and program periods.
24
• Regression to the mean effects: In many studies, speed enforcement cameras were
installed at high-crash sites—which could lead to significant regression to the
mean bias that needs to be accounted for—often leading to over-estimation of
safety impacts.
25
Chapter 3 Effects of the SEP on Speeding Behavior
and Speed
In this chapter, the effects of the SEP on speeding behavior and speed are examined. The
speeding behavior is analyzed by comparing the detection frequencies during the warning,
program, after, and reactivation periods, collected at the six enforcement camera
locations, and the impact on speed was compared by analyzing the mean speeds during
the before and program periods. The detection frequency data were obtained from
Redflex, the vendor of Scottsdale’s enforcement cameras during the program, and the
average speed data were obtained from ADOT and Redflex. In the following sections, all
relevant analysis results are discussed in detail.
3.1 Changes in the Detection Frequency
3.1.1 Data Description
The detection frequency data used in this analysis are the number of vehicles detected by
the six enforcement cameras, which were collected from the 4 periods of observation:
• warning period: 1/22/2006 – 2/21/2006 (31 days)
• program period: 2/22/2006 –10/23/2006 (244 days)
• after period: 10/24/2006 – 12/31/2006 (69 days)
• reactivation period: 2/22/2007– 6/29/2007 (128 days)
Note that no detection data were collected prior to the warning period.
Table 4: Summary statistics for daily detection frequency by site and period
Warning period
(N=31 days)
Program period
(N=244 days)
After period
(N=69 days)
Reactivation period
(N=128 days)
Site* Mean Std.Dev. Mean Std.Dev. Mean Std.Dev. Mean Std.Dev.
1 203.52 84.08 158.41 62.08 1624.26 615.77 134.21 47.73
2 117.16 47.1 87.20 34.96 1163.45 453.52 108.54 55.43
3 245.42 80.47 254.76 78.93 2742.71 966.66 227.16 78.30
4 38.84 19.53 31.09 18.30 431.23 241.57 52.32 28.61
5 186.32 71.68 132.39 58.03 1904.48 867.41 127.44 56.27
6 181.94 78.27 114.35 57.66 1028.07 520.22 160.34 69.00
Total 973.19 339.15 778.20 273.24 8894.20 3455.26 808.06 276.08
Mean 162.20 94.57 129.70 88.06 1482.37 981.21 134.68 78.41
Table 4 shows the summary statistics for daily detection frequency by period as well as
site, and the interval plot for the mean detection frequency by period (with 95%
Confidence Interval) is shown in Figure 10.
26
Figure 10: Average daily detection frequency by period
The detection frequencies vary over the enforcement sites—the detection frequencies at
site 3 (see Figure 9: site 3 is located on Frank Lloyd Wright Blvd. and Raintree Dr.) are
greater than those at other sites (see Figure 11).
Figure 11: Average daily detection frequency by period and site
27
Table 5: Summary statistics for the daily detection frequency per camera by day of week and period
Warning period Program period After period Reactivation period
Mean Std.Dev. Mean Std.Dev. Mean Std.Dev. Mean Std.Dev.
Monday 138 69 110 69 1154 681 111 55
Tuesday 131 61 98 63 1203 876 105 52
Wednesday 126 58 99 66 1231 911 110 54
Thursday 124 71 102 66 1157 795 109 56
Friday 140 78 114 76 1250 862 118 63
Saturday 230 104 190 104 1905 1109 193 94
Sunday 241 119 190 100 1854 899 198 93
Holiday . . 153 86 2304 1001 176 82
Total 162 95 130 88 1482 981 135 78
Since our interest is in comparing the change in the detection frequency resulting from
the SEP, the change in the average daily detection frequency per camera (i.e., site) by
period was analyzed. The time series plot illustrated in Figure 13 shows that the average
daily detection frequency per camera has periodic patterns–spikes for weekends and
holidays. Table 5 shows the summary statistics for the average daily detection frequency
per camera during the four periods by the day of the week. The list of holidays used in
this analysis is summarized in Table 6, which is equivalent to the list of holidays used in
the annual Arizona Crash Fact Summary Report (ADOT 2006). The daily detection
frequencies during weekends and holidays are relatively greater than those during
weekdays, while the detection frequencies during weekdays appear to be similar to each
other (see Table 5).
Table 6: A list of holidays in 2006 and 2007
Description Official observed date Holiday
Start End
New Year's Day Monday, January 2 December 31, 2005 January 2, 2006
Memorial Day Monday, May 29 May 27, 2006 May 29, 2006
Independence Day Tuesday, July 4 July 1, 2006 July 4, 2006
Labor Day Monday, September 4 September 2, 2006 September 4, 2006
Thanksgiving Day Thursday, November 23 November 23, 2006 November 26, 2006
Christmas Day Monday, December 25 December 23, 2006 December 25, 2006
New Year’s Day Monday, January 1 December 30, 2006 January 1, 2007
Memorial Day Monday, May 28 May 26, 2007 May 28, 2007
Table 7 shows the summary statistics for the average daily detection frequency per
camera during the four periods, in which each day is aggregated by two categories:
“weekdays” and “weekends and holidays.” Regardless of the periods, detection
frequencies during weekends and holidays are greater than those during weekdays as
shown in Figure 12, which indicates that the likelihood of speeding on weekends and
28
holidays is relatively high due to the low traffic demand on those days. This finding
suggests that the detection frequency needs to be analyzed by controlling for the day of
week effect.
Table 7: Summary statistics for the daily detection frequency during the 4 periods by the 2 categories
Weekdays Weekends and holidays Total
Mean Std. Dev. Mean Std. Dev. Mean Std. Dev.
Warning period 132.02 66.75 235.98 111.31 162.20 94.57
Program period 104.68 68.61 185.00 100.32 129.70 88.06
After period 1200.72 829.60 2045.66 1020.53 1482.37 981.21
Reactivation period 110.50 56.22 194.13 92.45 134.68 78.41
Figure 12: Average daily detection frequency by periods and day of week
The time series plots also suggest that the day of week is one of several important factors
that affect the detection frequency. As previously discussed, the time series plots have
periodical spikes when weekends and holidays are not excluded (see Figure 13).
However, more stable time series plots can be obtained when the day of week effects are
eliminated from the time series plots (see Figure 14 and Figure 15).
Figure 13: Average daily detection frequency per camera during the four periods
29
Figure 14: Average daily detection frequency per camera during the four periods (weekdays)
30
Figure 15: Average daily detection frequency per camera during the four periods (weekends and holidays)
31
3 2
3.1.2 Effect of SEP on the Detection Frequency
The preliminary explanatory analyses suggest that the change in speeding detection fre-quency
needs to be analyzed by accounting for the day of the week effects as well as the
presence (or operation) of the SEP. Therefore, the impact of the SEP on the speeding
detection frequency is analyzed by using the two sub-samples (weekdays vs. weekends
and holidays) in order to develop parsimonious models with the one factor (i.e., the
presence of the SEP). The one factor analyses are consistently used in this analysis be-cause
the interactions between the day of the week effect and the presence of the SEP are
not quite meaningful.
We observed the variances of speeding detection frequency are significantly different
according to the presence of the SEP as shown in Table 7. Regardless of the day of week,
the standard deviations of the speeding detection frequency during the after period are
remarkably larger than those during the remaining periods. The Brown-Forsythe (BF) test,
which is an extension of the Levene’s test, was conducted to investigate as to whether or
not the variance of speeding detection frequency in each period of observation is different.
Equation (1) shows the BF test statistic, which is insensitive to departures from normality
(Kutner et al. 2005):
2
2
( ) ( )
,
( 1) ( )
T i i
i
BF
ij i
i j
n s n d d
F
s d d
⋅ ⋅⋅
⋅
− −
=
− −
Σ
ΣΣ (1)
where ij d is the absolute deviations of the ij y (the detection frequency for the jth day
during the ith period of observation) about their respective medians i y ⋅
􀀄 , di⋅ ( d⋅⋅ ) indicates
an aggregation of the absolute deviations over the j index (over the j and i indexes), T n is
total number of days during the 4 periods, i n is the number of days for the ith period of
observation, s is the number of observation periods (i.e., s = 4 ). Under the null
hypothesis (H0: 2 2 i σ =σ ∀i ), the FBF follows approximately an F distribution with s −1
and Tn −s degree of freedom. In all tests, the program period was considered
consistently as a reference group.
Table 8: Brown-Forsythe test results for the homogeneity of variance
Weekdays Weekends and holidays
Period Pair
Test statistic (FBF) p-value Test statistic (FBF) p-value
Warning–Program 0.0715 0.7893 0.7451 0.3884
After– Program 1099.8168 <0.001 738.2187 <0.001
Reactivation– Program 18.1769 <0.001 3.4350 0.0643
All periods 612.5597 <0.001 389.1279 <0.001
33
The test results summarized in Table 8 show that the variance of speeding detection
frequency for each period of observation is significantly different at α=0.05. Therefore,
the impact of the SEP on the speeding detection frequency is analyzed by using weighted
least square (WLS) estimation, which is a standard modification of the general linear
models with the unequal variances (Greene 2003; Kutner et al. 2005; Washington et al.
2003).
Since the variances for each period of observation are often unknown, the sample
variances 2
i s (see Table 7) are used as the estimate. The weight ij w for the jth day of the
ith period of observation is:
2
1 , ij
i
w
s
= (2)
where the weight is the inverse of the variance in each group by the period and the day
the week. Table 9 shows the estimates for the difference in the daily speeding detections
per camera by period and the day of the week. The difference in the mean number of
speeding detections between the after (or warning) period and the program period is
significant at α=0.05. However, the mean speeding detection frequency between the
program period and the reactivation period is not significant at α=0.05, suggesting that
the activation of the SEP contributed to reducing the number of motorists exceeding
75mph. The WLS estimates summarized in Table 9 are used to calculate the relative
change in daily speeding detection frequency per camera, which is summarized in
Table 10.
Table 9: WLS estimates for the difference in daily speeding detection frequency per camera
Day of Week Period Pair Difference in Daily Speeding Detection 95% C.I.s
(p-value) Lower Upper
Warning–Program 27.33 (<0.001) 15.17 39.49
Weekdays After– Program 1096.04 (<0.001) 998.01 1194.06
Reactivation– Program 5.81 (0.072) –0.53 12.16
Warning–Program 50.98 (<0.001) 19.86 82.11
Weekends After– Program 1860.66 (<0.001) 1689.91 2031.42
and Holidays
Reactivation– Program 9.13 (0.241) –6.14 24.41
Table 10: Relative changes in daily speeding detection frequency per camera
Day of Week Period Pair Relative difference in 95% C.I.s
daily Speeding detection Lower Upper
Warning–Program 0.261 0.145 0.377
Weekdays After– Program 10.470 9.534 11.406
Reactivation– Program 0.056 -0.005 0.116
Warning–Program 0.276 0.107 0.444
After– Program 10.058 9.135 10.981
Weekends
and Holidays
Reactivation– Program 0.049 -0.033 0.132
34
The estimated results show that:
• After the SEP was implemented, the detection frequency decreased by 26% (or 27%)
from the warning to program period. The decrease in the speeding detection
frequency is statistically significant.
• After the SEP ended, the detection frequency increased by 1047 % (or 1006%) from
the program to after period.
• The detection frequency for the reactivation period is not statistically different than
that for the program period, indicating that the activation of the SEP contributed to
reducing drivers’ speeding behavior.
• The pairwise comparisons suggest that the activation of the SEP is an effective
countermeasure for reducing speeding behavior, resulting in significant reductions in
the number of motorists exceeding 75mph.
3.2 Changes in the Mean Speed
In this section, the effects of the SEP on the mean speed are analyzed by comparing the
mean speeds that were collected from the enforcement zone during the before and
program period. Unlike the analysis for the changes in the speeding detection frequency,
the mean speeds during the after and reactivation period are not compared in this analysis
due to insufficient data. The analysis was conducted using mean speeds during
unconstrained traffic conditions, since the SEP will not significantly affect peak-period
travel.
3.2.1 Data Description
In this subsection, the speed data obtained from the enforcement zone during the before
period (see Table 11) are summarized, and the speed data during the program period are
described in the analysis subsection.
Table 11: Description of the 6 measurement sites for the before period
ID Direction Location Measurement date
1 NB CACTUS RD & SHEA BLVD 4/13/2005 4/14/2005 4/15/2005
2 SB CACTUS RD & SHEA BLVD 4/13/2005 4/14/2005 4/15/2005
3 NB RAINTREE DR & CACTUS RD 4/19/2005 4/20/2005 4/21/2005
4 SB RAINTREE DR & CACTUS RD 4/19/2005 4/20/2005 4/21/2005
5 NB SCOTTSDALE RD & PIMA/PRINCESS DR 6/27/2005 6/28/2005 6/29/2005
6 SB SCOTTSDALE RD & PIMA/PRINCESS DR 6/27/2005 6/28/2005 6/29/2005
35
In order to reduce the variance from the different measurement dates, the middle of the
day (24 hours) was consistently used in this analysis (i.e., 4/14/2005; 4/20/2005;
6/28/2005). The descriptive statistics for the speed data are summarized in Table 12, in
which an individual speed data observation is the aggregated mean speed in each lane
during 15-minute intervals. For instance, the mean speed at site i ( i S i ) is estimated by the
aggregated mean speed at site i during the jth interval (Sij ).
1
ni
ij
j
i
i
S
S
n
= =
Σ
i
where i =1, 2,􀀢,6 and 1,2, , i j = 􀀢 n .
Table 12: Summary of statistics for speed by site
Site ID Mean Std. Dev. Min. Median Max. N (ni)
1 70.40 6.46 46 71 83 288
2 75.17 5.35 43 75 90 288
3 70.83 4.90 62 70 87 384
4 77.27 4.51 52 78 91 384
5 70.67 6.14 40 72 83 288
6 73.22 7.70 31 74 87 288
3.2.2 The Speed-Flow Relationship and Level of Service
Before comparing the speed data of the before period to those of the program period, the
relationship between speed and traffic flow is examined because the former is sensitive to
the latter. There are three commonly referenced macroscopic parameters to describe a
traffic stream: speed, density, and rate of flow. They are related as follows:
V=S×D
• V= Rate of flow (vehicle/hour/lane)
• S= Space mean speed (mph)
• D= Density (vehicles/mile/lane)
Density and speed are parameters for a specific section, while rate of flow is a parameter
for a point. There have been a number of studies to reveal the shape of these relations-hips,
but the relationship depends upon prevailing conditions. Figure 16 shows a recently
depicted speed-flow relationship (Transportation Research Board 2000), which is typical
of traffic patterns on uninterrupted flow facilities.
36
Figure 16: Speed-flow curve [Source: HCM 2000]
The modern speed-flow curve show in Figure 16 implies that the effects of traffic flow on
speed are different across regimes. Since focus in this study is on the speed distribution
in regime 1 rather than that in regimes 2 or 3, it is necessary to determine and classify
regime 1.
In order to extract the speed in the stable flow (i.e., regime 1), the concept of the level of
service (LOS) is used. In general, LOS is characterized using three performance
measures: density in terms of passenger cars per mile per lane, speed in terms of mean
passenger-car speed, and the volume-to-capacity (v/c) ratio. Each of these measures is an
indication of how well traffic flow is being accommodated by the freeway. For a basic
freeway section, the LOS is defined by reasonable ranges using the three critical flow
variables: speed, density, and flow rate.
37
The three identified regimes of the speed-flow curve in Figure 16 can be described as
follows (Roess et al. 2004):
• Regime 1: This regime is in the stable (or undersaturated) condition where drivers
can maintain a high speed that is unaffected by upstream or downstream conditions.
The flat portion of the curves usually defines free-flow speed. Speed begins to
decline in response to increasing flow rates. However, the total decline in speed
from free-flow speed to the speed at capacity is often 5 mph or less.
• The inflection point, which indicates the flow rate at which speed begins to
decline, is often in the range of 1,500–1,700 pc/h/ln (passenger cars per hour per
lane).
• Note that the path from free-flow speed to capacity is often associated with a
relatively small increase in the flow rate.
• Regime 2: This portion of the curve is called “queue discharge.” Once demand
exceeds capacity, a breakdown occurs and a queue propagates upstream of the point
of breakdown. Once the queue forms, flow is restricted to what is discharged from
the front of the queue. The variable speed for Regime 3 reflects the fact that vehicles
discharge from a queue into an uncongested downstream segment.
• Regime 3: This portion of the curve reflects the unstable operating conditions within
the queue, upstream of the breakdown, in which traffic flow is influenced by the
effects of a downstream condition. Traffic flow in the regime can vary over a broad
range of flows and speeds depending on the congestion severity.
38
Figure 17 shows the speed-flow curves that depend on free-flow speeds. All curves have
the same speed-flow relationship for regime 1 as illustrated in Figure 16, but each curve
has a different intercept that depends on free-flow speed. In addition, each LOS has the
minimum or maximum values for the three parameters. The minimum or maximum
values for the parameters are summarized in Table 13, which can be used to determine
LOS. In this study, a speed of 62.2 mph was used as the threshold average speed for
delineating congested and uncongested conditions, which is equivalent to the threshold
speed for ‘LOS E’ when free-flow speed is assumed as 75 mph.
Figure 17: Speed-flow curves and LOS on a basic freeway segment [Source: HCM 2000]
39
Table 13: LOS criteria for basic freeway sections
40
The general definitions of LOS are as follows (Transportation Research Board 2000):
• LOS A describes free-flow operations. Free-flow speeds prevail. Vehicles are
almost completely unimpeded in their ability to maneuver within the traffic
stream. The effects of incidents or point breakdowns are easily absorbed at this
level.
• LOS B represents reasonably free flow, and free-flow speeds are maintained. The
ability to maneuver within the traffic stream is only slightly restricted, and the
general level of physical and psychological comfort provided to drivers is still
high. The effects of minor incidents and point breakdowns are still easily
absorbed.
• LOS C provides for flow with speeds at or near the free-flow speed of the
freeway. Freedom to maneuver within the traffic stream is noticeably restricted,
and lane changes require more care and vigilance on the part of the driver. Minor
incidents may still be absorbed, but the local deterioration in service will be
substantial. Queues may be expected to form behind any significant blockage.
• LOS D is the level at which speeds begin to decline slightly with increasing flows
and density begins to increase somewhat more quickly. Freedom to maneuver
within the traffic stream is more noticeably limited, and the driver experiences
reduced physical and psychological comfort levels. Even minor incidents can be
expected to create queuing, because the traffic stream has little space to absorb
disruptions.
• LOS E describes operation at capacity. Operations at this level are volatile,
because there are virtually no usable gaps in the traffic stream. Vehicles are
closely spaced, leaving little room to maneuver within the traffic stream at speeds
that still exceed 49 mph. Any disruption of the traffic stream, such as vehicles
entering from a ramp or a vehicle changing lanes, can establish a disruption wave
that propagates throughout the upstream traffic flow. At capacity, the traffic
stream has no ability to dissipate even the most minor disruption, and any
incident can be expected to produce a serious breakdown with extensive queuing.
Maneuverability within the traffic stream is extremely limited, and the level of
physical and psychological comfort afforded the driver is poor.
• LOS F describes breakdowns in vehicular flow. Such conditions generally exist
within queues forming behind breakdown points.
41
3.2.3 Effect of the SEP on Mean Speeds
In order to control for the measurement date and day of week effects, the traffic volume
and speed data obtained from the enforcement zone during the program period were
carefully selected from the set of the speed and traffic flow data collected during the
program period. Therefore, the speed and traffic flow data during the three identical times
and days of the program period (Table 11) were selected: 4/13/2006 (Thursday),
4/19/2006 (Wednesday), and 6/27/2006 (Thursday). In addition, the data collected from
the unstable condition were excluded by using the speed threshold (i.e., 62.2 mph), which
is described in the previous subsection. The descriptive statistics for the speed data at
stable condition during the before and program period are summarized in Table 14.
Table 14: Summary statistics for the speed at stable condition during the before and program period
Period Mean Std.Dev. Min. Q1 Q2 Q3 Max.
Before 73.11 3.53 64.80 70.00 72.90 76.00 82.00
Program 64.36 1.20 62.33 63.67 64.33 65.00 68.33
Total 66.90 4.51 62.33 63.67 65.00 69.20 82.00
The statistics in Table 14 show that the mean speed decreased in the program period
from 73.1 mph to 64.4 mph, and the standard deviation of speed also reduced from
3.5 mph to 1.2 mph. Since one of the interests is also to estimate the impact of the SEP on
speed, the variance-weighted least square technique was used again due to the group-wise
heteroskedasticity in speed (the Brown-Forsythe test statistic=1193.78; p-value<0.001).
Unlike the WLS estimation used for analyzing the speeding detection frequency, the
variable traffic flow was included in the model because the speed is highly sensitive to
the change in traffic flow as discussed in the previous subsection (see "The Speed Flow
Relationship and Level of Service" on page 35). In addition, the interaction term between
the variable traffic flow and the period was added because the treatment effect is likely to
interact with the covariate traffic flow.
Table 15: WLS estimates for the impact of the SEP on speed (n=1934)
Variable Estimate Std. Err. t-value p-value 95% CIs
Lower Upper
Constant 65.297 0.047 1391.11 <0.001 65.297 65.481
Dummy variable for period
(1=before; 0=program) 10.286 0.242 42.49 <0.001 9.811 10.760
Traffic flow rate (vplph) -0.001 0.000 -26.63 <0.001 -0.002 -0.001
Interaction between the period dummy
variable and traffic flow rate -0.002 0.000 -6.41 <0.001 -0.002 -0.001
F-statistic (associated p-value) 1880.24 (<0.001)
Adjusted R2 0.7447
42
Equation (3) shows the WLS estimation results, where si is the mean speed for the ith
observation, Di is the dummy variable for period (1 for the before period; otherwise 0), Fi
is the mean flow rate for the ith observation, and Di ·Fi is an interaction term between Di
and Fi. The standard errors for each estimate are in parentheses (all estimates are
significant at α=0.05). All estimation outputs are also summarized in detail in Table 15.
( 0.04701) (0.24206) (0.00005) ( 0.00024)
65.39 10.29 0.0014 0.0016 ; 2 0.745 i i i i i s= + D− F− D⋅F Adj R = (3)
The significant negative estimate for the traffic flow rate reflects the well-known
relationship between speed and traffic flow in the stable regime: as traffic flow increases,
speed decreases. The significant negative estimate for the interaction indicates that the
speed of a driver for the program period is relatively insensitive to change in traffic flow
due to the SEP as shown in Figure 18.
Figure 18: Impact of the SEP on speed by period
Consequently, it is evident that the impact of the SEP on speed increases as traffic flow
decreases due to the well known relationship between speed and traffic flow. Thus, the
impact of the SEP on speed was estimated using quartiles of the flow rate during both
periods as shown in Table 16. Specifically, the mean speed decreased by 9.97 mph when
traffic flow was 206 vplph (Q1), while the mean speed decreased by 8.47 mph when
traffic flow was relatively high (i.e., 1,169 vplph: Q3).
43
Table 16: Estimated speed reduction (mph) due to the SEP
Period Pair Speed Reduction 95% C.I.s
(Std. Err.) Lower Upper
Before– Program (Flow=Q1*) 9.97 (0.201) 9.57 10.36
Before– Program (Flow=Q2) 9.04 (0.127) 8.79 9.29
Before– Program (Flow=Q3) 8.47 (0.149) 8.17 8.75
* Q1, Q2, and Q3 are quartiles for the flow rate: 206 vplph, 800 vplph, and 1,169 vplph respectively.
In summary, the estimated results reveal that:
• The SEP not only reduced the average speed at the enforcement camera sites by about
9 mph, but also contributed to reducing the speed dispersion at the enforcement
camera sites. Thus, as prior research has revealed, both the prerequisites for crash
reduction (safety improvement) are met with the SEP.
• The reduction in the mean and variance of speed resulting from the SEP depends on
traffic flow: the reduction increased as traffic flow decreased due to the well known
relationship between speed and traffic flow. Thus, the magnitude of speed effects of
the SEP is inversely related to traffic flow.
44
45
Chapter 4 Effects of the SEP on Traffic Safety
In this chapter, the effects of the SEP on traffic safety are comprehensively analyzed.
Target crashes are first carefully determined by using the detection trend in terms of time
of day, and the evaluation methodologies used in the study are described in detail. After
presenting some preliminary analysis concepts, we discuss the results of three analysis
methodologies, their assumptions, and the results of the analysis.
4.1 Preliminaries: Target Crashes and Data Description
4.1.1 Determining Target Crashes
Before estimating the impact of the SEP on traffic safety, it is necessary to define which
crashes are materially affected by the speed enforcement cameras—referred to as “target”
crashes. Since the crashes occurring during the peak travel periods are unlikely to be
affected by the photo enforcement cameras, target crashes should be defined as crashes
that occurred during the off-peak-periods.
Since traffic conditions for each crash are often unknown, we investigated the speeding
detection rate by time of day (TOD) in order to test whether or not the TOD can be used
as a proxy to determine the off-peak-period. Figure 19 shows the detection frequency by
TOD, in which the detection frequency is the average number of detections per 15-minute
interval at the enforcement sites for the program period. The detection frequency by TOD
indicates that detection frequency decreases during peak hours for weekdays, while they
are almost proportional to traffic flow for weekends and holidays. Therefore, TOD is
generally related to speeding behaviors on weekdays.
Weekdays Weekends and Holidays
TOD
Detec t ion frequenc y
Flow rate
0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00
3.0
2.5
2.0
1.5
1.0
0.5
0.0
1600
1400
1200
1000
800
600
400
200
0
Variable
Detection frequency
Flow rate
TOD
Detec t ion frequenc y
Flow Rate
0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00
3.0
2.5
2.0
1.5
1.0
0.5
0.0
1600
1400
1200
1000
800
600
400
200
0
Variable
Detection frequency
Flow Rate
Figure 19: Detection frequency by TOD
46
In addition, the relationships between TOD and detection rate shown in Figure 20
indicate that the detections could occur for weekends and holidays regardless of traffic
flow, while the detections are related to the changes in traffic flow, in which the detection
rate is the ratio of detection frequency to the average traffic volume per 15-minute
interval at the enforcement sites for the program period. For example, the detection rates
during peak hours for weekdays are remarkably low—less than 0.25% between 6:00 AM
and 9:00 AM.
Weekdays Weekends and Holidays
TOD
Detec t ion rate
Flow rate
0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00
0.025
0.020
0.015
0.010
0.005
0.000
1800
1600
1400
1200
1000
800
600
400
200
0
V ariable
Detection rate
Flow rate
TOD
Detec t ion rate
Flow rate
0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00
0.025
0.020
0.015
0.010
0.005
0.000
1800
1600
1400
1200
1000
800
600
400
200
0
V ariable
Detection rate
Flow rate
Figure 20: Detection rate by TOD
Since the detection trends by TOD suggest that TOD can be used to identify traffic flow
regimes, two traffic flow regimes (peak and off-peak periods) are defined by using TOD.
• Peak periods (6 hours)
• 06:00 AM — 09:00 AM
• 16:00 PM — 19:00 PM
• Off–peak periods
• The remaining 18 hours for weekdays
• 24 hours for weekends and holidays
Consequently, the target crashes in this analysis are the crashes that occurred within the
enforcement zone (milepost 34.51 – milepost 41.06: 6.5 miles) during the off-peak travel
periods defined by TOD (because of the limited expected influence of the cameras on
slow moving peak-period traffic). Note that the target crashes are “mainline” crashes
classified by ADOT, excluding crashes that occurred on Loop 101 ramps and frontage
roads. In the next subsection, the characteristics of the target crashes are discussed in
detail.
47
4.1.2 Crash Data Description
In this subsection, the characteristics of the target crashes determined in the previous
subsection are discussed. The durations of the target crash data are summarized below:
• Crash data during the before period
• Duration: 2/22 – 10/23 (2001 through 2005)
• Crash data during the program period
• Duration: 2/22/2006 – 10/23/2006 (244 days)
Note that the SEP was reactivated February 22, 2007, but the current analysis is based on
the crash data for the program period. Figure 21 shows the number of crashes that
occurred within the enforcement zone during the before period. It contains target crashes
as well as the crashes that occurred during the peak periods. Although the average
number of crashes during the two periods (peak and off-peak periods) cannot be
compared directly, three crash types are most frequent: single-vehicle, side-swipe (same),
and rear-end crashes. Therefore, the remaining crash types such as angle, left-turn, side-swipe
(opposite), head-on, and other crashes are aggregated as “other” in this analysis.
Figure 21: Number of crashes that occurred at the enforcement zone during the before period
48
Figure 22 and Figure 23 show the percentage of the peak or off-peak crashes by crash
type, which occurred during the before period. The most frequent crash type was single-vehicle
crashes (54%) for the off-peak periods, while rear-end crashes type (51%) was
most frequent for the peak periods.
Figure 22: Percentage of off-peak crashes by crash type (before period)
Figure 23: Percentage of peak-period crashes by crash type (before period)
Although it is evident that the characteristics of crashes are different for the two periods,
the analysis using the target crashes is conservative because the peak period is likely to
increase over time (the before to program period). Therefore there is increasing
constraint on speed over time, or lesser constraint on speed going back in time (the before
period), resulting in target crashes in the before period being eliminated from the analysis
(because they occurred during the peak period). Fewer before crashes reduce the
estimated effectiveness of a countermeasure; therefore this approach is conservative.
49
4.2 The Four-Step Procedures for Before-and-After Study
In this section, the basic concepts of the before-and-after (hereafter BA) study are
described, and the basic four-step procedure for estimating the effects of SEP is also
provided. This analysis approach used in this study is an expansion of the generally
accepted and widely applied methods described by Hauer (Hauer 1997; Hauer et al.
2002).
The key objective of the BA study is to estimate the change in safety for the program
period as a result of the treatment. The key notations used are:
• π: Expected number of crashes for the program period without the SEP;
• λ: Expected number of crashes for the program period with the SEP;
• κ: Expected number of crashes for the before period;
• δ = π–λ: Change in safety resulting from the SEP;
• θ = λ/π: Index of the effectiveness of the SEP;
• K: Observed number of crashes in the enforcement zone for the before period;
• L: Observed number of crashes in the enforcement zone for the program period;
• M: Observed number of crashes in the comparison site for the before period;
• N: Observed number of crashes in the comparison site for the program period.
If either δ is greater than 1 or θ is less than 1, then we conclude that the treatment is
effective. The parameters π, λ, δ, and θ are unknown parameters and must be estimated
using the available data. There are numerous arduous aspects of estimating these
unknown parameters. Generally, the value of λ is being estimated using the observed
number of crashes in the program period (i.e., L). It might seem that the observed number
of crashes in the before period would be employed to predict the value of π.
Figure 24 illustrates the basic concept of the BA study. As discussed, the key objective of
the analysis is to predict the expected number of crashes in the program period if the SEP
had not been implemented. If we do not assume any change from before to program
periods, the estimates of the π’s are the same as the observed target crash frequency
during the before period (i.e., K). However, it is insufficient to predict the value of π
using the observed number of crashes in the before period. Problems arise because there
are either potentially many recognizable and unrecognizable factors which may have
changed from the before to after periods, or the regression to the mean bias that has
resulted from sites being selected based on prior crash histories. Thus, often more
50
rigorous evaluation methodologies are needed to obtain accurate estimates of π, which
are described in detail in the following subsection.
Figure 24: Basic concept of the before-and-after study
Regardless of the corrections made to the BA study, a basic four-step procedure is used
(with modifications) to estimate the safety effect of a treatment. In the next subsections,
we introduce the four-step procedure for the simple or naïve BA study approach, which is
based on the following assumptions:
• Traffic volume, roadway geometry, road user behavior, weather, and many other
factors have not significantly changed from the before to the program period.
• There are no treatments or improvements other than the installation of the speed
enforcement cameras during the program period.
• The probability that crashes are reported is the same in both periods, and the
reporting threshold has not changed.
Step 1: Estimate λ and predict π
The first step is to estimate λ and π. The estimate of λ is equivalent to the sum of the
observed number of target crashes in the program period. Also, the predicted value of π
is equal to the sum of the observed number of crashes in the before period. In the simple
BA study, these estimates are:
1
ˆ
B
t
t
π K K
=
= Σ = (4)
and
51
1
ˆ ,
B P
t
t B
λ L L
+
= +
= Σ = (5)
where B and P are the number of durations for the before and program period
respectively, and Kt and Lt are the observed target crash frequencies during the before and
program period.
Step 2: Estimate σ􀁬 2[λˆ] and 􀁬 2 σ [πˆ]
The second step is to estimate the variance of λ��� and π􀀃 . Suppose that the number of
target crashes is Poisson distributed (which is often the case at a single site), then the
variance is equal to the mean.
σ􀁬 2[λˆ]=λ (6)
and
􀁬 2 σ [πˆ]=π. (7)
Of course, the estimate of variance of ˆπ will depend on the method chosen to consider
various assumptions.
Step 3: Estimate δ and θ
The estimates of treatment effectiveness δ can be estimated:
δ􀀃 =π􀁬 −λ􀀃 =K−L. (8)
The estimator of θ was obtained by using the well-known delta approximation, because θ
is a non-linear function of two random variables. Since the applications of the delta
method are necessarily brief, the interested reader can refer to two references for a full
derivation and justification (Hauer 1997; Shin and Washington 2007a) and consult two
of a variety of references for the delta method (Greene 2003; Hines et al. 2003).
( )
{ 􀁭[􀁬] 2}
ˆ / ˆ
ˆ
1Var /ˆ
λ π
θ
π π
≅
+
(9)
Equation (9) shows that it is also necessary to estimate the variance of π􀀃 in order to
estimate the index of the effectiveness θ. The variance for π􀀃 can be estimated by using
the assumption that the number of target crashes is Poisson distributed.
5 2
Step 4: Estimate σˆ2[δˆ] and σˆ2[θˆ]
The final step is to estimate the variance of the effects obtained by using four different
methods, which can be used to approximate the “level of confidence” of the results.
Equation (10) shows the unbiased estimators for the variances of δ􀀃
and θ􀀃
, in which the
variance of θ􀀃
is also obtained by using the delta (Hauer 1997; Shin and Washington
2007a).
􀁭[􀀃] 􀁬 􀀃 􀁭[ ]
􀁭[􀀃] 􀁭[ ]
􀁭[ ]
2
2 2
2
2
ˆ ˆ
= ; ˆ ˆ ˆ .
1 ˆ
ˆ
Var Var
Var Var
Var
θ λ π
δ π λ θ λ π
π
π
⎛ ⎞
⋅⎜ + ⎟
+ ≅ ⎝ ⎠
⎛ ⎞
⎜ + ⎟
⎝ ⎠
(10)
Table 17 shows the goal and formulas for each step in simple BA study four-step
processes.
Table 17: The four-step procedure for simple before-and-after study
Step Goals Formulas for simple before-and-after study
Step 1 Estimate λ and predict π
λˆ = L
πˆ = K
Step 2 Estimate σˆ 2[λˆ] and σˆ2[πˆ]
σˆ 2 ⎡⎣λˆ⎤⎦ =λˆ
σˆ2 [πˆ] =πˆ
Step 3 Estimate δ and θ
δˆ=πˆ −λˆ=K−L
􀁬
2 2
ˆ
ˆ ˆ
1 [ˆ] 1
ˆ
L
K
V K
K
λ
π
θ
π
π
⎛⎜ ⎞⎟ ⎛⎜ ⎞⎟
≅ ⎝ ⎠ = ⎝ ⎠
⎛⎜⎜⎝ + ⎞⎟⎟⎠ ⎛⎜⎝ + ⎞⎟⎠
Step 4 Estimate σˆ 2[δˆ] and σˆ 2[θˆ]
σˆ2 ⎣⎡δˆ⎦⎤ = πˆ+λˆ=K+L
􀁬 􀁬
􀁬
2 2
2 2 2 2
2
2 2
2 2
ˆ [ ˆ] ˆ (ˆ ˆ) (ˆ ˆ) ˆ
1 (ˆ) 1
ˆ
V V L K
L K
V K
K
λ π
θ λ π θ
σ θ
π
π
≅ ⋅⎡⎢⎣⎢ + ⎤⎥⎦⎥= ⋅⎣⎡⎢ + ⎦⎤⎥
⎢⎣⎡⎢ + ⎥⎦⎤⎥ ⎡⎢⎣ + ⎤⎥⎦
5 3
4.3 Before-and-After Study with a Comparison Group
The simple BA study assumes that no changes other than the SEP have been
implemented from the before to the program period. However, the assumptions in the
simple BA study are often invalid because a number of factors affecting traffic safety can
change over time. In general, the factors can be divided into two categories: recognizable
and unrecognizable factors (Hauer 1997). While the recognizable factors are measurable
and can be modeled directly, unrecognizable factors such as the unobserved changes in
driving population, traffic, weather, etc. can not be measured directly. The latter are
commonly modeled by accounting for the effect of time trends (Harwood et al. 2002). In
this section, the impact of the SEP on safety is estimated by a comparison group approach
in order to account for the change in the unrecognizable factors.
4.3.1 Overview of the Before-and-After Study
with a Comparison Group
The basic concept of the before-and-after study with a comparison group is illustrated in
Figure 25, in which Kt and Lt represent the observed number of target crashes at the
treatment entity during the before and program period respectively, while Mt and Nt
represent the observed number of target crashes at the comparison group during the
before and program period respectively.
Figure 25: Basic concept of the before-and-after study with comparison group
5 4
Again, K, L, M, and N represent the sums of the observed number of crashes during each
period. Table 18 shows the observed counts of crashes and the expected crash counts
(Greek letters). These quantities are used to obtain the estimates in BA study with a
comparison group.
Table 18: Key notations used in the before and after study with a comparison group
Target crashes at treated sites Target crashes at comparison sites
Before K (κ ) M (μ )
After L (λ ) N (ν )
The key assumption for the BA study with a comparison group is that the crash time
series data between the enforcement zone and a comparison group exhibit the same trend
in the absence of the treatment (i.e., SEP). If the trends in the two time series data are not
statistically different, the value of π can be estimated by using the change in the crash
frequency of the comparison group from the before to program period. Therefore, it is
vital that the crash time series data of the comparison group have a similar trend to those
of the enforcement zone. It is not necessary for the magnitudes of the crash frequency in
the enforcement zone (K) to be the same as those of the comparison group (M). Con-sequently,
it is more important that the crash time series data in the treated entity change
in the same way as the comparison group during the before period as shown in Figure 25.
The first step is to estimate λ and predict π. The estimate of λ is equal to the sum of the
observed number of crashes during the program period. Unlike the simple before-and-after
study approach, the comparison ratio can be used in order to estimate π:
, T C r r π ν
κ μ
⎛⎜ = ⎞⎟=⎛⎜ = ⎞⎟
⎝ ⎠ ⎝ ⎠
(11)
where these two ratios (rT and rC) are identical under the comparison group method
assumption. Since the ratio rC is a random variable consisting of a non-linear combination
of two random variables (μ and ν) and the observed counts of target crashes at compari-son
sites are Poisson distributed, the estimate of π can be represented as Equation (12):
􀁬 .
1 1
C T C
N
r K r K M K
M
π
⎛ ⎞
⎜ ⎟
= ⋅ = ⋅ = ⎝ ⎠ ⋅
⎛⎜ + ⎞⎟
⎝ ⎠
􀀃 􀀃 (12)
The estimate of variance for π􀀃 can be obtained by using the delta approximation:
􀁬2􀁬 2􀁬2[ ] 2􀁬2[ˆ ] C T T σ ⎡⎣π ⎤⎦ =r ⋅σ K+K⋅σ r (13)
5 5
For convenience, the ratio of rT and rC is defined as the odds ratio.
C T ω =r r (14)
Then, the variance for rˆT is:
􀁬2 􀁬2
2
[ˆ ] 1 1 [ ] .
T C [ ]
r r VAR
M N E
ω
σ
ω
⎛ ⎞
≅ ⋅⎜ + + ⎟
⎝ ⎠
(15)
By plugging Equation (15) into Equation (13), the estimate of the variance for π􀀃 can be
rewritten as Equation (16), in which the variance of 􀁬π C can be approximated by using
the estimate of the comparison ratio when the sample size of M and N is large enough:
􀁬2 􀁬 􀁬2 􀁬2
2
1 1 1 [ ] .
[ ] C C C
VAR r K
K M N E
ω
σ π π ω
⎧ ⎛ ⎞⎫
⎡⎣ ⎤⎦= ⋅⎨ +⎜ + + ⎟⎬ ⋅
⎩ ⎝ ⎠⎭
􀀘 (16)
With these corrections to the four-step process, the remaining steps continue as before as
shown in Table 19.
Table 19: The four-step procedure for the BA study with a comparison group
Step Goals Formulas for simple before-and-after study
Step 1 Estimate λ and predict π
λˆ = L
􀁬 􀁬
1 1
C
N
r K M K
M
π
⎛ ⎞
⎜ ⎟
= ⋅ = ⎝ ⎠ ⋅
⎛⎜ + ⎞⎟
⎝ ⎠
Step 2 Estimate σˆ 2[λˆ] and σˆ2[πˆ]
σˆ 2 ⎡⎣λˆ⎤⎦ =λˆ
ˆ2 [ˆ] 􀁬2 Cσ π =r ⋅K
Step 3 Estimate δ and θ
δˆ=πˆ −λˆ=K−L
􀁬
2
ˆ
ˆ ˆ
1 [ˆ]
ˆ
V
λ
π
θ
π
π
⎛ ⎞
⎜ ⎟
≅ ⎝ ⎠
⎛ ⎞
⎜⎜ + ⎟⎟
⎝ ⎠
Step 4 Estimate σˆ 2[δˆ] and σˆ 2[θˆ]
σˆ2 ⎣⎡δˆ⎦⎤ = πˆ+λˆ=K+L
􀁬 􀁬
􀁬
2
2 2
2
2
2
ˆ ( ˆ) (ˆ)
ˆ [ ˆ] ˆ ˆ
1 (ˆ)
ˆ
V V
V
λ π
θ
λ π
σ θ
π
π
⎡ ⎤
⋅⎢ + ⎥
≅ ⎢⎣ ⎥⎦
⎡ ⎤
⎢ + ⎥
⎢⎣ ⎥⎦
5 6
4.3.2 Estimating Comparison Ratios
In order to estimate the comparison ratio (i.e., rC), we used the comparison ratios
estimated by using a comparison group instead of using a single comparison section, in
which the comparison group is a set of comparison sections. Of course, it is also possible
to estimate the comparison ratio by using a single comparison section through one-to-one
matching between the enforcement and comparison zones, which is known as the BA
study with yoked comparisons (Griffin and Flowers 1997; Harwood et al. 2002).
However, the BA study with yoked comparisons is not preferable because there is only
one matching comparison zone for the enforcement zone, which also leads to relatively
wide confidence intervals for the crash reduction estimates (Harwood et al. 2002). In
addition, the variances of the comparison ratios obtained from the comparison group are
generally less than those from a single comparison section because of the increased
sample size (Harwood et al. 2002; Hauer 1997).
Figure 26: Enforcement zone and comparison group
5 7
In this study, the potential sections for the comparison group were limited to the sections
on Loop 101 in order to reduce unwanted spatial variability in crashes. However, several
sections which are close to the enforcement zone were excluded from the comparison
group because it should not be affected by spillover effect. In order to define the sections
that can be influenced by the spatial spillover effect, we used a 2.8-mile influence zone,
which is devised based on the exponential decay model proposed by Hauer (Hauer et al.
1982). The exponential decay model shows that the effect of enforcement on speed
reduction is reduced by half for every 0.56 mile. Thus, we assumed that the spillover
effect could almost be eliminated after the 2.8-mile influence zone in each direction.
Specifically, the enforcement zone and comparison group (zone) in this analysis
illustrated in Figure 26 are:
• Enforcement zone: MP 34.5 – MP 41.06 (6.5 miles)
• Influence zone: MP 31.7—MP 34.5 and MP 41.06 – MP 43.9 (5.6 miles)
• Comparison zone: MP 1 – MP 31.7 and MP 43.9 – MP 61 (48 miles)
Consequently, the comparison zone used in this analysis (approximately a 48-mile stretch
on Loop 101) does not include the influence zone in addition to the enforcement zone.
Although some of comparison sections in the comparison zone illustrated in Figure 26
can be different in traffic flow and physical characteristics, it is more important that the
comparison zone resembles the enforcement zone as a whole (Harwood et al. 2002;
Hauer 1997). In other words, the past crash trends of the comparison zone should be
similar to those within the enforcement zone.
In order to investigate the degree of agreement in the crash time series data between the
enforcement and comparison zone, mean crash frequencies between the two zones were
compared over time. Figure 27 shows the change in total target crashes within the two
zones by year, in which the average crash frequency in the comparison zone is corrected
as “average crash frequency/6.5 miles/244days” for comparison. The two time series
show that they moved together and did not stray apart during the before period: curves
are almost parallel. Note that it is not necessary that the magnitudes of the two time series
are the same as discussed in the previous subsection. The findings from the comparison
can be summarized:
• Total target crashes in the enforcement zone decreased in 2006, while those in the
comparison zone increased in 2006. This inconsistency increases confidence that
target crashes in the enforcement zone were reduced by implementing the SEP.
• It is highly unlikely that the expected number of crashes on Loop 101 is constant
over time, indicating time-varying κ.
• It is likely that the enforcement zone was not the ‘least safe’ zone on Loop 101
prior to the SEP program since the observed crash counts from the comparison
zone are greater than those from the enforcement zone.
5 8
The change in total PDO crashes illustrated in Figure 28 also shows similar movement
although they are not perfectly parallel. Consequently, the results of the exploratory
analysis suggest that the two crash time series from the comparison and enforcement
zone are analogous, which is distinguishable from random fluctuation.
Figure 27: Change in total target crashes by year (comparison group vs. enforcement zone)
Figure 28: Change in total PDO crashes by year (comparison group vs. enforcement zone)
5 9
In order to test whether or not the past crash trends within the comparison zone are
statistically similar to those within the enforcement zone, we used the odds ratio as in
prior studies (Hauer 1997; Wong et al. 2005). If the past crash trends within the
comparison zone are similar to those at the enforcement zone, the population odds ratio
defined in Equation (14) should be equal to 1. Since the estimate of the odds ratio is non-linear,
an unbiased estimator is obtained using the delta approximation:
􀁬
1
1
1 1
t t 1 1 1 ,
t
t t t t
M K
K M K M
ω
−
+
+ +
⋅ ⎛ ⎞
= ⋅ ⋅⎜⎝ + + ⎟⎠
(17)
where 􀁬t ω
is the estimate for the odds ratio during period t and the rest of the notation is
as defined previously (see ‘The Four-Step Procedures for Before-and-After Study’ on
page 49). Therefore, the average of the estimates for the odds ratios is
􀁬 1
1
1 ,
1
B
t
B t
ω ω
−
=
= ⋅
− Σ (18)
and the variance of the mean of the odds ratios is
􀁬 2 1 2 2
1
[ ] 1 1 ( 1) .
1 2
B
t
t
S B
B B
ω ω ω
−
=
⎡ ⎧ ⎫⎤
= − ⋅⎢⎣ − ⎩⎨ − − ⎭⎬⎥⎦
Σ (19)
Table 20: Estimates for the odds ratios and 95% CI for the estimates
Crash type and severity Estimate for the 95% confidence interval
odds ratio Lower Upper
Single-Vehicle 1.01 0.94 1.08
Side-swipe (same) 1.75 0.06 3.44
Rear-end 0.82 0.57 1.07
Other 1.14 0.68 1.59
All crashes
Total 1.02 0.84 1.20
Single-Vehicle 1.02 0.88 1.17
Side-swipe (same) 1.32 0.33 2.32
Rear-end 0.77 0.52 1.03
Other 0.92 0.46 1.38
PDO
crashes
Total 1.00 0.84 1.16
Single-Vehicle 1.07 0.04 2.11
Side-swipe (same) 0.87 -0.09 1.84
Rear-end 0.87 0.34 1.40
Other 0.83 0.21 1.45
Injury
crashes
Total 1.02 0.65 1.40
Table 20 shows the odds ratio test results for the comparison zone illustrated in Figure 26.
Since the estimates for the odds ratios are close to 1 and all 95% CIs contains the
expected value 1 under the assumption of the BA study with a comparison group, the
comparison ratios from the comparison zone are suitable. Note that the selected
60
comparison zone should not be employed in the BA study with a comparison group if the
confidence interval of the odds ratios does not include 1.
Consequently, we estimated the comparison ratios from the comparison zone. Note that
the comparison ratio, (N/M)/(1+1/M), is the ratio of the number of crashes in the before
period to the number of crashes in the program period in the comparison zone. Table 21
shows the estimated comparison ratios and associated standard deviations, in which the
comparison ratios were estimated by crash type, severity, and year. It is also noteworthy
that we used annual comparison ratios instead of using a single comparison ratio because
the safety of the enforcement zone changed over time as shown in Figure 27 and Figure
28. For example, the comparison ratio of the single-vehicle crashes in year t is:
1 ( ) P 1 1 ,
C
t t
r t N
M M
− ⎛ ⎞
= ⋅⎜ + ⎟
⎝ ⎠
􀀃 (20)
where t M is the observed number of the single-vehicle crashes that occurred in the
comparison zone in year t, and P N is the observed number of the single-vehicle crashes
that occurred in the comparison zone in the program period.
The comparison ratios greater than 1 indicate an increase in crashes, while ratios less than
1 indicate a decrease in crashes in the comparison zone during the program period. For
example, the total number of single-vehicle crashes increased by 58% in the comparison
zone from 2001 to 2006, and the total number of single-vehicle crashes increased by 8%
in the comparison from 2005 to 2006.
Table 21: Estimates of the comparison ratio
Crash type and severity Year
2001 2002 2003 2004 2005
Single-Vehicle 1.58 0.98 1.09 1.02 1.08
Side-swipe (same) 2.31 1.56 1.36 1.15 1.13
Rear-end 4.36 2.39 1.86 1.16 1.20
All crashes
Other 2.04 1.28 1.28 1.19 1.09
Single-Vehicle 1.45 0.90 1.03 0.98 1.00
Side-swipe (same) 2.37 1.66 1.35 1.17 1.14
Rear-end 4.46 2.57 1.97 1.14 1.25
PDO crashes
Other 1.82 1.03 1.15 1.15 0.92
Single-Vehicle 1.72 1.16 1.16 1.06 1.18
Side-swipe (same) 1.48 1.01 1.09 0.87 0.90
Rear-end 3.46 1.88 1.55 1.13 1.06
Injury crashes
Other 1.51 1.51 1.12 0.91 1.20
61
4.3.3 Results of the Before-and-After Study with a Comparison Group
Using the estimated comparison ratios shown in Table 21, the predicted values of π for
each crash type and severity are obtained. For example, the π for the total single-vehicle
crash was predicted as shown in Equation (21):
􀁬 ( ) ,
B
C d C t
t
π =r⋅Σr􀀃 t⋅K (21)
where Kt is the observed number of single-vehicle crashes in year t, r􀀃C(t) is the
estimated comparison ratio for the single-vehicle crashes in year t, B is the total number
of years during the before period, and rd is the ratio for duration. Equation (21) is a
variation of Equation (12) to account for the change in safety for year, crash type, and
severity. Table 22 shows the estimated values for π, λ, δ, and θ as well as the estimated
standard deviation for δ and θ of four collision types: single-vehicle, side-swipe (same),
rear-end, and other crashes. In addition, the estimates are provided for three categories:
total crashes, property-damage-only (PDO) crashes, and injury crashes (all non-PDO
crashes). The significance of the estimates was tested with the conditional binomial test
as well as the normal approximation test (Griffin and Flowers 1997; Hauer 1996;
Przyborowski and Wilenski 1940; Shin and Washington 2007a).
Table 22: Results of the BA study with a comparison group
Crash estimates Impact estimates
Crash type and severity 􀁬 π
􀀃 λ
􀀃θ 1 􀀃δ 2
Single-Vehicle 46.53 19 0.41 (0.10)3*** 27.53 (5.62) ***
Side-swipe (same) 17.68 12 0.67 (0.21) * 5.68 (4.19) *
All target crashes Rear-end 23.36 23 0.96 (0.24) 0.36 (5.85)
Other 12.47 2 0.16 (0.11) *** 10.47 (2.40) ***
Single-Vehicle 9.42 6 0.62 (0.27) * 3.42 (2.93) *
Side-swipe (same) 3.44 2 0.55 (0.39) 1.44 (1.67)
Injury crashes Rear-end 6.67 8 1.14 (0.46) -1.33 (3.23)
Other 3.94 1 0.24 (0.23) ** 2.94 (1.48) **
Single-Vehicle 35.56 13 0.36 (0.10) *** 22.56 (4.71) ***
Side-swipe (same) 13.38 10 0.73 (0.25) 3.38 (3.78)
PDO crashes Rear-end 16.23 15 0.90 (0.27) 1.23 (4.84)
Other 7.46 1 0.13 (0.13) ** 6.46 (1.74) **
Total target crashes 100.03 56 0.56 (0.08) *** 44.03 (8.95) ***
Total injury crashes 23.47 17 0.72 (0.19) * 6.47 (4.73) **
Total PDO crashes 72.63 39 0.54 (0.09) *** 33.63 (7.56) ***
Note: * p<0.2;** p<0.1;***p<0.01 for H0: θ=1 or H0: δ=0.
1 Percent change in crash from the before to the program period is (θ–1)×100.
2 Positive sign indicates decrease in crash for the program period
3 For parameter estimates, the associated standard deviations are in parentheses.
Figure 29 illustrates the percent changes in target crash for each collision type and
category, in which the percent changes are (􀀃θ − 1)×100. Therefore, the negative values
indicate the crash reduction, while the positive values indicate the increase in crashes
62
during the program period. For example, the percent change for total single-vehicle
crashes (–59%) in