SAFETY PERFORMANCE ANALYSIS OF TSMO: 

A PRACTICAL APPROACH FOR ASSESSING 

TRAFFIC SIGNAL COORDINATION EFFECTS 

ON CRASH PROBABILITY AND SEVERITY 

FHWA Safety Program 

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http://safety.fhwa.dot.gov 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

ii

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Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

iii

TECHNICAL DOCUMENTATION PAGE

1. Report No.

FHWA-SA-19-043

2. Government Accession 

No.

3. Recipient's Catalog No.

 

4. Title and Subtitle

Safety Performance Analysis of TSMO: A Practical Approach for Assessing 

Traffic Signal Coordination Effects on Crash Probability and Severity

5. Report Date

November 2019 

6. Performing Organization Code

7.Author(s) 

Porter, R.J., Gooch, J., and Dunn, M. 

8. Performing Organization Report No.

9. Performing Organization Name and Address

Vanasse Hangen Brustlin, Inc (VHB)

940 Main Campus Drive, Suite 500

Raleigh, NC 27606 

10. Work Unit No.

11. Contract or Grant No.

DTFH61-05-D-00024 (VHB)

12. Sponsoring Agency Name and Address

Federal Highway Administration Office of Safety 

1200 New Jersey Ave., SE

Washington, DC 20590

13. Type of Report and Period

Final Report, July 2017 – November 

2019 

14. Sponsoring Agency Code FHWA

15. Supplementary Notes

The contract manager for this report was Jerry Roche, Federal Highway Administration Office of Safety. 

16. Abstract

The Federal Highway Administration (FHWA) Office of Safety, in cooperation with the Highway Safety Manual (HSM) 

Implementation Pooled Fund Study, recently completed a safety analysis needs assessment for TSMO. The safety analysis 

needs assessment characterized the current state of practice, knowledge, and skills for quantifying the safety performance 

effects of TSMO. It also identified gaps in the existing body of knowledge and corresponding needs, which will provide the 

foundation for future research activities and advancements in practice. One group of needs focused on exploring sub-annual 

safety data collection and analysis methods to address the dynamic conditions under which TSMO strategies operate. This 

document presents one such sub-annual analysis method: probabilistic models of crash occurrence and severity to estimate 

how the characteristics of vehicle arrivals in relation to traffic signal timing affect safety performance at a signalized 

intersection. The analysis method is presented in the context of evaluating the effects of traffic signal coordination on the 

occurrence and severity of common intersection crash types. Little is known to date on the safety performance impacts of 

traffic signal timing due to the inability of commonly used annual analysis methods to capture the microscopic variability 

in traffic signal timing plans, vehicle arrivals, and resulting safety performance over the course of a day. The method in this 

document is a shorter-term analysis option (e.g., 15-minute time periods). The analysis focuses on rear-end and right-angle 

crashes, as those are common intersection crash types assumed to be affected by traffic signal timing. The results of the 

analysis are models that relate the probability of these crash types and their severity on a signalized intersection approach to 

the characteristics of vehicle arrivals in relation to traffic signal timing on that same intersection approach. 

17. Key Words: 

traffic signal coordination; safety performance; 

crash probability; crash severity 

18. Distribution Statement

No restrictions.

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this 

page) Unclassified

21. No. of Pages

 42

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed pages authorized 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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Table of Contents

INTRODUCTION......................................................................................... 1

SAFETY PERFORMANCE ANALYSIS QUESTION................................ 3

DATA NEEDS............................................................................................... 4

SAFETY PERFORMANCE ANALYSIS STEPS – ESTIMATING 

EFFECTS OF TRAFFIC SIGNAL COORDINATION .............................. 8

SUPPORTING TOOLS.............................................................................. 29

DOCUMENTING ANALYSIS AND REPORTING RESULTS............... 30

BROADER APPLICATIONS..................................................................... 31

REFERENCES .............................................................................................. 32
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

vi

List of Tables

Table 1. Notation and definitions for crash probabilities and model functions.......... 5

Table 2. Notation and definitions for traffic signal timing and other intersection 

variables. ............................................................................................................................. 6

Table 3. Example data structure for estimating the effects of vehicle arrival 

characteristics in relation to signal timing on rear-end and right-angle crash 

probability........................................................................................................................... 7

Table 4. Multinomial logistic regression results from Li & Tarko.(8).......................... 12

Table 5. Average model inputs under existing conditions at the approach. ............15

Table 6. Average model inputs under proposed conditions at the approach...........16

Table 7. The probability of a crash within an average 15-minute period with and 

without coordination.......................................................................................................19

Table 8. Example data structure for estimating the rear-end severity model.........23

Table 9. Example binary logistic regression model of crash severity for rear-end 

crashes estimated by Li & Tarko.(8) ...............................................................................25

Table 10. Example binary logistic regression model of crash severity for right-angle 

crashes estimated by Li & Tarko.(8) ...............................................................................25

Table 11. Crash type and severity probability during the average 15-minute period.

...........................................................................................................................................28

 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

vii

List of Figures

Figure 1. Graphic. Potential outcomes for a 15-minute period on a signalized 

intersection approach. ...................................................................................................... 8

Figure 2. Equation. Function associated with a rear-end crash occurring on the 

approach within a 15-minute analysis period. ................................................................ 9

Figure 3. Equation. Function associated with a right-angle crash occurring on the 

approach within a 15-minute analysis period. ................................................................ 9

Figure 4. Equation. Probability of a rear-end crash on the approach within a 15-

minute analysis period. ...................................................................................................10

Figure 5. Equation. Probability of a right-angle crash on the approach within a 15-

minute analysis period. ...................................................................................................10

Figure 6. Equation. Probability that neither a right-angle nor rear-end crash occurs 

on the approach within a 15-minute analysis period. ..................................................11

Figure 7. Equation. Example function associated with a rear-end crash occurring on 

the approach within a 15-minute analysis period. .......................................................13

Figure 8. Equation. Example function associated with a right-angle crash occurring 

on the approach within a 15-minute analysis period. ..................................................13

Figure 9. Equation. Example calculation of function of rear-end crash with no signal 

coordination. ....................................................................................................................17

Figure 10. Equation. Example calculation of function of right-angle crash with no 

signal coordination. .........................................................................................................17

Figure 11. Equation. Example calculation of probability of rear-end crash with no 

signal coordination. .........................................................................................................17

Figure 12. Equation. Example calculation of probability of right-angle crash with no 

signal coordination. .........................................................................................................18

Figure 13. Equation. Example calculation of probability of other outcome with no 

signal coordination. .........................................................................................................18

Figure 14. Equation. Example calculation of function of rear-end crash with signal 

coordination. ....................................................................................................................18

Figure 15. Equation. Example calculation of function of right-angle crash with signal 

coordination. ....................................................................................................................18

Figure 16. Equation. Example calculation of probability of rear-end crash with 

signal coordination. .........................................................................................................18

Figure 17. Equation. Example calculation of probability of right-angle crash with 

signal coordination. .........................................................................................................18

Figure 18. Equation. Example calculation of probability of other outcome with 

signal coordination. .........................................................................................................19

Figure 19. Equation. Probability that a rear-end crash will result in at least one 

fatality or injury................................................................................................................21

Figure 20. Equation. Probability that a right-angle crash will result in at least one 

fatality or injury................................................................................................................21
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

viii

Figure 21. Equation. Probability that a rear-end crash will not result in a fatality or 

injury. ................................................................................................................................24

Figure 22. Equation. Probability that a right-angle crash will not result in a fatality 

or injury.............................................................................................................................24

Figure 23. Equation. Probability that a rear-end crash will result in at least one 

fatality or injury................................................................................................................26

Figure 24. Equation. Probability that a right-angle crash will result in at least one 

fatality or injury................................................................................................................26

Figure 25. Equation. Example calculation of probability of a rear-end crash resulting 

in a fatality or injury with no signal coordination.........................................................26

Figure 26. Equation. Example calculation of probability of a rear-end crash resulting 

in property damage only with no signal coordination.................................................26

Figure 27. Equation. Example calculation of probability of a right-angle crash 

resulting in a fatality or injury with no signal coordination. .......................................26

Figure 28. Equation. Example calculation of probability of a right-angle crash 

resulting in property damage only with no signal coordination.................................27

Figure 29. Equation. Example calculation of probability of a rear-end crash resulting 

in a fatality or injury with signal coordination..............................................................27

Figure 30. Equation. Example calculation of probability of a rear-end crash resulting 

in property damage only with signal coordination. .....................................................27

Figure 31. Equation. Example calculation of probability of a right-angle crash 

resulting in property damage only with signal coordination. .....................................27

Figure 32. Equation. Example calculation of probability of a right-angle crash 

resulting in property damage only with signal coordination. .....................................27
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

ix

ACRONYMS 

AASHTO American Association of State Highway and Transportation Officials

CMF crash modification factors

FHWA Federal Highway Administration

FI fatal or injury crash

HSM Highway Safety Manual

MAP-21 Moving Ahead for Progress in the 21st Century

PDO property-damage only

RA right-angle crash

RE rear-end crash

TSMO Transportation Safety Management and Operations 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

1 

INTRODUCTION

Moving Ahead for Progress in the 21st Century (MAP-21) defines Transportation Systems 

Management and Operations (TSMO) as an “integrated set of strategies to optimize the 

performance of existing infrastructure through the implementation of multimodal and 

intermodal cross-jurisdictional systems, services, and projects designed to preserve capacity and 

improve security, safety, and reliability of the transportation system.” TSMO offers agencies a 

wide range of potential strategies for addressing system- and project-level performance needs 

with cost-effective, tailored solutions. State and local agencies are increasingly recognizing 

TSMO as a core business area in support of maximizing the performance of their transportation 

infrastructure and making better use of resources. Some regions in the United States have 

found it useful to develop TSMO plans to define a common vision for TSMO in the region, 

develop performance objectives to guide the selection of TSMO strategies, and identify 

performance measures that will enable a region to track progress towards their objectives. 

TSMO plans also identify potential policies, services, and projects to make progress towards 

the performance objectives.

Performance analysis helps agencies make sound decisions on which TSMO policies, services, 

and projects to pursue as part of performance-based planning and programming. A performance 

analysis of a TSMO strategy might quantify, for example, how the strategy would be expected 

to affect measures of travel time, travel time reliability, pollutants/air quality, and the number 

and severity of traffic crashes. An agency could monetize these changes and determine an 

overall benefit-cost ratio for the investment. 

The ability for agencies to quantify the effects of TSMO strategies on the number and severity 

of traffic crashes is limited when compared to similar abilities for other performance measures 

(e.g., travel times, vehicle emissions). The Federal Highway Administration (FHWA) Office of 

Safety, in cooperation with the Highway Safety Manual (HSM) Implementation Pooled Fund 

Study, recently completed a safety analysis needs assessment for TSMO. While safety and 

TSMO have clear interrelationships, the needs assessment concluded there is incompatibility 

between many existing safety performance analysis methods and tools and the characteristics of 

TSMO. For example, few TSMO strategies have robust crash modification factors (CMFs). In 

addition, the predictive analysis methods in the First Edition of the American Association of 

State Highway and Transportation Officials (AASHTO) HSM do not consider daily, hourly, or 

sub-hourly variations in traffic characteristics and the road environment that are a key part of 

fully assessing the safety performance of TSMO.(1) The safety analysis needs assessment 

characterized the current state of practice, knowledge, and skills for quantifying the safety 

performance effects of TSMO. It also identified gaps in the existing body of knowledge and 

corresponding needs, which will provide the foundation for future research activities and 

advancements in practice. 

One group of needs focused on exploring sub-annual safety data collection and analysis 

methods to more effectively address the dynamic conditions under which TSMO strategies 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

2 

operate. This document presents one such sub-annual analysis method: probabilistic models of 

crash occurrence and severity to estimate how the characteristics of vehicle arrivals in relation 

to traffic signal timing affect safety performance on a signalized intersection approach. The 

analysis method is presented in the context of evaluating the effects of traffic signal 

coordination on the occurrence and severity of common intersection crash types. Little is 

known to date about the safety performance impacts of traffic signal timing and coordination 

due to the inability of commonly used annual analysis methods to capture the microscopic 

variability in traffic signal timing plans, vehicle arrivals, and resulting safety performance over the 

course of a day. The method in this document is a shorter-term analysis option (e.g., 15-minute 

time periods). 

This document is intended to assist researchers and practitioners interested in exploring and 

testing probabilistic models of crash occurrence and severity in the traffic signal coordination 

context. Following an overview of traffic signal coordination and the analysis question, the 

content covers the data definitions and requirements, analysis steps, supporting tools, and 

effective practices for reporting the results and documenting assumptions and limitations. The 

document concludes with a section on other potential TSMO-related safety analysis applications 

of the method.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

3 

SAFETY PERFORMANCE ANALYSIS QUESTION

Traffic signal coordination involves the synchronization of multiple signalized intersections to 

enhance the operation of one or more directional movements in a system. The synchronization 

occurs by coordinating traffic signal timing patterns and algorithms.(2) The primary intent of 

coordinating traffic signals is to improve vehicle flow along the coordinated street by reducing 

travel times, stops, and delay. Coordination can be a relatively low-cost method for improving 

the operational performance of a corridor or network. While operational improvements are 

generally the primary motivation for implementing traffic signal coordination, several studies have 

explored its potential safety effects.(3,4,5,6,7,8) The results of these studies are mixed and suggest 

that determining the safety performance effects of traffic signal coordination is a challenging

pursuit. One published paper by Li & Tarko noted that crash prediction model development and 

analysis conducted at the annual level (common to safety performance analysis) cannot capture 

the microscopic variability of traffic signal timing plans, vehicle arrivals, and resulting safety 

performance over the course of a day.(9,10)

 They performed a study that examined 36 coordinated 

arterial intersections in Indiana and developed probabilistic models of crash occurrence and 

severity to quantify how the characteristics of vehicle arrivals in relation to traffic signal timing 

affected safety performance of the intersection approaches. 

Based on the work of Li & Tarko, this document outlines a method for analyzing how the 

characteristics of vehicle arrivals in relation to traffic signal timing affect the safety performance 

of signalized intersection approaches. The document focuses on two crash types: 1) rear-end 

crashes involving two or more vehicles on a major street approach and 2) right-angle crashes

between a vehicle entering an intersection from a major street and a vehicle entering the 

intersection from the minor street, regardless of their intended maneuvers at the intersection. 

These are two intersection crash types assumed to be affected by traffic signal timing and 

coordination. In incorporating crash severity, the analysis covers four crash type/severity 

classifications: rear-end fatal or injury crash (FI|RE), rear-end property-damage only crash 

(PDO|RE), right-angle fatal or injury crash (FI|RA), and right-angle property-damage only crash 

(PDO|RA). The results of the analysis are models that relate the probability of these crash 

types and their severity on an intersection approach to the characteristics of vehicle arrivals in 

relation to traffic signal timing on that same intersection approach. Flexibility exists to extend 

the analysis method to other crash types that may be affected by the level of traffic signal 

coordination along a street, such as crashes involving pedestrians and bicyclists. 

 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

4 

DATA NEEDS

Access to several datasets is key to performing this analysis. The two most crucial are crash data 

and traffic signal timing data, including the characteristics of vehicle arrivals. Crash data can come 

from police records or other similar sources and should be limited to the influence area of the 

studied intersections. Determining the extent of an intersection’s influence area is a subject of 

ongoing research, but there are several commonly used practices. For example, Harwood et al. 

used 250 feet as the influence area for urban and suburban arterial intersections when developing 

predictive methods for the HSM.

(11) Any crashes within that distance must have also been coded 

in the crash report as “at intersection” or “intersection-related” for consideration in their 

analysis. The crash data should include the date, time, location, intersection approach, type, and 

severity of the crash as well as any other relevant information. Because these analyses are 

performed using short time intervals (e.g., 15-minutes) and at the intersection approach level, it 

is important to verify the reported time of crash is accurate enough for the periods used in the 

analysis and the location-related information is accurate enough for assignment to a specific 

intersection approach. The traffic signal timing data should include coordination-related variables 

like cycle lengths, offsets, and splits. Other variables that may inform the analysis include yellow 

times, all-red times, and minimum and maximum green times. 

It is necessary to collect information on vehicle arrival characteristics for the intersection

approaches being studied. The vehicle arrival characteristics of interest are those related to the 

level of coordination through the corridor. Some data collected and analyzed by Li & Tarko 

included vehicle arrival rates in the first and second half of the green and red phases, the number

of vehicles arriving in the first two seconds of the green and red phases, and the total vehicle 

arrival rate at the intersection approach. The most desirable way to collect these data is likely 

through acquiring counts taken by the signal system itself (i.e., detector-based high-resolution 

traffic data). Using data collected by the traffic signal controller allows for the vehicle arrival 

characteristics to be easily integrated with the active traffic signal phases for the analysis. 

Geometric data, such as the distance between intersections, the number of through and turning 

lanes, speed limits, and intersection widths, can also be incorporated into the analysis of crash 

probability and severity. For instance, the presence of dedicated right turn lanes at an intersection 

may be associated with a decreased probability of rear-end crashes. The distance between 

intersections is an important factor for developing traffic signal coordination. Table 1 and table 2

contain the notation and definitions of the variables needed for the safety performance analysis. 

Table 3 shows an example structure of a database for estimating the models described in this

document. In this example, one row of the database represents one intersection approach 

observed for a 15-minute period. The entries of crash type (rear-end, right-angle) and crash 

severity (FI, PDO) columns indicate whether a crash of the given type or severity occurred on 

the approach during the 15-minute period (0 indicates a crash of the given type/severity did not 

occur; 1 indicates a crash of the given type/severity did occur). Analysts applying this method can 

try different analysis periods (e.g., 30 minutes, 60 minutes) and include vehicle arrival and other 

intersection variables that are of most interest to their agencies.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

5 

Table 1. Notation and definitions for crash probabilities and model functions. 

Variable Description

URE Function that can be used to calculate the probability of a rear-end crash

URA Function that can be used to calculate the probability of a right-angle crash

PRE Probability that a rear-end crash will occur within a 15-minute interval on the approach

PRA Probability that a right-angle crash will occur within a 15-minute interval on the 

approach

POther Probability that neither a right-angle nor rear-end crash will occur within a 15-minute 

interval on the approach

PFI Probability that a right-angle or rear-end crash will result in a fatality or injury

PFI|RE Probability that a rear-end crash will result in at least one fatality or injury

PPDO|RE Probability that a rear-end crash will not result in a fatality or injury

PFI|RA Probability that a right-angle crash will result in at least one fatality or injury

PPDO|RA Probability that a right-angle crash will not result in a fatality or injury
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

6 

Table 2. Notation and definitions for traffic signal timing and other intersection 

variables. 

Variable Description (Units)

R1 Indicator variable for whether more than 25 percent of traffic on an intersection 

approach arrives in the first half of the red phase (1 if true; 0 otherwise)

(unitless) 

BRVolMax The number of vehicles arriving on the approach in the first two seconds of the 

red phase (vehicles)

BGVolMax The number of vehicles arriving on the approach in the first two seconds of the 

green phase (vehicles)

Wint Indicator variable for winter (observation is in January, February, November, 

December) (1 if true; 0 otherwise) (unitless) 

AM Indicator variable for morning (observation is before noon) (1 if true; 0 

otherwise) (unitless) 

RL Indicator variable for right-turn lane on approach (1 if present; 0 otherwise)

(unitless) 

PSL Posted speed limit on the approach roadway (miles per hour)

TrTimeLt15 Indicator variable if the travel time from the upstream intersection is less than 15 

seconds (1 if true; 0 otherwise) (unitless) 

TrTimeGt40 Indicator variable if the travel time from the upstream intersection is greater 

than 40 seconds (1 if true; 0 otherwise) (unitless) 

G2 Indicator variable for whether more than 25 percent of traffic on an intersection 

approach arrives in the second half of the green phase (1 if true; 0 otherwise)

(unitless) 

CPH The average number of cycles per hour at the intersection (cycles per hour)

xi Covariates describing the intersection approach during a fifteen-minute period, 

including traffic and signal conditions (units vary)

a, bi Regression constant (aa) and coefficients corresponding to each covariate (bbii) 

(unitless) 

VolTotal Total approach volume rate (vehicles per hour per lane)

YShort Indicator variable noting if the yellow interval on the approach is shorter than

what is recommended by the Manual on Uniform Traffic Control Devices 

(MUTCD)(12) (1 if true; 0 otherwise) (unitless) 

SR135 Indicator variable noting if the approach was at an intersection along State Route 

135 (1 if true; 0 otherwise) (unitless)

SR431 Indicator variable noting if the approach was at an intersection along State Route 

431 (1 if true; 0 otherwise) (unitless)
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic Signal Coordination Effects on 

Crash Probability and Severity

7 

Table 3. Example data structure for estimating the effects of vehicle arrival characteristics in relation to signal 

timing on rear-end and right-angle crash probability. 

Observation 

ID

Approach Start 

Time

End 

Time

Date Primary 

Road

Secondary 

Road

Posted 

Speed 

Limit 

[MPH]

RearEnd 

Crash

RightAngle 

Crash

FI PDO Distance to 

Upstream 

Intersection 

[Miles]

RR11 GG22

158497 NB 6:30 

AM

6:45 

AM

6/7/2018 Route 1 Route 146 45 0 0 0 0 0.10 0 1 

158498 NB 6:45 

AM

7:00 

AM

6/7/2018 Route 1 Route 146 45 0 0 0 0 0.10 1 0 

158499 NB 7:00 

AM

7:15 

AM

6/7/2018 Route 1 Route 146 45 0 0 0 0 0.10 0 1 

158500 NB 7:15 

AM

7:30 

AM

6/7/2018 Route 1 Route 146 45 0 0 0 0 0.10 0 1 

158501 NB 7:30 

AM

7:45 

AM

6/7/2018 Route 1 Route 146 45 0 0 0 0 0.10 1 0 

158502 NB 7:45 

AM

8:00 

AM

6/7/2018 Route 1 Route 146 45 1 0 0 1 0.10 1 1 

158503 NB 8:00 

AM

8:15 

AM

6/7/2018 Route 1 Route 146 45 0 0 0 0 0.10 1 0 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

8 

SAFETY PERFORMANCE ANALYSIS STEPS – ESTIMATING 

EFFECTS OF TRAFFIC SIGNAL COORDINATION

This section describes a five-step procedure for estimating the probability of a crash (for 

different crash types and severities) on an intersection approach as a function of vehicle arrival

characteristics and traffic signal timing. The analysis is performed at the approach level for 

individual 15-minute periods. Each 15-minute period has five potential outcomes, as shown in 

figure 1. 

Source: FHWA.

Figure 1. Graphic. Potential outcomes for a 15-minute period on a signalized 

intersection approach. 

1. Collect intersection data.

Identify signalized arterial intersections with a range of traffic and signal timing characteristics. 

Collect traffic counts, signal timing plans, vehicle arrival characteristics, geometrics, and crash 

data for the intersection approaches of interest at these study intersections. Combine the 

data into a database with a structure like that in table 3, where one row represents one 

intersection approach observed for a 15-minute period. The “Data Needs” section of this 

document provides additional detail.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

9 

2. Estimate the crash probability model.

Develop a model that predicts the probability that either a rear-end crash occurs, a rightangle crash occurs, or another outcome occurs in a 15-minute period given vehicle arrival, 

signal timing, and other intersection approach characteristics within that same 15-minute 

period. 

Multinomial logistic regression can be used for this step of the analysis because of the three 

possible outcomes for a 15-minute period. A multinomial logistic regression model is used to 

estimate the probabilities of different categorical outcomes occurring when there are more 

than two possible outcomes.(13) 

Estimating a multinomial logistic regression model produces functions (i.e., equations) for all 

outcomes except for a base outcome that is selected by the analyst. In this analysis, the base 

outcome is the “other outcome” that neither a rear-end or right-angle crash occurs. Figure 

2 and figure 3 are examples of functions associated with the two crash types.

Figure 2. Equation. Function associated with a rear-end crash occurring on the 

approach within a 15-minute analysis period.

Figure 3. Equation. Function associated with a right-angle crash occurring on 

the approach within a 15-minute analysis period.

It is worth noting the work from Li & Tarko used as an example focuses solely on crashes 

involving two or more motor vehicles; a vehicle-pedestrian or vehicle-bicycle crash would be 

considered an “other” outcome. However, the method proposed in this guide can be used 

for any crash type. Agencies considering coordination on corridors with significant pedestrian 

or bicycle volumes should consider explicitly incorporating the probability of pedestrian and 

bicyclist crashes as an outcome into the multinomial logit model. In this case, there could be 

four possible outcomes: 1) a rear-end crash occurs, 2) a right-angle crash occurs, 3) a 

pedestrian or bicyclist crash occurs, or 4) another outcome occurs.

The multinomial logistic regression model provides a high level of flexibility in terms of 

model specification, allowing exploration of various possible crash probability relationships 

such as:

• Certain intersection and signal timing characteristics impacting the probability of one 

crash type, but not impacting others. 

• Certain intersection and signal timing characteristics increasing (or decreasing) the 

probability of one crash type, while having the opposite effect on another crash type. 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

10

The main disadvantage of the multinomial logistic regression model is that it is characterized 

by the independence of irrelevant alternatives (IIA) assumption, meaning that it may not 

appropriately handle scenarios with two or more outcomes that are close substitutes. One 

example could be two crash type outcomes that are sometimes difficult to distinguish, such 

as same direction sideswipe versus rear-end crashes of major-road, through moving vehicles 

with minor-road, right-turning vehicles.

As with any statistical method, analysts should be aware of how to assess the analysis dataset 

for accuracy and sample size, including whether there are adequate numbers of the different 

outcomes being modeled occurring in the dataset. Analysts should also be familiar with how 

to specify models, assess the model goodness of fit, test the model against model assumptions 

(like the IIA assumption), and validate the model by testing its predictive performance on 

different datasets than that used to develop the model. Multinomial logistic regression is one 

of several approaches available to analyze more than two discrete outcomes. Other 

alternatives include nested logit regression, classification and regression trees, or a series of 

binary logistic regression models of one of the outcomes versus all others (e.g., a binary 

logistic regression model of rear-end crash probability versus all other outcomes; a second 

binary logistic regression model of right-angle crash probability versus all other outcomes. 

3. Predict the probability of the different crash outcomes as a function of vehicle 

arrival and signal timing characteristics. 

The equations in figure 4 through figure 6 illustrate how to calculate probabilities using the 

functions produced by multinomial logistic regression. For any set of covariates, the sum of 

probabilities across all three outcomes is one. Note that the functions used to calculate 

probability (URE and URA) produce very small results in this particular context of predicting 

crash occurrence during a short time period. As such, the denominators of these probability 

functions are virtually one (i.e., 1 + URE + URA ≈ 1), resulting in probabilities (PRE and PRA) 

which are nearly equal to the respective function results (URE and URA).

Figure 4. Equation. Probability of a rear-end crash on the approach within a 15-

minute analysis period. 

Figure 5. Equation. Probability of a right-angle crash on the approach within a 

15-minute analysis period. 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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Figure 6. Equation. Probability that neither a right-angle nor rear-end crash 

occurs on the approach within a 15-minute analysis period. 

 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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Example – Steps 1 through 3

To demonstrate the application of the method outlined in this document, this example adopts 

the probabilistic models of crash occurrence and severity reported by Li & Tarko to quantify 

how the characteristics of vehicle arrivals in relation to traffic signal timing affected safety 

performance at a sample of intersection approaches in Indiana.(9,10) 

Table 4 provides the multinomial logistic regression model output from Li & Tarko. Figure 7

and figure 8 are examples of how the model output translates to the functions associated 

with each crash type. It is important to note the addition of two indicator variables in Li & 

Tarko’s model (SR135, SR431) that signify whether an intersection approach was on a 

specific route. For example, the variable SR135 has a value equal to one when the intersection 

approach is on State Route 135. It has a value equal to zero if the intersection approach is on 

any other route. These types of variables can be explored when a significant number of 

intersection approaches in the dataset (e.g., 10 percent or more) are from a series of 

signalized intersections along the same route. These types of variables are intended to capture 

the effects of characteristics common to these routes and locations, but not captured in the 

models (e.g., surrounding land use, driver population). They help in obtaining more accurate 

estimates of the traffic signal timing and vehicle arrival effects. 

Table 4. Multinomial logistic regression results from Li & Tarko.(9) 

Variable Rear-End 

Coefficient

RearEnd 

Standard 

Error

RearEnd tStatisticRightAngle 

Coefficient

RightAngle 

Standard 

Error

RightAngle tStatistic

SR135 -2.35 0.345 -7.34 -0.831 0.407 -2.04 

SR431 0.864 0.359 2.41 -1.261 0.460 -2.74 

R1 ∗

BRVolMax

0.0280 0.00813 3.45 0.0334 0.0197 1.69 

BGVolMax 0.0384 0.0110 3.50 0.0370 0.0258 1.44 

Wint -0.290 0.121 -2.41 - - - 

AM -0.291 0.122 -2.39 -0.559 0.279 -0.559 

RL -2.75 0.321 -8.56 -1.15 0.339 -1.145 

PSL 0.158 0.0305 5.17 0.159 0.0394 0.159 

TrTimeLt15 -0.764 0.202 -3.78 -0.668 0.381 -0.668 

TrTimeGt40 0.861 0.163 5.27 - - - 

G2 -0.215 0.122 -1.77 -0.471 0.301 -1.57 

CPH -0.0444 0.0157 -2.82 - - - 

Constant -11.2 1.61 -6.94 -14.00 1.82 -7.70 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

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Figure 7. Equation. Example function associated with a rear-end crash occurring on 

the approach within a 15-minute analysis period.

Figure 8. Equation. Example function associated with a right-angle crash occurring 

on the approach within a 15-minute analysis period.

The sign of the coefficient in front of each variable indicates the direction of the correlation 

between the variable and the outcome’s probability. A positive coefficient indicates that 

increases in the variable result in increases in the probability of that outcome; negative 

coefficients indicate increases in the variable result in decreases in probability of that outcome. 

For example, the models estimated by Li & Tarko show the following associations between 

vehicle arrival characteristics and crash probabilities:

• Higher concentrations of vehicles arriving in the first half of the red signal, especially 

during the first two seconds (R1 ∗ BRVolMax) were associated with higher probabilities 

of both the rear-end and right-angle crash outcomes, as shown by the positive 

coefficients of 0.0280 and 0.0334 in table 4.

• Higher concentrations of vehicles arriving in the first two seconds of the green signal 

(BGVolMax) were associated with higher probabilities of both the rear-end and rightangle crash outcomes, as shown by the positive coefficients of 0.0384 and 0.0370 in

table 4. 

• Higher concentrations of vehicles arriving during the second half of the green signal 

(G2) were associated with lower probabilities of both the rear-end and right-angle 

crash outcomes, as shown by the negative coefficients of -0.215 and -0.471 in table 4, 

respectively.

If an agency were to develop an arterial coordination strategy around these Li & Tarko 

models in order to reduce the probability of crashes, the plan would seek to minimize 

arrival rates during the red phase and the very beginning of the green phase, encouraging 

platooned arrivals towards the second half of the green phase. When the proportion of 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

14

vehicles arriving in the second half of the green phase exceeds 0.25, the Li & Tarko models 

suggest a 19.3 percent reduction in the probability of a rear-end crash and a 37.6 percent 

reduction in the probability of a right-angle crash.

To demonstrate a possible application of these example models, assume that city 

engineers are interested in coordinating traffic signals along an arterial that leads to the 

city center during the AM peak period (6 AM to 10 AM). One of the signalized 

intersections along the arterial is a known safety hot-spot, consistently ranked as a top 

crash location in the city. City officials are interested in whether coordination will affect 

safety performance at this intersection and to what degree. 

To develop inputs for the model, the engineers observed vehicle arrivals at the main 

intersection approach of interest during the AM peak over a period of a few weeks. 

They collected vehicle and signal data in fifteen-minute increments. The data were 

averaged; the results are provided in table 5. 

Traffic engineers for the city then developed a proposed signal coordination plan for the 

arterial corridor. Based on a series of calibrated microsimulations, they were able to 

estimate average inputs for the intersection approach of interest under the proposed 

coordination plan during the AM peak period. The goal of coordination was to 

synchronize vehicle arrivals at each intersection to encourage smooth vehicle flow along 

the corridor. These inputs are summarized in table 6. This proposed coordination plan 

adjusts the signal timing so that fewer than 25 percent of vehicles are predicted to arrive 

during the first half of the red phase and fewer vehicles arrive in the first two seconds of 

the red and green phases (a reduction of 2 vehicles and 7 vehicles every 15 minutes, 

respectively).
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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Table 5. Average model inputs under existing conditions at the approach. 

Variable Description Average

R1 Indicator variable for whether more than 25 percent of traffic on an 

intersection approach arrives to the approach in the first half of the 

red phase (1 if true; 0 otherwise) (unitless) 

1 

BRVolMax The number of vehicles arriving on the approach in the first two 

seconds of the red phase (vehicles)

4 

BGVolMax The number of vehicles arriving on the approach in the first two 

seconds of the green phase (vehicles)

13 

Wint Indicator variable for winter (interval is in January, February, 

November, December) (1 if true; 0 otherwise) (unitless) 

0 

AM Indicator variable for morning (interval is before 12:00 noon) (1 if 

true; 0 otherwise) (unitless) 

1 

RL Indicator variable for right-turn lane on approach (1 if present; 0 

otherwise) (unitless) 

1 

PSL Posted speed limit on the approach roadway (miles per hour) 35 

TrTimeLt15 Indicator variable if the travel time from the upstream intersection 

is less than 15 seconds (1 if true; 0 otherwise) (unitless) 

0 

TrTimeGt40 Indicator variable if the travel time from the upstream intersection 

is greater than 40 seconds (1 if true; 0 otherwise) (unitless) 

0 

G2 Indicator variable for whether more than 25 percent of traffic on an 

intersection approach arrives to the approach in the second half of 

the green phase (1 if true; 0 otherwise) (unitless) 

0 

CPH The average number of cycles per hour at the intersection (cycles 

per hour)

40 

VolTotal Total approach volume rate (vehicles per hour per lane) 470 

YShort Indicator variable noting if the yellow interval on the approach is 

shorter than what is recommended by the MUTCD (1 if true; 0 

otherwise) (unitless) 

0 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

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Table 6. Average model inputs under proposed conditions at the approach. 

Variable Description Average

R1 Indicator variable for whether more than 25 percent of traffic on an 

intersection approach arrives to the approach in the first half of the 

red phase (1 if true; 0 otherwise) (unitless) 

0 

BRVolMax The number of vehicles arriving on the approach in the first two 

seconds of the red phase (vehicles)

2 

BGVolMax The number of vehicles arriving on the approach in the first two 

seconds of the green phase (vehicles)

6 

Wint Indicator variable for winter (interval is in January, February, 

November, December) (1 if true; 0 otherwise) (unitless) 

0 

AM Indicator variable for morning (interval is before 12:00 noon) (1 if 

true; 0 otherwise) (unitless) 

1 

RL Indicator variable for right-turn lane on approach (1 if present; 0 

otherwise) (unitless) 

1 

PSL Posted speed limit on the approach roadway (miles per hour) 35 

TrTimeLt15 Indicator variable if the travel time from the upstream intersection is 

less than 15 seconds (1 if true; 0 otherwise) (unitless) 

0 

TrTimeGt40 Indicator variable if the travel time from the upstream intersection is 

greater than 40 seconds (1 if true; 0 otherwise) (unitless) 

0 

G2 Indicator variable for whether more than 25 percent of traffic on an 

intersection approach arrives to the approach in the second half of 

the green phase (1 if true; 0 otherwise) (unitless) 

1 

CPH The average number of cycles per hour at the intersection (cycles 

per hour)

40 

VolTotal Total approach volume rate (vehicles per hour per lane) 470 

YShort Indicator variable noting if the yellow interval on the approach is 

shorter than what is recommended by the MUTCD (1 if true; 0 

otherwise) (unitless) 

0 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

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Using the inputs in table 5 and table 6, the city engineers calculate the probability of a rear end 

crash or a right-angle crash occurring with and without coordination on the intersection 

approach. A sample of these calculations is provided below.

No Coordination

Figure 9. Equation. Example calculation of function of rear-end crash with no signal 

coordination.

Figure 10. Equation. Example calculation of function of right-angle crash with no 

signal coordination.

Figure 11. Equation. Example calculation of probability of rear-end crash with no 

signal coordination.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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Figure 12. Equation. Example calculation of probability of right-angle crash with no 

signal coordination.

Figure 13. Equation. Example calculation of probability of other outcome with no 

signal coordination.

Coordination

Figure 14. Equation. Example calculation of function of rear-end crash with signal 

coordination.

Figure 15. Equation. Example calculation of function of right-angle crash with signal 

coordination.

Figure 16. Equation. Example calculation of probability of rear-end crash with 

signal coordination.

Figure 17. Equation. Example calculation of probability of right-angle crash with 

signal coordination.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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Figure 18. Equation. Example calculation of probability of other outcome with 

signal coordination.

The crash probabilities are summarized in table 7. As shown in the right-side column, the 

proposed coordination plan reduces the probability of a rear-end crash on the approach by 

almost 45 percent and a right-angle crash by almost 58 percent. 

Table 7. The probability of a crash within an average 15-minute period with and 

without coordination. 

Probability with 

No 

Coordination

Probability with 

Coordination

Percent Change in 

Probability

Rear-End 5.14 ∗ 10-5 2.83 ∗ 10-5 -44.9 

Right-Angle 7.28 ∗ 10-5 3.07 ∗ 10-5 -57.9 

Other 0.99987 0.99994 +6.52 ∗ 10-5

While the individual probabilities seem negligible, one must consider their aggregated effect. 

The probability represents a single fifteen-minute period on one approach; within the four 

hours representing the AM peak period, there are 16 fifteen-minute periods every weekday. 

With five weekdays per week and 52 weeks per year, there are 4,160 fifteen-minute periods 

per year during which this coordination plan will be active. Assuming that no more than one 

crash occurs on the approach during the analysis period, this probability can be converted to an 

expected number of crashes. Summing this number of crashes over the 4,160 potential periods, 

the engineers expect 0.21 rear-end crashes and 0.30 right-angle crashes without coordination, 

while they expect 0.12 rear-end crashes and 0.13 right-angle crashes with coordination.

Given that probabilistic models of crash occurrence over short time periods are relatively new 

to their agency, the city engineers decide to compare the results to adjusted predictions from 

the predictive methodology for urban and suburban four-leg signalized intersections in the HSM

for a check of reasonableness. They use the HSM to develop an annual crash frequency 

prediction under the following assumptions:

• Major road has 3 lanes in each direction.

• Hourly volume per lane (470 vehicles from table 5) represents 8 percent of total daily 

traffic volume and is equal to the traffic volume in the opposite direction, resulting in an 

annual average daily traffic volume of 35,250 vehicles per day.

• Exclusive left-turn lanes on both the major and minor approaches. 

• Left turns are protected on the major approaches and protected/permitted on the 

minor approaches.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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• Minor road daily traffic volume equals 24,000 vehicles per day.

The HSM predictive methodology produces a predicted number of crashes for one year at the 

intersection. This prediction can be converted to rear-end and right-angle crash frequency by 

applying the default crash type distribution for this facility type. These assumptions produce an 

annual crash frequency of 3.4 rear-end crashes per year and 2.0 angle crashes per year. To 

convert these to an estimate of AM peak period crashes on one major road approach on 

weekdays, the city engineers applied the following additional assumptions: 

• The frequency was multiplied by 5/7 to adjust for the ratio of weekdays to number of 

days in the week.

• The frequency was then multiplied by 25 percent, assuming the AM peak period 

represented 1/4 of crashes during weekdays.

• The frequency was multiplied by 35 percent, assuming this major road approach 

accounted for 35 percent of AM peak period crashes at the intersection.

These assumptions resulted in predictions of 0.21 rear-end crashes and 0.13 angle crashes 

during AM peak periods at this approach on weekdays over the course of a year. These values

estimated using the HSM methodology are similar in general magnitude to the predicted 

number of crashes estimated using the probability-driven approach described in this guide. This 

confirms that the individual probabilities over 15-minute periods aggregate to reasonable annual 

predictions. 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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4. Estimate crash severity models and predict severity probabilities.

The next step of the analysis consists of estimating binary logistic regression models to predict 

the probability that right-angle and rear-end crashes that occur result in a fatality or injury 

(FI) or property-damage only (PDO). 

Binary logistic regression can be used to model dependent variables with two possible 

outcomes (e.g., a crash results in at least one fatality or injury or it does not). (13) The resulting 

model predicts the probabilities of the binary outcomes occurring as a function of variables 

that affect the probabilities. In this case, the probability being predicted is the probability of a 

right-angle or rear-end crash resulting in at least one fatality or injury, while the predictive 

variables describe traffic conditions, vehicle arrivals, and signal timing on the approach. 

Figure 19 illustrates the form of the binary logistic regression model describing the 

probability of a fatality or injury given that a rear-end crash occurs (PFI|RE).

Figure 19. Equation. Probability that a rear-end crash will result in at least one

fatality or injury.

Where:

PFI|RE = the probability of at least one fatality or injury given that a rear-end crash occurs. 

xi = covariates describing the traffic and signal conditions. Example covariates include traffic 

volume (VolTotal), duration of the yellow interval (YShort), and vehicle arrival rate in the 

second half of the green phase (G2).

a, bi= regression coefficients.

Similarly, figure 20 illustrates the form of the binary logistic regression model describing the 

probability of a fatality or injury given that a right-angle crash occurs (PFI|RA) 

Figure 20. Equation. Probability that a right-angle crash will result in at least 

one fatality or injury.

Where:

PFI|RA = the probability of at least one fatality or injury given that a right-angle crash occurs.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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xi = covariates describing the traffic and signal conditions. Example covariates include traffic 

volume (VolTotal), duration of the yellow interval (YShort), and vehicle arrival rate in the 

second half of the green phase (G2).

a, bi= regression coefficients.

Analysts can consider the same variables and variable combinations used for the multinomial

logit models in Step 2. The databases used for each severity model are specific subsets of 

the full database previously used for model estimation in Step 2 and illustrated in table 3. 

The database for estimating the severity model for rear-end crashes will only include the 

rows from the full database where the entry for the rear-end crash column equals one (i.e., 

a rear-end crash occurred in that 15-minute period). Similarly, the database for estimating 

the severity model for right-angle crashes will only include the rows from the full database 

where the entry for the right-angle crash column equals one (i.e., a right-angle crash 

occurred in that 15-minute period). Table 8 provides an example for the rear-end crash 

severity model. 

Binary logistic regression is a relatively robust and informative method for modeling 

dependent variables with two possible outcomes. Model results are straight forward to 

interpret. Researchers have applied binary logistic regression in multiple contexts in the 

TSMO-related literature.(9,14,15,16)

 

As with multinomial logistic regression, analysts should be aware of how to assess the 

analysis dataset for accuracy and sample size, including whether there are adequate numbers 

of the rarer of the binary outcomes being modeled occurring in the dataset (e.g., higher 

severity crashes in this case). Analysts should also be familiar with how to specify models, 

assess the model goodness of fit, and validate the model by testing its predictive 

performance on different datasets than that used to develop the model. Binary logistic 

regression is one of several approaches available to analyze binary outcomes. Other 

alternatives include probit regression, classification and regression trees, and rare event 

logistic regression.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic Signal Coordination Effects on 

Crash Probability and Severity

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Table 8. Example data structure for estimating the rear-end severity model.

Observation 

ID

Approach Start 

Time

End 

Time

Date Primary 

Road

Secondary 

Road

Posted 

Speed 

Limit 

[MPH]

RearEnd 

Crash

RightAngle 

Crash

FI PDO Distance to 

Upstream 

Intersection 

[Miles]

RR11 GG22

723609 NB 6:30 

AM

6:45 

AM

6/7/2018 Route 1 Route 146 45 1 0 1 0 0.10 1 0 

231584 SB 7:15

AM

7:30 

AM

6/19/2018 Route 12 Route 13 35 1 0 0 1 0.20 1 0 

153851 SB 6:00

AM

6:15 

AM

6/22/2018 Route 

361

Route 14 55 1 0 0 1 0.12 1 1 

125201 NB 8:15 

AM

8:30 

AM

6/24/2018 Route 28 Route 61 55 1 0 0 1 0.40 0 0 

974845 SB 7:30 

AM

7:45 

AM

6/26/2018 Route 1 Route 111 35 1 0 1 0 0.18 0 0 

315467 NB 6:45 

AM

7:00 

AM

6/29/2018 Route 91 Route 808 45 1 0 0 1 0.61 1 1 

188874 NB 8:00 

AM

8:15 

AM

6/31/2018 Route 12 Route 146 25 1 0 1 0 0.45 0 1 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

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The equations in figure 19 and figure 20 can be used to estimate the probability that a rearend or right-angle crash will result in a fatality or injury. Figure 21 and figure 22 show how 

to estimate PDO probability given these FI probabilities. 

Figure 21. Equation. Probability that a rear-end crash will not result in a fatality 

or injury.

Figure 22. Equation. Probability that a right-angle crash will not result in a 

fatality or injury.

5. Predict the combined crash type and crash severity probabilities. 

Finally, the equations presented in Step 3 and Step 5 can be used to compute the 

probabilities of five outcomes:

1. A rear-end crash with at least one fatality or injury occurs (PRE ∗ PFI|RE). 

2. A rear-end crash without a fatality or injury occurs (PRE ∗ PPDO|RE). 

3. A right-angle crash with at least one fatality or injury occurs (PRA ∗ PFI|RA). 

4. A right-angle crash without a fatality or injury occurs (PRA ∗ PPDO|RA). 

5. No rear-end or right-angle crash occurs (POther).
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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Example – Steps 4 through 5 

In continuing the example application, Table 9 and table 10 show the model coefficients 

estimated by Li & Tarko for the crash severity models for rear-end and right-angle crashes, 

respectively.

Table 9. Example binary logistic regression model of crash severity for rear-end 

crashes estimated by Li & Tarko. (9)

Variable Coefficient Standard Error t-Statistic

SR431 -0.726 0.270 -2.69 

VolTotal -0.00129 0.0005 -2.65 

G2 0.520 0.273 1.90 

Constant -0.538 0.305 -1.76 

Table 10. Example binary logistic regression model of crash severity for right-angle 

crashes estimated by Li & Tarko.(9)

Variable Coefficient Standard Error t-Statistic

YShort 1.720 0.562 3.06 

Wint -1.250 0.634 -1.97 

G2 -1.485 0.660 -2.25 

Constant -0.538 0.305 -1.76 

As with the multinomial logit models in Step 2, coefficients in table 9 and table 10 represent 

the associations between each covariate and the probability of an FI crash. A positive 

coefficient indicates that increases in the variable increase the probability of a crash resulting 

in a fatality or injury; a negative coefficient indicates that increases in the variable decrease 

the probability of a crash resulting in a fatality or injury. For example, the model presented 

in table 9 shows that the probability that a rear-end crash results in a fatality or injury 

increases if more than 25 percent of vehicles arrive in the second half of the green phase 

(G2) with a coefficient of 0.520, while, with a coefficient of -0.00129, the probability 

decreases as total volume on the approach increases (VolTotal). The negative coefficient for 

SR431 (-0.726) implies that rear end crashes on approaches along that route are less likely 

to result in a fatality or injury than the other routes used to develop the model. 

Figure 23 and figure 24 include example models from Li & Tarko for the probability of an 

injury or fatality given that either a rear-end or right-angle crash occurs. 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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Figure 23. Equation. Probability that a rear-end crash will result in at least one 

fatality or injury.

Figure 24. Equation. Probability that a right-angle crash will result in at least 

one fatality or injury.

Having already calculated the change in probability of rear-end and right-angle crashes, the 

engineers wanted to consider the potential change in the severity of these crashes. Example 

applications of the models in table 9 and table 10 are provided below.

No Coordination

Figure 25. Equation. Example calculation of probability of a rear-end crash resulting 

in a fatality or injury with no signal coordination.

Figure 26. Equation. Example calculation of probability of a rear-end crash resulting 

in property damage only with no signal coordination.

Figure 27. Equation. Example calculation of probability of a right-angle crash 

resulting in a fatality or injury with no signal coordination.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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Figure 28. Equation. Example calculation of probability of a right-angle crash 

resulting in property damage only with no signal coordination.

Coordination

Figure 29. Equation. Example calculation of probability of a rear-end crash resulting 

in a fatality or injury with signal coordination.

Figure 30. Equation. Example calculation of probability of a rear-end crash resulting 

in property damage only with signal coordination.

Figure 31. Equation. Example calculation of probability of a right-angle crash 

resulting in property damage only with signal coordination.

Figure 32. Equation. Example calculation of probability of a right-angle crash 

resulting in property damage only with signal coordination.

Multiplying these probabilities with the crash probabilities produces probabilities of the five 

potential outcomes for a fifteen-minute period at this intersection approach with and 

without signal coordination. These probabilities are summarized in table 11. 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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Table 11. Crash type and severity probability during the average 15-minute period. 

Potential 

Outcome 

Equation Probability with 

No 

Coordination

Probability with 

Coordination

Percent 

Change in 

Probability

FI|RE PRE ∗ PFI|RE 1.24 ∗ 10-5 9.88 ∗ 10-6 -20.4%

PDO|RE PRE ∗ PPDO|RE 3.89 ∗ 10-5 1.84 ∗ 10-5 -52.7%

FI|RA PRA ∗ PFI|RA 2.68 ∗ 10-5 3.58 ∗ 10-6 -86.6%

PDO|RA PRA ∗ PPDO|RA 4.59 ∗ 10-5 2.71 ∗ 10-5 -41.1%

Other 0.99988 0.99994 0.017%

Aggregating these number over the 4,160 potential 15-minute periods during weekday AM 

peaks accumulated over one year, the engineers predict 0.05 FI|RE crashes, 0.16 PDO|RE 

crashes, 0.11 FI|RA crashes, and 0.19 PDO|RA crashes without coordination at the intersection 

approach of interest. With coordination, they predict 0.04 FI|RE crashes, 0.08 PDO|RE crashes, 

0.02 FI|RA crashes, and 0.11 PDO|RA crashes.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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SUPPORTING TOOLS

Statistical modeling software is required for estimating the logistic regression models for crash 

probability and crash severity. Statistical software with regression models can be found for free 

or at a cost. As previously mentioned, analysts developing the models should have experience in 

how to assess the analysis dataset for accuracy and sample size, specify models, assess the model 

goodness of fit, test underlying model assumptions, and validate the models by testing their 

predictive performance on different datasets than that used to develop the model. The rest of 

the analysis steps can be executed using Microsoft Excel or another spreadsheet software.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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DOCUMENTING ANALYSIS AND REPORTING RESULTS

Consistent documentation of analyses that inform investment decisions improves the 

transparency and defensibility of those decisions. It helps future officials, planners, and engineers 

know why and how certain decisions were made and provides data and context for those 

decisions. Consistent documentation also provides a valuable record in the event of public or 

legal challenges to a decision and encourages the establishment of a consistent, repeatable analysis 

process. Documentation of the analysis described in this document should generally include:

• A description of the traffic signal coordination project or program. 

• The estimated models developed. 

• Descriptive statistics for each model. 

• A list of any assumptions, along with justification. 

• A summary of the results.

The following information is necessary for this analysis and should form part of the analysis 

documentation: 

• The average traffic arrival characteristics for existing and proposed conditions under the 

signal coordination plan. 

• The average signal phase characteristics for existing and proposed conditions under the 

signal coordination plan.

In addition, the procedure in this document has the following methodological assumptions:

• The method assumes only one crash can occur within the 15-minute observation period. 

The possibility of multiple crashes within one 15-minute observation period is not 

considered. 

• The method assumes that characteristics of vehicle arrivals with respect to signal timing 

can be accurately predicted for a proposed condition.
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

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BROADER APPLICATIONS

This document describes a methodology for estimating the change in safety performance that 

can be expected after enhancing traffic signal coordination on an arterial. Safety performance 

effects are estimated by first developing a multinomial logistic regression model of crash 

outcomes and then developing a binary logistic regression model of crash severity. These same 

general steps can be used to analyze other TSMO strategies where shorter analysis periods are 

desired to capture the microscopic variability of TSMO operation, vehicle arrivals and 

departures, operational conditions, and resulting safety performance over the course of a day. 

Examples may include variable speed limits, dynamic lane use control, adaptive ramp metering, 

and adaptive signal control. 

When extended to other contexts, analysts should tailor the same general steps of this method 

to the strategy of interest. When predicting crash outcomes, the prediction should be limited 

to the times and facilities on which the strategy of interest will have an impact. For example, in 

the case of ramp metering, required data will include the timing of the ramp metering algorithm, 

the periods during which it is operational (if it operates dynamically or at set times of day), and 

the area of analysis should be limited to the road segments in the direct vicinity of the ramps in 

question. Furthermore, the crash type or types analyzed can be changed based on the TSMO 

strategy in question. Analysts should review the strategy to identify which crash types will be 

specifically targeted by the strategy. In the case of the ramp metering example, it may be 

desirable to predict same-direction sideswipe (or merging) crashes along with rear-end crashes.

In addition to these applications, the use of logistic regression for short-term crash prediction 

has other potential applications to safety performance analyses of TSMO. A companion 

noteworthy practice report shows the application of binary logistic regression to estimating 

changes in the occurrence of secondary crashes due to implementing traffic incident 

management strategies aimed and reducing primary incident duration.(17) A final report 

documenting a safety analysis needs assessment for TSMO synthesizes research that used 

logistic regression to relate traffic operational performance to safety performance.(18)
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

32

REFERENCES 

1. AASHTO (2010). Highway Safety Manual. 1st Ed. Washington, D.C. American Association 

of State Highway and Transportation Officials.

2. Koonce, P., Rodegerdts, L., Quayle, S., Beaird, S., Braud, C., Bonneson, J., ..., & Urbanik, 

T. (2008). In Traffic Signal Timing Manual (Chapter 6).

3. Williamson, M.R., Fries, R.N., Qi, Y., & Mandava, P. (2018). Identifying the Safety Impact 

of Signal Coordination Projects Along Urban Arterials Using a Meta-Analysis Method. 

Journal of Traffic and Transportation Engineering, 6, 61-72.

4. Rakha, H., Medina, A., Sin, H., Dion, F., Van Aerde, M., & Jenq, J. (2000). Traffic Signal 

Coordination Across Jurisdictional Boundaries: Field Evaluation of Efficiency, Energy, 

Environmental, and Safety Impacts. Transportation Research Record 1727. 

5. Jolovic, D., Mudgal, A., Tasic, I., Stevanovic, A., & Martin, P.T. (2016). The Impact of 

Traffic signal Control Parameters on Frequency and Severity of Intersection-Related 

Crashes.

6. Tindale, S.A. & Hsu, P. (2005). Crash Data and Signal Coordination: A One-Way Pair 

Case Study. Journal of Safety Research, 36, 481-482.

7. Guo, F., Wang, X., & Abdel-Aty, M. A. (2010). Modeling signalized intersection safety 

with corridor-level spatial correlations. Accident Analysis & Prevention, 42(1), 84-92. 

8. Stevanovic, A., Stevanovic, J., & Kergaye, C. (2013). Optimization of Traffic Signal 

Timings Based on Surrogate Measures of Safety. Transportation Research Part C, 32, 159-

178. 

9. Li, W. & Tarko, A.P. (2011). Effect of Arterial Signal Coordination on Safety. 

Transportation Research Record: The Journal of the Transportation Research Board, 2237, 51-

59.

10. Li, W. & Tarko, A.P. (2008). Methods of Safety Improvements at Coordinated Signals. 

Report No. FHWA/IN/JTRP-2008/3, SPR-3101, Indiana Department of Transportation 

Division of Research, West Lafayette, Indiana. 

11. Harwood, D.W., K.M. Bauer, K.R. Richard, D.K. Gilmore, J.L. Graham, I.B. Potts,..., & E. 

Hauer (2007). Methodology to Predict the Safety Performance of Urban and Suburban 

Arterials. Web-Only Document 129: Phases I and II. NCHRP Project 17-26. Transportation 

Research Board, Washington, D.C.

12. Federal Highway Administration. (2003). MUTCD 2003: Manual on Uniform Traffic Control 

Devices. Federal Highway Administration, Washington, D.C.

13. Kennedy, P. (2008). A Guide to Econometrics. 6th Edition. Malden, MA. Blackwell 

Publishing. 

14. Lee, C., Saccomanno, F., & Hellinga, B. (2002). Analysis of Crash Precursors on 

Instrumented Freeways. Transportation Research Record: Journal of the Transportation 

Research Board, 1784, 1-8. 

15. Abdel-Aty, M., Uddin, N., Pande, A., Abdalla, F., & Hsia, L. (2004). Predicting Freeway 

Crashes From Loop Detector Data by Matched Case-Control Logistic 

Regression. Transportation Research Record: Journal of the Transportation Research Board, 

1897, 88-95. 
Safety Performance Analysis of TSMO: A Practical Approach for Assessing Traffic 

Signal Coordination Effects on Crash Probability and Severity

33

16. Golob, T. F., Recker, W., & Pavlis, Y. (2008). Probabilistic Models of Freeway Safety 

Performance Using Traffic Flow Data as Predictors. Safety Science, 46(9), 1306-1333. 

17. Porter, R.J., Gooch, J., & Dunn, M. (2019). Safety Performance Analysis of TSMO: A Practical 

Approach for Assessing Safety Service Patrol Effects on Secondary Crashes. Report No. 

FHWA-SA-19-042. Federal Highway Administration, Washington, D.C.

18. Porter, R.J., Dunn, M., Hamilton, I., Gooch, J., & Gayah, V. (2019). Safety Analysis Needs 

Assessment for Transportation Systems Management and Operations. Report No. FHWASA-19-041. Federal Highway Administration, Washington, D.C. 
For More Information:

https://safety.fhwa.dot.gov/

FHWA, Office of Safety

Jerry Roche

Jerry.Roche@dot.gov

515-233-7323

FHWA-SA-19-043