Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Introduction of Cooperative Vehicle-toInfrastructure Systems to Improve

Speed Harmonization

PUBLICATION NO. FHWA-HRT-16-023 MARCH 2016
FOREWORD

Cooperative vehicle-highway systems coordinate vehicle communications and remote traffic 

microwave sensors to increase overall system performance and sustainability. One strategy of 

cooperative vehicle-highway systems is speed harmonization, which dynamically adjusts vehicle 

speed recommendations in order to reduce speed differentials. This report describes a 

preliminary experiment of vehicle-to-infrastructure-based speed harmonization in which speed 

guidance is communicated directly to vehicles. This report reviews a set of micro-simulation 

experiments and a limited number of prototype field runs, including site selection, setup, and 

analysis. This report will be of interest to researchers concerned with implementation and utility 

of early cooperative vehicle-highway system deployments.

Paul Pisano

Acting Director, Office of Operations

Research and Development

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

in the interest of information exchange. The U.S. Government assumes no liability for the use of 

the information contained in this document. This report does not constitute a standard, 

specification, or regulation.

The U.S. Government does not endorse products or manufacturers. Trademarks or 

manufacturers’ names appear in this report only because they are considered essential to the 

objective of the document.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve 

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

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ensure continuous quality improvement.
TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-16-023

2. Government Accession No. 3. Recipient’s Catalog No.

4. Title and Subtitle

Introduction of Cooperative Vehicle-to-Infrastructure 

Systems to Improve Speed Harmonization

5. Report Date

March 2016

6. Performing Organization Code: 

7. Author(s)

David Hale, Thomas Phillips, Kelli Raboy, Jiaqi Ma, Patrick 

Su, Xiao-Yun Lu, Hesham Rakha, and Daniel J. Dailey

8. Performing Organization Report No.

9. Performing Organization Name and Address

Leidos, Inc.

11251 Roger Bacon Drive

Reston, VA 20190

10. Work Unit No.

11. Contract or Grant No.

DTFH61-12-D-00020

12. Sponsoring Agency Name and Address

Office of Operations Research and Development

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101-2296

13. Type of Report and Period Covered

Research Report

14. Sponsoring Agency Code

HRDO-20

15. Supplementary Notes

The Contracting Officer’s Representative was Joe Bared, HRDO-20.

16. Abstract

This project executed a preliminary experiment of vehicle-to-infrastructure (V2I)-based speed harmonization 

in which speed guidance was communicated directly to vehicles. This experiment involved a set of microsimulation experiments and a limited number of prototype field runs. The simulation experiments produced 

mixed results in terms of system-wide benefits. The field runs demonstrated that connected and automated 

vehicles can successfully implement V2I-based speed harmonization and significantly reduce speed oscillations 

in their vicinity but do not have a significant impact on aggregate average speeds or travel times. 

17. Key Words

Research, Connected vehicles, Automated 

vehicles, Speed harmonization, Field testing, 

Simulation

18. Distribution Statement

No restrictions. This document is available to the public 

through the National Technical Information Service, 

Springfield, VA 22161.

http://www.ntis.gov

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

50

22. Price

N/A

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized.
ii

SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

NOTE: volumes greater than 1000 L shall be shown in m3

MASS oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") 

TEMPERATURE (exact degrees) o

F Fahrenheit 5 (F-32)/9 Celsius o

C 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit o

F 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

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. 

(Revised March 2003)
iii

TABLE OF CONTENTS

EXECUTIVE SUMMARY .......................................................................................................... 1

SITE SELECTION................................................................................................................. 1

RESEARCH RESULTS......................................................................................................... 4

NEXT STEPS .......................................................................................................................... 4

CHAPTER 1. SIMULATION EXPERIMENTS ....................................................................... 5

SPEED-BASED ALGORITHM............................................................................................ 5

Description.......................................................................................................................... 5

Testing................................................................................................................................. 7

DENSITY-BASED ALGORITHM ....................................................................................... 9

Description.......................................................................................................................... 9

Testing (Part 1: INTEGRATION© Platform) ................................................................... 17

Testing (Part 2: VISSIM® Platform)................................................................................. 19

CHAPTER 2. FIELD EXPERIMENTS ................................................................................... 23

VEHICLE AND INFRASTRUCTURE SETUP ................................................................ 23

Vehicles............................................................................................................................. 23

Infrastructure..................................................................................................................... 23

METHODOLOGY ............................................................................................................... 25

ANALYSIS ............................................................................................................................ 27

Vehicle Control................................................................................................................. 28

Probe Vehicles/Sensors..................................................................................................... 28

Potential Benefits.............................................................................................................. 35

CHAPTER 3. CONCLUSIONS................................................................................................. 37

ACKNOWLDGEMENTS.......................................................................................................... 39

REFERENCES............................................................................................................................ 41
iv

LIST OF FIGURES

Figure 1. Map. Geographic scope of the study area and typical traffic situation in afternoon 

peak hours........................................................................................................................................2

Figure 2. Graph. I-66 probe vehicle actual and average speed trajectories.....................................3

Figure 3. Graph. I-66 probe vehicle actual and average speed trajectories with 

harmonic model ...............................................................................................................................3

Figure 4. Equation. Speed-based algorithm speed advisory in bottleneck ......................................5

Figure 5. Equation. Speed-based algorithm speed advisory upstream of bottleneck ......................5

Figure 6. Equation. Speed-based algorithm minimum group speed approach ................................6

Figure 7. Equation. Speed-based algorithm average group speed approach ...................................7

Figure 8. Equation. Speed-based algorithm TTT adjustment..........................................................8

Figure 9. Equation. Speed-based algorithm TD adjustment............................................................8

Figure 10. Equation. Speed-based algorithm TNOS adjustment.....................................................8

Figure 11. Illustration. Lane-drop bottleneck ................................................................................10

Figure 12. Equation. Steady-state flow as a function of density ...................................................10

Figure 13. Equation. Steady-state speed as a function of density..................................................10

Figure 14. Illustration. Fundamental diagram of traffic flow ........................................................11

Figure 15. Equation. Mathematical formulation of the density-based algorithm..........................12

Figure 16. Equation. Estimation of flow rates...............................................................................12

Figure 17. Equation. Steady-state density as a reverse function of speed .....................................13

Figure 18. Equation. Steady-state density as a reverse function of flow.......................................13

Figure 19. Flowchart. Density-based algorithm logic and advisory speed recommendations ......14

Figure 20. Equation. Density-based algorithm step 1—advisory speed recommendation............15

Figure 21. Equation. Density-based algorithm step 1—optimal flow rate ....................................15

Figure 22. Equation. Density-based algorithm step 2—flow and density conditions ...................15

Figure 23. Equation. Density-based algorithm step 2—time lag...................................................15

Figure 24. Equation. Density-based algorithm step 2—advisory speed recommendation 1.........15

Figure 25. Equation. Density-based algorithm step 2—target flow rate 1 ....................................16

Figure 26. Equation. Density-based algorithm step 2—target flow rate 2 ....................................16

Figure 27. Equation. Density-based algorithm step 2—advisory speed recommendation 2.........16

Figure 28. Equation. Density-based algorithm step 3—advisory speed recommendation 1.........16

Figure 29. Equation. Density-based algorithm step 3—advisory speed recommendation 2.........16

Figure 30. Equation. Density-based algorithm step 3—target flow rate .......................................16

Figure 31. Graph. Vehicle trajectories before and after applying the density-based 

algorithm in INTEGRATION©......................................................................................................19

Figure 32. Map. Field experiment map of system integration.......................................................24

Figure 33. Map. Test segment and trailer locations.......................................................................24

Figure 34. Illustration. Research and probe vehicle placement.....................................................26

Figure 35. Equation. Field experiment speed recommendation ....................................................27

Figure 36. Graph. Control vehicle trajectories and recommendations ..........................................28

Figure 37. Graph. Temporal speed trajectories..............................................................................29

Figure 38. Graph. Spatial speed trajectories..................................................................................29

Figure 39. Graph. Control speed trajectory and smoothed profile ................................................30

Figure 40. Graph. Detrended probe vehicle speed trajectories......................................................31

Figure 41. Graph. PDF of raw data following probe speed trajectory...........................................32
v

Figure 42. Graph. PDF of detrended following probe speed trajectory.........................................32

Figure 43. Graph. PDF of detrended leading probe speed trajectory ............................................33

Figure 44. Graph. PSDs of detrended speed trajectories of the probe vehicles on 

July 8, 2014....................................................................................................................................34

Figure 45. Graph. PSDs of detrended speed trajectories of the probe vehicles on 

September 29, 2015 .......................................................................................................................34

Figure 46. Graph. PSDs of detrended speed trajectories of the probe vehicles on 

October 15, 2015............................................................................................................................35

Figure 47. Graph. PSDs of detrended speed trajectories of the probe vehicles on 

October 21, 2015............................................................................................................................35
vi

LIST OF TABLES

Table 1. System performance impacts of the speed-based algorithm in Aimsun®..........................9

Table 2. Speed harmonization algorithm settings..........................................................................18

Table 3. Density-based algorithm simulation results in INTEGRATION© with limited 

research vehicles............................................................................................................................18

Table 4. Operational MOEs in VISSIM® (three-car case).............................................................20

Table 5. Safety surrogate MOEs in VISSIM® (three-car case) .....................................................20

Table 6. Travel times at various market penetration rates in VISSIM® ........................................21

Table 7. Speeds at various market penetration rates in VISSIM® .................................................21

Table 8. Throughput at various market penetration rates in VISSIM®..........................................21

Table 9. Stops at various market penetration rates in VISSIM® ...................................................21

Table 10. Lane changes at various market penetration rates in VISSIM®.....................................21

Table 11. Cumulative speed difference at various market penetration rates in VISSIM® ............22
vii

LIST OF ABBREVIATIONS

ACC adaptive cruise control

CO2 carbon dioxide

CO carbon monoxide

CMTS connected mobile traffic sensing

CAV connected and automated vehicle

HC hydrocarbons

LHS Latin hypercube sampling

LTM log transformation method

MOE measures of effectiveness

NOx nitrogen oxides

OEM original equipment manufacturer

OD origin-destination

PSD power spectral density

PDF probability density function

RMSE root mean square error

RTMS remote traffic microwave sensor

TD total delay

TNOS total number of stops

TTD total travel distance

TTT total travel time

TFHRC Turner-Fairbank Highway Research Center

V2I vehicle-to-infrastructure

1

EXECUTIVE SUMMARY

The U.S. Department of Transportation’s Federal Highway Administration has initiated a 

research program on cooperative vehicle-to-infrastructure (V2I) highway systems with the 

goal of increasing overall system performance and sustainability, including safety, mobility, 

and environmental impacts. Cooperative vehicle-highway systems coordinate vehicle

communications and remote traffic microwave sensors (RTMSs) in pursuit of these goals. One 

strategy of cooperative vehicle-highway systems is speed harmonization, which dynamically 

adjusts vehicle speed recommendations in order to reduce speed differentials. Speed 

harmonization can be applied near areas of congestion, accidents, or special events to optimize 

mobility and safety. Speed harmonization has been implemented in a few locations in the United 

States with some success, but the current approach faces significant challenges. As presently 

implemented, speed harmonization is conducted with the use of variable speed limit signs or 

dynamic message signs. This method of implementation is susceptible to unpredictable and 

uncoordinated driver response. Moreover, these signs are costly for State and local agencies to 

deploy, operate, and maintain.

Despite these challenges, simulation has shown that speed harmonization does not require 

perfect driver compliance to significantly improving traffic flow and performance.(1,2) In this 

project, researchers performed a preliminary experiment of V2I-based speed harmonization in 

which speed guidance was communicated directly to vehicles. This experiment involved a set 

of micro-simulation experiments and a limited number of prototype field runs.

SITE SELECTION

Speed harmonization is believed to produce significant benefits at sites where excessive vehicle

speed oscillations cause premature formation of congestion and bottlenecks. The section of I-66 

inside the beltway (I-495) approaching Washington, DC, is a congested roadway with one of the 

least dependable travel times in the United States.

(3) Daily recurring congestion at the merge 

of VA-267 into I-66 (and the subsequent lane drops) leads to a “stop-and-go” formation. At 

this site, shown in figure 1, it was hypothesized that speed harmonization could have a 

positive impact.
2

©2016 Google®

Figure 1. Map. Geographic scope of the study area and typical traffic situation in afternoon 

peak hours.

(4)

In order to understand the traffic dynamics on this section of freeway, a number of field runs

were used to identify typical speed trajectories during weekday peak periods. These field runs 

were performed by probe vehicles equipped with Global Positioning System receivers, cell 

phones, and computers. The computers transmitted vehicle trajectories in real time to servers at

the Saxton Transportation Operations Laboratory in McLean, VA. Trajectories were transmitted 

before and during the recurring congested period. Figure 2 illustrates actual probe speed 

trajectories shown in blue plus a computed average trajectory shown in red. The average

trajectory shows a significantly trended periodic component. Large features of the average

trajectory can be described by a sinusoid, as shown in figure 3. The oscillatory trend shown in 

figure 3 will increase fuel consumption and may impact mobility and safety. Given this recurring 

structure in the speed profiles along I-66, the corridor was deemed a suitable candidate for the 

experiment on speed harmonization using connected and automated vehicles (CAVs).
3

1 mi/h = 1.61 km/h

Figure 2. Graph. I-66 probe vehicle actual and average speed trajectories.

1 mi/h = 1.61 km/h

Figure 3. Graph. I-66 probe vehicle actual and average speed trajectories with 

harmonic model.
4

RESEARCH RESULTS

Due to resource constraints, the field experiments could only deploy a maximum of three CAVs. 

Simulation results across three software platforms (VISSIM®, INTEGRATION©, and Aimsun®) 

showed that the introduction of three CAVs, with a goal of harmonizing overall speeds, did not 

produce macroscopic traffic benefits.

(5–7) When analyzing higher CAV penetration rates, the 

simulation experiments produced mixed results.

On the Aimsun® platform, all penetration rates above 10 percent produced corridor-wide travel 

time reductions between 8 and 10 percent. The researchers concluded that this was due to 

congested conditions that minimized lane changing (i.e., if 10 percent of vehicles reduced

their speeds, most other vehicles were impacted). Similar results were observed on the 

INTEGRATION© platform, where all penetration rates above 10 percent produced corridor-wide 

delay reductions between 7 and 11 percent. On the VISSIM® platform, a 1,000-ft (300-m)

freeway segment believed to be most impacted by speed harmonization saw 32, 39, and 

42 percent travel time reductions under penetration rates of 10, 25, and 50 percent, respectively. 

However, corridor-wide travel time reductions were only 1, 2, and 3 percent, respectively.

Although the simulation experiments produced mixed results, the results were positive enough to 

warrant follow-up field experiments. These experiments demonstrated that with modifications to 

the manufacturer-supplied adaptive cruise control (ACC), CAVs can successfully implement 

V2I-based speed harmonization, at least from a mechanical standpoint. From an operational 

standpoint, the field experiments were constrained by the availability of only three CAVs. These 

vehicles were shown to significantly reduce speed oscillations in their vicinity but did not have a 

significant impact on aggregate average speeds or travel times, which is consistent with the 

simulation outcomes.

NEXT STEPS

Future field experiments should thus include a larger number of CAVs. Future algorithm 

development should optimize vehicle speeds to achieve maximum safety benefits. If a bottleneck 

is not yet formed, slowing the right proportion of vehicles could prevent or delay the onset of 

bottleneck formation. If a bottleneck is already formed, slowing all vehicles by the right amount 

could mitigate bottleneck severity. Other factors subject to optimization include CAV

penetration rates, speed reduction magnitudes, and lane-specific congestion levels. The 

remainder of this report summarizes the technical details from phase 1 of the V2I-based speed 

harmonization research.
5

CHAPTER 1. SIMULATION EXPERIMENTS

Prior to the field runs, speed harmonization algorithms were analyzed in micro-simulation 

environments. The simulation experiments examined various levels of CAV market penetration. 

Two speed harmonization algorithms were tested: speed-based and density-based. The speedbased algorithm was tested using Aimsun®, and the density-based algorithm was tested using

INTEGRATION© and VISSIM®. 

SPEED-BASED ALGORITHM

Description

The speed-based algorithm determines advisory speeds for freeway segments upstream and 

downstream of a known bottleneck location based on measured speeds within the bottleneck 

area. The speed-based algorithm is intended to increase throughput and prevent bottleneck 

formation.

Within a bottleneck area, the speed-based algorithm tends to generate advisory speeds 10 to 

50 percent higher than measured bottleneck speeds (see figure 4). Although the algorithm looks 

very simple, its function realizes the control philosophy in previous work.

(8) This approach does 

not claim system optimization yet emphasizes simplicity and practical field implementation.

Figure 4. Equation. Speed-based algorithm speed advisory in bottleneck.

Where:

um(k) = Variable speed advisory at time step k in section m.

= Proportional control gain in section m, where [1.1, 1.5]; default value: = 1.3.

= Measured speed of the bottleneck.

Upstream of a bottleneck area, when traffic congestion approaches capacity levels, the speedbased algorithm tends to generate advisory speeds 10 to 30 percent below measured bottleneck 

speeds (see figure 5). Figure 5 shows that when bottleneck speed decreases, upstream advisory 

speed is proportionally reduced. This is equivalent to reducing flow to the bottleneck. When 

bottleneck speed increases, upstream advisory speed is proportionally increased. This increases 

bottleneck throughput towards its capacity. 

Figure 5. Equation. Speed-based algorithm speed advisory upstream of bottleneck.

Where:

um + 1(k) = Variable speed advisory at time step k in section m + 1.

Vfree = Free-flow speed.

= Measured occupancy in bottleneck section.

um(k) = αm× v�m(k)

αm αm∈ αm

v�m(k)

um + 1(k) = �

Vfree, if o�m(k) < Osw

βm× v�m(k), if o�m(k) ≥ Osw �

o�m(k)
6

Osw = Switch threshold of occupancy close to the capacity flow (suggested value is between 

10.0 and 12.5 percent). 

= Proportional control gain in section m, where [0.7, 0.9]; default value: = 0.8.

The speed-based speed harmonization algorithm streamlines traffic flow on each freeway 

segment. When there are multiple bottlenecks on a segment, advisory speeds for the segments 

between bottlenecks can be determined by distance-based interpolation.

To implement the advisory speeds for each freeway segment, CAVs are assumed to be 

discharged in platoons. The objective is for these vehicles to drive in parallel at the same speed 

on adjacent lanes in order to block all upstream vehicles. This forces all following vehicles to 

comply with the advisory speed.

Due to large variations in driver behavior on I-66, traffic speeds cannot be considered 

homogenous in both time and space. As a result, CAVs could use advisory speeds as set speeds 

but may not be able to drive at those speeds. Moreover, there would be speed differences 

between these CAVs on different lanes. When blocked by other vehicles in slow lanes, CAVs

are expected to lag behind. Such situations have been observed in simulation. Therefore, it is 

necessary to adjust advisory speeds according to CAV speeds at a microscopic level. The 

following describes two methods of speed fusion tested through simulation: minimum group 

speed and average group speed.

Minimum Group Speed

Figure 6 implements an approach that uses the minimum speed of a group of research vehicles 

(i.e., the minimum group speed approach). First, the minimum speed among a group of CAVs is 

selected using lead vehicle speed in each lane. Then for each group and section that the group 

currently resides in, minimum speed is fused with global advisory speed (see figure 6). In 

essence, this fusion approach (based on market penetration rates) dictates that all CAVs must 

drive either at a similar speed or side-by-side. 

( )

( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

min

min min

min min

,

min min

min min

, 50

0.3 0.7 , 40 50

0.5 0.5 , 30 40

0.7 0.3 , 15 30

0.85 0.15 15

m i

im i

des

i m im i

im i

i mi

u k V k

V k uk V k

u k V k uk V k

V k uk V k

V k uk V k

 ≥  + ≤≤ 

 =  + ≤≤

 + ≤≤ 

 + ≤ 

Figure 6. Equation. Speed-based algorithm minimum group speed approach.

Where:

= Variable speed advisory at time step k in section m for a typical group i of CAVs.

= Minimum measured speed at time step k for a typical group i of CAVs.

βm βm∈ βm

ui,m

des(k)

Vi

min(k)
7

Average Group Speed

Figure 7 implements an approach that uses the average speed of a group of research vehicles 

(i.e., the average group speed approach). First, the average speed among a group of CAVs is 

estimated. If there is more than one vehicle in each lane, this is accomplished by selecting the 

average speed among leader vehicles in each lane. Then for each group and each section that the 

group currently resides in, average speed is fused with global advisory speed (see figure 7). In 

contrast with the minimum group speed approach, the average group speed approach dictates that 

CAVs do not need to drive side-by-side. They are allowed to have more speed differential within 

the same group but retain a close proximity, as determined by the weighting factors.

( )

( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

,

, 50

0.3 0.7 , 40 50

0.5 0.5 , 30 40

0.7 0.3 , 15 30

0.85 0.15 15

ave

m i

ave ave

im i

des ave ave

i m im i

ave ave

im i

ave ave

i mi

u k V k

V k uk V k

u k V k uk V k

V k uk V k

V k uk V k

 ≥  + ≤≤ 

 =  + ≤≤

 + ≤≤ 

 + ≤ 

Figure 7. Equation. Speed-based algorithm average group speed approach.

Where:

= Average measured speed at time step k for a typical group i of CAVs.

Testing

The speed-based algorithm was tested on the Aimsun® simulation platform. The results are 

presented in the following subsections.

Calibration

Most default values for parameters such as time headway distribution and variance, maximum 

acceleration and variation, etc., were obtained from Performance Measurement System and Next 

Generation SIMulation data analyses. Two performance parameters were used to quantify the 

discrepancy between field-measured and simulated results in terms of throughput: relative root 

mean square error (RMSE) and the GEH statistic. Throughput comparisons were performed at all 

freeway mainline sensors, and speed comparisons were performed at three sensors.

An iterative calibration process was used. This process included progressive calibration at each 

sensor location from downstream to upstream and then in the reverse direction. This progressive 

calibration was necessary because upstream and downstream flows and speeds affect each other. 

The objective was to match both flows and time-mean speeds at fixed sensor locations. Minor 

demand adjustments were made to correct some sensor measurement errors, which were usually 

about 5 to 10 percent in practice. Engineering judgment was used to perform trial-and-error 

adjustments of both flows and speeds for upstream and downstream traffic situations. To obtain 

unbiased (i.e., “apples-to-apples”) comparisons, it was important to confirm that all demand 

volumes were discharged at the end of each simulation run.

Vi

ave(k)
8

Analysis

The proposed speed-based algorithm was simulated using the calibrated Aimsun® network for 

3 virtual days with compliance rates of 10, 25, 50, and 100 percent. Each date was simulated 

for 10 replications (random number seeds) to get their mean. The following macroscopic 

performance measures were used to evaluate the algorithms’ implementations within simulation: 

total travel time (TTT), total travel distance (TTD), total delay (TD) (obtained by deducting 

hypothetical free-flow travel times from simulated travel times), speed variation (directly reflects 

fluctuations in system-wide speed), total number of stops (TNOS) (used as a system-wide 

performance parameter for traffic smoothness in Aimsun®), and outflow (throughput) changes 

at bottlenecks.

CAV groups were regularly dispatched into the freeway segment from upstream of the 

I-66 and VA-267 merge. All CAVs were in ACC mode with fused speeds as set speeds, and all 

other vehicles were in human driver mode. Dispatching time intervals of 60, 90, 120, 900, and 

1,800 s were used in simulation. In addition to the speed harmonization set speed, two other 

factors affected the practical speeds: downstream traffic and the speed of other vehicles in the 

group. Each lane had at least one CAV lane controlled through the Aimsun® application 

program interface.

Since the simulation model was set during the afternoon peak hours between 3 and 9 p.m., 

different random number seeds produced different demand flow patterns (from entrance ramp 

and freeway mainline), resulting in slightly different total (cumulative) demands. Higher total 

demands within any simulation time interval could result in longer TTT even if the speed 

harmonization algorithm was functioning properly. To overcome this bias, the following 

adjustments shown in figure 8 through figure 10 were applied when estimating percentage time 

improvements for TTT, TD, and TNOS. For example, if TTD increased by 10 percent after 

simulation, then TTT and TD were decreased by 10 percent as a penalty. Here the subscripts 

indicate whether parameters were estimated from the default scenario (default) or from data 

with speed control activated (vsa).

Figure 8. Equation. Speed-based algorithm TTT adjustment.

Figure 9. Equation. Speed-based algorithm TD adjustment.

Figure 10. Equation. Speed-based algorithm TNOS adjustment.

Table 1 shows that the system-wide performance measures when using the average group speed

approach improved under faster dispatch rates. In a real-world field test, the fastest dispatching 

TTT%Change = 

TTTdefault − TTTvsa

TTTdefault

− TTDdefault − TTDvsa

TTDdefault

TD%Change = 

TDdefault − TDvsa

TDdefault

− TTDdefault − TTDvsa

TTDdefault

TNOS%Change = 

TNOSdefault − TNOSvsa

TNOSdefault

− TTDdefault − TTDvsa

TTDdefault
9

rates would be constrained by the total number of CAVs available and the time needed to finish a 

run cycle.

Table 1. System performance impacts of the speed-based algorithm in Aimsun®.

CAV 

Dispatch 

Rate 

(s)

TTT 

(Percent)

TTD

(Percent)

TD

(Percent)

Speed 

Variation

(Percent)

Average

Number 

of Stops

(Percent)

Flow 

Downstream 

of Bottleneck

(Percent)

Flow at

Bottleneck

(Percent)

1,800 -0.63 -0.04 -1.84 0.19 0.070 -0.18 -0.41

900 -1.54 -0.03 -3.46 -0.17 0.180 0.01 -0.31

120 -4.08 0.52 -7.09 -0.97 0.013 0.49 -0.39

90 -4.45 0.66 -5.82 -1.01 -0.230 0.42 -0.57

60 -6.53 0.87 -9.14 -1.94 0.190 0.67 -0.65

DENSITY-BASED ALGORITHM

Description

The objective of the density-based algorithm is to prevent upstream density from exceeding a 

critical density. The algorithm also tries to maximize bottleneck throughput by metering 

upstream flows. The algorithm searches for an optimal density that can maximize the bottleneck 

discharge rates while eliminating capacity drops. In the density-based algorithm, this optimal 

density is called the “target density.”

Figure 11 illustrates a lane-drop bottleneck. The road section is divided into three zones: the 

speed harmonization zone, the acceleration zone, and the bottleneck. In order to develop a speed 

harmonization algorithm, three sets of sensors are placed: one in the speed harmonization zone, 

one directly upstream of the bottleneck, and one directly downstream of the bottleneck. If onand/or off-ramps exist between the speed harmonization zone and the bottleneck, sensors are 

needed on the on- and off-ramps to record traffic flow. Sensors gather volume, speed, and 

occupancy data for use in the algorithm. CAVs in the speed harmonization zone receive advisory 

speed recommendations from a traffic management center to control flow arriving at the 

bottleneck.
10

Figure 11. Illustration. Lane-drop bottleneck.

Where:

SH Zone = Speed harmonization zone.

qs(t) = Flow rate in the speed harmonization zone at time t.

ks(t) = Density of the speed harmonization zone at time t.

vs(t) = Speed in the speed harmonization zone at time t.

= On-ramp flow rate at time t.

= Off-ramp flow at time t.

qu(t) = Capacity of the bottleneck zone at time t.

ku

(t) = Density at capacity of the bottleneck zone at time t.

vu(t) = Speed in the bottleneck zone at time t.

qd(t) = Downstream capacity of the bottleneck at time t.

kd

(t) = Downstream density at capacity of the bottleneck at time t.

vd(t) = Speed downstream of the bottleneck at time t.

The speed harmonization approach assumes that a steady-state fundamental diagram exists to 

relate the traffic stream flow (q), density (k), and speed (v) given the functions in figure 12 and 

figure 13.

Figure 12. Equation. Steady-state flow as a function of density.

Where:

Q(k) = General function Q of k based on a calibrated fundamental diagram.

Figure 13. Equation. Steady-state speed as a function of density.

Where:

V(k) = General function V of k based on a calibrated fundamental diagram.

qi

in(t)

qi

out(t)

q = Q(k)

v = V(k)
11

Figure 14 shows the fundamental diagram for upstream and downstream sections of the 

bottleneck.

Figure 14. Illustration. Fundamental diagram of traffic flow.

Where:

= Capacity directly upstream of the bottleneck.

= Downstream capacity of the bottleneck.

v0 = Advisory speed recommendation.

= Downstream density at capacity of the bottleneck.

= Density at capacity directly upstream of the bottleneck.

= Downstream jam density of the bottleneck.

= Jam density directly upstream of the bottleneck.

In order to avoid a traffic breakdown upstream of the bottleneck, arrivals are constrained at the 

bottleneck. Here, target density k0 (or its equivalent occupancy given that density cannot be 

measured in the field) is set in order to achieve the desired objective. The in-flow rate of the 

bottleneck at the capacity of the bottleneck is controlled.

The primary objective function of the speed harmonization algorithm is to maximize a weighted 

combination of flow downstream of the bottleneck and to minimize speed variability within the 

speed harmonization section, as shown in figure 15.

qc

u

qc

d

kc

d

kc

u

kj

d

kj

u
12

Subject to:

;

;

;

Figure 15. Equation. Mathematical formulation of the density-based algorithm.

Where:

v0(t) = Set of all possible advisory speed recommendations in the speed harmonization zone at 

time t.

T = Total simulation time.

wq = Weight assigned to the flow directly downstream of the bottleneck.

wv = Weight assigned to the speed variability in the speed harmonization zone.

(t) = Measure of speed variability in the speed harmonization zone (i.e., the standard deviation 

of the speed in the speed harmonization zone at the control duration).

= Flow rate at time t in speed harmonization zone.

qr(t) = Sum of flow rates at all on- and off-ramps between the speed harmonization zone and the 

bottleneck at instant t.

= Difference between speed advisory speed recommendations over the control interval in 

the speed harmonization zone at time t.

= Maximum allowed change in control speed in the speed harmonization zone.

= Advisory speed recommendation in the speed harmonization zone at time t.

vmin = Minimum advisory speed recommendation.

One criterion to determine when the speed harmonization should be activated can be expressed 

as = k0. Also, qr(t) can be estimated using figure 16. 

Figure 16. Equation. Estimation of flow rates.

Where:

= Lag for vehicles traveling from speed harmonization zone to off-ramp j.

= Lag from speed harmonization zone to on-ramp i.

Lags are computed assuming that vehicles travel from the speed harmonization zone to given 

locations at the free-flow speed or, potentially, at the prevailing space-mean speed. In that sense, 

some form of prediction is needed to predict these flows.

max

v0(t) ��wqqd(t)+ 

wv

v�

s

(t)

�

T

t = 1

k

u

(t) ≤ kc

u

q�

s

(t) ≤ qc

d + qr

(t)

Δv(t) ≤ Δvthr

v�0(t) ≥ vmin

v�

s

q�

s

(t)

Δv(t)

Δvthr

v�0(t)

kc

u

qr

(t) =�qj

out�t + lj

out� − �qi

in

i

�t + li

in�

lj

out

lj

in
13

can be estimated to achieve optimal flow rates in the speed harmonization zone, . 

Reverse functions for flow-density and speed-density relationships under congested traffic can 

be defined to reflect the area upstream of the bottleneck as follows:

Figure 17. Equation. Steady-state density as a reverse function of speed.

Figure 18. Equation. Steady-state density as a reverse function of flow.

Figure 19 illustrates a flowchart of the algorithm, which is described in the succeeding list.

v�0(t) q�0(t)

k = V -1

(v), kc

u ≤ k < kju

k = Q-1

(q), kc

u ≤ k < kju
14

Figure 19. Flowchart. Density-based algorithm logic and advisory speed recommendations.
15

1. When t ≤ t0 (starting time when the algorithm is activated), assign the speed harmonization 

zone advisory speed recommendation, as shown in figure 20.

Figure 20. Equation. Density-based algorithm step 1—advisory speed recommendation.

Where:

vf = Free flow speed.

Optimal flow rate in the speed harmonization zone is set, as shown in figure 21.

Figure 21. Equation. Density-based algorithm step 1—optimal flow rate.

2. At each time step t, check the two conditions, as shown in figure 22.

Figure 22. Equation. Density-based algorithm step 2—flow and density conditions.

Where:

l = Time lag for vehicles traveling from speed harmonization zone to bottleneck

(see figure 23).

Figure 23. Equation. Density-based algorithm step 2—time lag.

Where:

L = Distance from speed harmonization zone to bottleneck.

vl = Either the free-flow or space-mean speed of prevailing traffic streams.

If both conditions are satisfied, set the advisory speed recommendation, as shown 

in figure 24.

Figure 24. Equation. Density-based algorithm step 2—advisory speed recommendation 1.

If either one of the conditions is violated, first compute a target flow rate in the speed 

harmonization zone, as shown in figure 25.

v�0(t) = vf

q�0

(t) = qc

d + qr

(t)

� qs

(t) < qc

d + qr

(t)

k

u

(t + l) ≤ kc

u

l = 

L

vl

v�0(t + 1) = vf
16

Figure 25. Equation. Density-based algorithm step 2—target flow rate 1.

Where:

= Coefficient for bottleneck capacity. 

If and , set = 0.

Where:

0 = Coefficient of bottleneck capacity.

If 0 < 1, then, is less than the maximum bottleneck discharge flow rate when capacity 

drops happen. Otherwise, let = 1.

Target flow rate is computed in the next time step, as shown in figure 26.

Figure 26. Equation. Density-based algorithm step 2—target flow rate 2.

Where:

= Smoothing factor.

An advisory speed recommendation is made at t + 1, as shown in figure 27.

Figure 27. Equation. Density-based algorithm step 2—advisory speed recommendation 2.

3. If , then the equation shown in figure 28 is followed.

Figure 28. Equation. Density-based algorithm step 3—advisory speed recommendation 1.

Let , for example, as shown in in figure 29.

Figure 29. Equation. Density-based algorithm step 3—advisory speed recommendation 2.

Also the target flow rate is set, as shown in figure 30.

Figure 30. Equation. Density-based algorithm step 3—target flow rate.

4. If t < T, t = t + 1, then go back to step 2. Otherwise stop the iterations.

q�0

(t + 1) = β × qc

d + qr

(t)

β

k

u

(t + l) > kc

u |v�(t) − v�(t − 1)| < Δvthr β β

β

β β × qc

d

β

q�0

(t + 1) = αq�0(t + 1) + (1 − α)q�0(t)

α

v�0(t + 1) = V �Q-1 �q�0

(t + 1)��

Δv(t) = |v�0(t + 1) − v�0(t)| > Δvthr

v�0(t + 1) = �

v�0(t) + Δvthr, v�0(t + 1) > v�0(t)

v�0(t) − Δvthr, v�0(t + 1) ≤ v�0(t)

vmin ≤ v�0(t + 1) ≤ vf

v�0(t + 1) = max�min�v�0(t + 1), vf�,vmin�

q�0

(t + 1) = Q �V-1

�v�0(t + 1)��
17

With the settings in step 2, the algorithm attempts to ensure that bottleneck flow rates approach 

bottleneck capacities. When the bottleneck is active, the algorithm reduces vehicular throughput 

from the speed harmonization zone. Alternatively, if the bottleneck is not active, the algorithm 

increases maximum throughput in the speed harmonization zone, allowing more vehicles to 

traverse the bottleneck. Moreover, is introduced to smooth target speeds and flows in the speed 

harmonization zone. The value of ranges between 0 and 1.

Testing (Part 1: INTEGRATION© Platform)

Calibration

Calibration of the INTEGRATION© software entailed two efforts: calibrating roadway supply 

parameters and calibrating traffic demand. Basic input files for INTEGRATION© include the 

network files and traffic demand file. Network files describe the network-wide topologic 

attributes and roadway features. The traffic demand file contains a time-varying origindestination (OD) demand. Network files were converted from a shape file using the PYTHONTM

program developed in an ArcGIS® environment.

(9) Roadway attributes such as number of lanes, 

segment lengths, and speed limits were imported into INTEGRATION© from the shape file.

Traffic demands for the individual model years were estimated using the maximum likelihood 

synthetic OD estimation software, QueensOD©.

(10) QueensOD© estimated the maximum 

likelihood OD table in order to replicate empirically observed link flows. The numerical solution 

begins by building a minimum path tree and performing an all-or-nothing traffic assignment of 

the seed matrix. A relative or absolute link flow error is computed depending on user input. 

Using the link-flow errors, OD adjustment factors are computed and used to modify the OD seed 

matrix. Adjustment of the OD matrix continues until one of two criteria are met: namely the 

change in OD error reaches a user-specified minimum or the number of iterations criterion is 

met. To estimate the traffic demand file, traffic count data from the trailers were used. 

Final comparisons between observed counts and speeds suggest the following:

• Simulated speeds differed significantly from field-measured speeds.

• Simulated traffic counts were consistent with the field measurements.

• Simulated congestion temporally lagged behind field observations at some locations, but 

trends were consistent.

• End-of-corridor congestion was not captured because the downstream bottleneck was not 

modeled. Ideally, the network should have been extended to capture spillback from 

downstream bottlenecks.

• Simulated trajectories seemed to be consistent with the field observations.

Analysis

The proposed density-based algorithm was simulated using the calibrated INTEGRATION©

software. Advisory speed recommendations were provided to CAVs entering I-66 from the 

α

α
18

Route 7 on-ramp every 30 min. Table 2 shows the speed harmonization algorithm settings.

Simulation results across the entire 6-h simulation are summarized in table 3. For 60 random 

seed replications, the scenario of three abreast CAVs was compared to baseline conditions 

(non-speed-controlled vehicles), with individual results recorded once every 30 min. Results 

demonstrate that the three CAVs had minimal impact on overall traffic conditions and minor 

savings in hydrocarbons (HC), carbon monoxide (CO), and nitrogen oxides (NOx) emissions. 

Specifically, t-test p-values for total travel delay, bottleneck discharge flow rate, fuel 

consumption, and carbon dioxide (CO2) emissions were all much greater than 0.05. Thus,

measures of effectiveness (MOEs) were not significantly different before and after applying the 

speed harmonization algorithm when only three abreast CAVs were controlled.

Table 2. Speed harmonization algorithm settings.

Parameter Value

Target flow rate 5,100 vehicle/h

Target density 23.7 vehicle/mi/lane (14.7 vehicle/km/lane)

Maximum speed change 5 mi/h (8 km/h)

Minimum advisory speed recommendation 5 mi/h (8 km/h)

Update interval 30 s

Start time 1,200 s

End time 18,000 s

Coefficient of bottleneck capacity 0.6

Smoothing factor 0.5

Table 3. Density-based algorithm simulation results in INTEGRATION© with limited 

research vehicles.

Condition TD Fuel HC CO NOx CO2

Flow at 

Bottleneck

Base 60.83 s/km 24.54 g/km 25,355.26 g/km 0.1193 g/km 0.568 g/km 14.500 g/km 2,996 vehicle/h

Speed 

harmonization

60.88 s/km 24.58 g/km 25,323.12 g/km 0.1187 g/km 0.564 g/km 14.401 g/km 2,998 vehicle/h

Difference

(percent)

0.08 0.15 -0.13 -0.12 -0.59 -0.69 0.07

p-value

(t-test)

0.9177 0.1947 0.0000 0.0000 0.0647 0.5278 0.8414

1 s/km = 1.61 s/mi

1 g/km = 0.057 oz/mi

Figure 31 compares CAV trajectories with and without the speed harmonization algorithm. The 

algorithm’s influence indicates that if more CAVs were introduced into the network, traffic 

conditions downstream of the bottleneck would be improved.
19

1 mi/h = 1.61 km/h

Figure 31. Graph. Vehicle trajectories before and after applying the density-based 

algorithm in INTEGRATION©.

Testing (Part 2: VISSIM® Platform)

Calibration

VISSIM® model calibration was conducted by a stochastic experimental design approach based 

on Latin hypercube sampling (LHS).

(11) The LHS method was used to reduce the number of 

combinations to a sensible level while still reasonably covering the entire parameter surface. 

From several relevant calibration efforts performed in the past, it has been empirically observed 

that when the total number of calibration parameters is close to 10, approximately 500 to 

1,000 LHS samples produce 1 or 2 optimal solutions.

The adopted performance measures included speed and traffic counts. To determine the quality 

of model calibration, performance measures obtained from field-deployed sensors were adjusted 

by the log transformation method (LTM). LTM is widely applied in practice where data are 

skewed, contain a significant number of outliers, or have unequal variations (e.g., travel time and 

traffic volumes).

In addition to several critical lane-changing model parameters, the VISSIM® Wiedemann-99 

model was the primary target of calibration. Initial parameter ranges were set up as symmetric to 
20

each side of the default value. Some parameter ranges were based on the project team’s 

engineering judgment. Initial ranges for car-following and lane-changing parameters were 

obtained from prior research. Input volumes for VISSIM® were treated as calibration parameters 

to be adjusted. For the two target sections, preliminary calibration efforts from initial OD 

matrices produced significant discrepancies in field-observed travel times. This was mainly 

because initial OD matrices were estimated using older datasets from 2006, which did not reflect 

current traffic conditions. To overcome this, the OD matrices were converted to 30-min-interval 

input volumes for VISSIM®. Each 30-min interval volume was then added to the set of 

parameters to be calibrated.

LHS generated 500 initial parameter sets, and each set was simulated 5 times. RMSE values 

were computed by comparing average speeds and counts from simulation to those from field 

data. The best set (i.e., producing the lowest RMSE) was chosen by inspection and was used as 

the base parameter in creating two subsequent groups having 50 parameter sets each. Again after 

five simulations of each parameter set, the most promising set was chosen by inspection. Finally, 

the selected parameter set was fine-tuned to match field data.

With the final candidate parameter set demonstrating the lowest fitness value based on RMSE, 

fine-tuning efforts were conducted to obtain acceptable calibration results. The calibrated 

VISSIM® model matched the field data very well.

Analysis

The density-based algorithm was examined in the case of three CAVs and for a variety of market 

penetration rates through VISSIM®. However, it is important to note that due to the macroscopic 

nature of this simulation, it was not completely reflective of field test conditions. The CAVs 

received advisory speeds from the speed harmonization algorithm. They also received 

instructions to avoid lane changes and to keep moving parallel with adjacent CAVs. CAVs 

were dispatched every 30 min from the Route 7 on-ramp onto I-66 eastbound.

It was challenging to clearly observe impacts from the simulation results because only

three CAVs were used. At the moment when CAVs were actually deployed, only a few 

temporary changes were observed, as shown in table 4 and table 5.

Table 4. Operational MOEs in VISSIM® (three-car case).

Average Travel Time 

(min)

Average Speed 

(mi/h)

Throughput

(1,000 vehicle/h)

Base Three Cars Base Three Cars Base Three Cars

4.6 4.6 17.2 16.4 21.2 20.7

1 mi/h = 1.61 km/h

Table 5. Safety surrogate MOEs in VISSIM® (three-car case).

Number of Lane Changes Number of Stops

Base Three Cars Base Three Cars

702.0 660.2 2,513.0 2,449.0
21

Operational performance of the density-based algorithm was also captured at the 10, 25, and 

50 percent market penetration rates compared to the base case over 3 days. Results are shown in

table 6 through table 8. The change in total distance appears insignificant, and each OD pair 

carrying a fixed traffic volume for each date consisted of a single route. This implies the total 

number of vehicles passing through the network was almost identical. Unlike total distance, the 

simulation showed that TTT was significantly affected. Given the insignificant changes in total 

distance, travel time reductions (up to 4 percent) suggest that the algorithm mitigated traffic 

congestion in simulation.

Table 6. Travel times at various market penetration rates in VISSIM®.

Metric Base 10 Percent 25 Percent 50 Percent 

Travel time (min) 4.6 4.6 4.5 4.4

Difference versus base case (percent) — 0.9 -1.3 -2.5

— Indicates that no comparison was made.

Table 7. Speeds at various market penetration rates in VISSIM®.

Metric Base 10 Percent 25 Percent 50 Percent 

Speed (mi/h) 10.7 10.7 10.7 10.6

Difference versus base case (percent) — 0.0 0.0 0.1

— Indicates that no comparison was made.

Table 8. Throughput at various market penetration rates in VISSIM®.

Metric Base 10 Percent 25 Percent 50 Percent 

Throughput (1,000 vehicle/h) 18.5 19.8 20.3 20.7

Difference versus base case (percent) — 6.9 9.6 11.9

— Indicates that no comparison was made.

Impacts of the simulation were further examined by reviewing surrogate safety measures (i.e., 

number of stops, number of lane changes, and cumulative speed difference). Results are shown 

in table 9 through table 11. The algorithm appears to significantly reduce the number of stops, 

particularly in the critical upstream segments. Additionally, the total number of lane changes on 

these segments increased. Given the mobility improvement on those segments, such changes in 

stops and lane changing suggest the algorithm improved traffic flow. Cumulative speed 

difference exhibited little change throughout all segments.

Table 9. Stops at various market penetration rates in VISSIM®.

Metric Base 10 Percent 25 Percent 50 Percent

Number of stops 3,759.1 3,868.5 3,773.4 3,753.8

Difference versus base case (percent) — 2.9 0.4 -0.1

— Indicates that no comparison was made.

Table 10. Lane changes at various market penetration rates in VISSIM®.

Metric Base 10 Percent 25 Percent 50 Percent

Number of lane changes 704.9 768.6 810.0 585.5

Difference versus base case (percent) — 9.0 14.9 21.8

— Indicates that no comparison was made.
22

Table 11. Cumulative speed difference at various market penetration rates in VISSIM®.

Metric Base 10 Percent 25 Percent 50 Percent

Cumulative speed difference 1,675.3 1,739.7 1,772.4 1,782.5

Difference versus base case (percent) — 3.8 5.8 6.4

— Indicates that no comparison was made.
23

CHAPTER 2. FIELD EXPERIMENTS

Field runs were performed using three CAVs with V2I-based speed harmonization capability, 

which were used to control traffic streams on sections of I-66 in Northern Virginia during 

periods of increasing congestion. By communicating to roadside equipment capable of accessing 

real-time roadway speeds and volume, a surrogate traffic management center at the TurnerFairbank Highway Research Center (TFHRC) was used to calculate variable speed 

recommendations. These speeds were transmitted to the CAVs. These field runs tested the 

impacts of optimized variable speed targets, including changes to speed oscillations, travel time, 

and traffic throughput. A total of 19 runs were conducted in June 2014, July 2014, September 

2015, and October 2015. This chapter reviews the setup, methodology, results, and analysis of 

the field testing conducted on the selected test corridor.

VEHICLE AND INFRASTRUCTURE SETUP

Vehicles

To execute the speed harmonization experiment on a microscopic scale but in active traffic on a 

congested freeway, the project team built a fleet of three CAVs.(12) These vehicles were modified 

such that longitudinal control (e.g., vehicle set speed and gap) was accomplished from a central 

control center using V2I communication over a cellular digital network. Commands were sent 

over a V2I connection into an onboard computer. Commands generated by the onboard computer 

were communicated over a controller area network bus to the original equipment manufacturer 

(OEM)-supplied ACC system. This experimental equipment allowed remote control over the 

longitudinal speed of individual vehicles. The modified vehicles were operated by drivers in a 

mode where safety was enhanced, as the OEM-supplied ACC maintained a minimum headway 

(1.1 s). Vehicle operators had complete control over the latitudinal control (steering) and could 

override V2I recommendations using the brake and accelerator pedals. The intent for the vehicle 

fleet was that speed recommendations based on measurements from a variety of locations on the

roadway could be used with algorithms selected for laboratory testing. These allowed algorithms

were implemented in the laboratory to be used for live freeway testing in a living laboratory 

environment.(13)

Infrastructure

Input to the CAVs was based on corridor traffic speed measurement processing, as shown in

figure 32. The project team developed a connected mobile traffic sensing (CMTS) trailer,

including an RTMS measuring 15-s averaged speeds, volumes, and occupancies. These CMTS 

trailers were deployed along the roadway corridor. Measurements were relayed in real time to a 

central computer. The computer used this data to calculate recommendations to be sent to the

CAVs. Figure 33 shows the CMTS trailer locations along I-66 as labeled trailers 4 through 6 

containing the RTMSs used as sensors. Input to the CAVs was therefore based on macroscopic 

measures obtained along the test corridor.
24

©2016 Google® (Modifications: See Acknowldgements).

Figure 32. Map. Field experiment map of system integration.(14)

©2016 Google® (Modifications: See Acknowldgements).

Figure 33. Map. Test segment and trailer locations.

(15)
25

METHODOLOGY

The experiment hypothesized that by controlling traffic flow speeds in a congested region, traffic 

flows could be smoothed and that smoothing may provide operational and safety benefits. The 

experiment was performed on I-66 using the following:

• Three CAVs equipped with V2I to control the traffic speed.

• A lead probe vehicle placed in the traffic stream approximately 328.08 ft (100 m) ahead 

of the CAVs to measure traffic flows downstream of the speed control effort.

• Two probe vehicles approximately 164.04 ft (50 m) behind the CAVs to measure traffic 

flows upstream of the speed control effort. 

Each vehicle had an onboard computer to record and communicate vehicle state (e.g., location, 

speed, acceleration, etc.) at a 10-Hz frequency to the laboratory in real time. The experiment was 

microscopic in nature, as the traffic flow monitoring was localized by probe vehicles to several 

hundred feet (meters) around the CAVs.

Mechanics of the experiment called for time periods in which the freeway would transition into 

congested conditions. Real-time speed data from the RTMSs were used to determine when to 

initiate the experiment. The experimenter at TFHRC monitored speeds recorded by the RTMSs.

The experiment was initiated when speed measurements at the ends of the test corridor met 

threshold requirements. In this study, threshold requirements had an upstream speed 

recommendation approximately equal to the 60 mi/h (96.56 km/h) (i.e., free-flow speed) and a 

downstream speed approximately 10 mi/h (16.1 km/h) below the upstream speed. The 

six vehicles used in the experiment were staged near the test corridor’s on-ramp so as to be 

launched into the traffic stream at the appropriate time.

The leading probe, which was used to measure existing traffic conditions, was sent down the 

roadway first. Its driver was instructed to travel in the center lane (out of three) at prevailing 

typical speeds. Figure 34 illustrates the experimental fleet configuration when vehicles were 

fully deployed on the freeway. It was assumed that on a microscopic traffic flow level, the 

leading probe trajectory represented typical traffic flow behavior.
26

Figure 34. Illustration. Research and probe vehicle placement.

Next, the three CAVs entered the freeway as a group. They traveled at prevailing traffic speeds 

while adopting a parallel formation across the three lanes. The CAVs were switched into 

automated longitudinal control mode (speed and braking) upon entering the control section. The 

control section start was demarcated by location of the upstream CMTS trailer (trailer 4). The 

control section end was demarcated by the furthest downstream CMTS trailer (trailer 5). Drivers 

of the CAVs were instructed to remain in the lane assigned to each. CAV speeds were controlled 

from a central computer, which generated a longitudinal (along the roadway) speed profile as a 

function of position along the roadway. Automation within the vehicles downloaded speed 

recommendations every 2 s and directed the ACC to adjust speed accordingly. These vehicles 

traversed the control section under the automated speed recommendation algorithm executed by 

the central computer. At the end of the control section, the CAVs stopped downloading speed 

recommendations and once again mimicked the prevailing typical speeds.

The two following probes entered the freeway last. They positioned themselves in the 

two leftmost lanes (see figure 34) some distance 164.04 to 328.08 ft (50 to 100 m) behind the 

CAVs. Probe vehicle drivers were instructed to travel at prevailing typical speeds. Trajectory 

characteristics of the following probes, as recorded and relayed to the laboratory in real time, 

were the surrogate for measuring traffic impacts resulting from speed harmonization. Probe 

vehicle trajectory statistics were used to represent the results on a microscopic scale of the speed 

harmonization experiment.
27

The test corridor for the experiment consisted of a control section followed by a section of 

roadway where no control was applied. This allowed for comparing mobility benefits on nearby 

and similar sections of roadway, with and without speed harmonization impacts.

The algorithm created to produce speed recommendations was influenced by but differed from 

the work done in microscopic simulation for this corridor.

(13,16) During pilot testing, the initial 

algorithm implementation reduced speeds too rapidly before following probes entered the 

congested test corridor. The three CAVs (travelling at near free-flow speeds of 50–60 mi/h

(80.5–96.6 km/h)) received reduced-speed recommendations from the algorithm and adopted it 

as their set speed; however, the initial algorithm, upon detecting congestion in the test corridor, 

recommended a speed of 25 mi/h (40.2 km/h), the lowest possible set speed under cruise control. 

With surrounding vehicles travelling at free flow speeds, this created highly unsafe conditions. 

Therefore, a simplified speed-space relationship was developed. This approximated the complex 

relationships developed by past speed harmonization simulation efforts.

In these field experiment runs, the speed recommendation s(x,t) was a linear function of space (x) 

depending upon temporal (t) speed measurements from the roadside RTMSs as seen in figure 35

as follows: 

ss(xx,tt) = �

ssnn(tt) − ssmm(tt)

∆xxnn

� xx + ssnn(tt)

Figure 35. Equation. Field experiment speed recommendation.

Where:

sn(t) = Speed measurement at trailer n at time t.

sm(t) = Speed measurement at trailer m at time t. ∆xnm = Distance between trailers n and m.

This simplified speed-space relationship was used to test both performance of the CAVs and 

impacts on existing traffic flow. The speed recommendation has a floor value of 25 mi/h

(40.2 km/h). 

ANALYSIS

Data from the experimental probe and CAVs were used to answer the following basic questions:

1. Does speed control from the simple algorithm result in appropriate behavior in terms of 

speed as a function of location along the corridor?

2. Are statistics from the leading and following probes significantly different?

3. In characterizing the change in statistics between leading and following probes, do there 

appear to be significant potential benefits?
28

Vehicle Control

Speed recommendations for the CAVs were generated every 2 s using the linear speed 

harmonization algorithm based on speed values measured by RTMSs. There was a minimum 

value of 25 mi/h (40.2 km/h) enforced on the recommendations. 

Figure 36 illustrates an example of CAV performance in this experiment. In the figure, CAV

trajectory is plotted as a solid line, and the speed recommendations are plotted as points. CAVs 

generally followed the recommendations in all cases. The exceptions, exemplified near mile 

marker 68.25, occurred when CAVs were impeded by existing traffic. This is likely due to the 

use of radar to sense downstream vehicles, which would then set a minimum headway of 1.1 s. 

When the headway decreased past this threshold, the vehicular OEM systems performed braking 

maneuvers.

1mi/h = 1.61 km/h

Figure 36. Graph. Control vehicle trajectories and recommendations.

The conclusion, with regard to the first question in the previous list, is that CAVs operating in 

traffic can be expected to operate at recommended speeds (provided that speed is at or below 

existing traffic speed) with a small time delay. This affirmation of a positive answer to 

question 1 is a similar result to other CACC tests without a closed loop controller.(17)

Probe Vehicles/Sensors

The probe vehicles were intended to act as high-resolution sensors of traffic conditions over a 

small region surrounding the CAVs in an effort to answer questions 2 and 3. Figure 37 shows the 

probe and CAV speed trajectories as a function of time. Figure 38 shows the speed trajectories as 

a function of mile marker. The probe and CAVs were released onto the roadway at slightly 

different times. As a result, the temporal and spatial relationships between experimental vehicles 
29

were not equivalent. It was asserted for this experiment that the recurring traffic congestion on 

this segment of roadway set up a stable but oscillatory structure along the roadway. In order to 

observe this behavior, the trajectories are best compared with space as the independent variable, 

as shown in figure 38.

1mi/h = 1.61 km/h

Figure 37. Graph. Temporal speed trajectories.

1mi/h = 1.61 km/h

Figure 38. Graph. Spatial speed trajectories.
30

Trajectories of the probe and CAVs were impacted by both the surrounding traffic and by speed 

control enforced by the CAVs. CAV deviations from the programmed speed profile were 

primarily caused by slowing in response to exiting traffic. The resulting CAV speed profile had a 

large-scale spatial trend associated with control and congestion around which there were 

stochastic fluctuations. For example, the overall trend can be represented by a smooth version of 

the resulting CAV speed profile (see figure 39).

1mi/h = 1.61 km/h

Figure 39. Graph. Control speed trajectory and smoothed profile.

In order to characterize the trajectories, changes in the stochastic traffic flow component before 

and after probe vehicle passage were considered. To examine the stationary statistics of the 

trajectories, the overall trend was removed from the probe vehicle trajectories. The detrended 

trajectories are shown in figure 40. 
31

1mi/h = 1.61 km/h

Figure 40. Graph. Detrended probe vehicle speed trajectories.

The probability density function (PDF) for a following probe trajectory is shown in figure 41, 

and the detrended PDF is shown in figure 42. The detrended data were approximately secondorder stationary (constant temporal mean and variance for each probe) and thus could be 

examined using typical time series techniques in order to address question 2.
32

1mi/h = 1.61 km/h

Figure 41. Graph. PDF of raw data following probe speed trajectory.

1mi/h = 1.61 km/h

Figure 42. Graph. PDF of detrended following probe speed trajectory.

The impact of speed harmonization could be observed in both the time and frequency domains. 

In the time domain, a stochastic process could be characterized by its PDF. In this study, the 

0 10 20 30 40 50 60 70

0

50

100

150

200

250

Speed (MPH)

Frequency

-20 -15 -10 -5 0 5 10 15 20 25 30

0

50

100

150

200

250

300

Relative Speed (MPH)

Frequency
33

process histograms were used as a surrogate for the PDF. The PDF of the leading probe 

detrended speed trajectory, which characterizes traffic flow before speed harmonization is 

applied, is shown in figure 43. The PDFs clearly indicate different processes were measured 

before and after the control. The PDF shapes imply that the resulting traffic flow had lesser 

variability and was distributed about a single mode. In the time domain, it can thus be concluded 

that speed harmonization did indeed change the statistics and nature of the traffic flow.

Figure 43. Graph. PDF of detrended leading probe speed trajectory.

Temporal characteristics of a stationary stochastic process are often characterized by the 

frequency content of the measured signals. In this study, the independent variable of distance

along the roadway (i.e., mile marker) was treated as an ordered sampling base in the same way 

that time was used in time-series applications. The detrended speed trajectories were Fourier 

transformed (i.e., using a padded fast Fourier transform), and the power spectral density (PSD) 

was estimated.(18) PSD describes the amount of signal energy found at each frequency in the 

signal. For example, a signal consisting of a pure sinusoid will appear as a single peak in the 

PSD. A large PSD indicates oscillatory behavior. Figure 44 through figure 47 present the PSDs 

for the leading (P0) and following (P1 and P2) detrended trajectories on four separate field runs. 

In each case, the PSD for the leading probe vehicle shows large peaks. This indicates a 

significant oscillatory behavior in the traffic flow, which occurs on the order of one to two cycles 

per mile. PSDs for the following probes did not have these strong peaks at low frequencies.

-20 -15 -10 -5 0 5 10 15 20 25 30

0

20

40

60

80

100

120

Relative Speed (MPH)

Frequency
34

Figure 44. Graph. PSDs of detrended speed trajectories of the probe vehicles on 

July 8, 2014.

Figure 45. Graph. PSDs of detrended speed trajectories of the probe vehicles on 

September 29, 2015.

0 1 2 3 4 5 6 7 0

5

10

15

20

25

30

35

40

45

50

Normalized Power

Frequency (Cycles per Mile)

Leading Probe Vehicle P0

Following Probe Vehicle P1

Following Probe Vehicle P2

0 1 2 3 4 5 6 7 0

2

4

6

8

10

12

14

Normalized Power

Frequency (Cycles per Mile)

Leading Probe Vehicle P0

Following Probe Vehicle P1

Following Probe Vehicle P2
35

Figure 46. Graph. PSDs of detrended speed trajectories of the probe vehicles on 

October 15, 2015.

Figure 47. Graph. PSDs of detrended speed trajectories of the probe vehicles on 

October 21, 2015.

The PSD trends imply that speed harmonization acted effectively as a low-pass filter for speed 

fluctuation of the traffic stream. These PSD estimates indicate that the answer to question 2 is 

that traffic flow stream statistics were significantly different as a result of speed harmonization. 

The speed trajectories resulting from this control were indeed harmonized in the sense that 

measured oscillations in the traffic stream were dampened.

Potential Benefits

The answer to the third question regarding potential benefits has two aspects: first, are the 

impacts observed in some way beneficial, and, second, is there a disbenefit that offsets the 

possible benefits?

The reduction in oscillatory behavior has been shown to improve (reduce) fuel consumption in 

past work.

(19) Results from this limited test indicate that for cases where the traffic stream was 

not broken down (e.g., became purely stop and go), there was a significant reduction in 

oscillatory traffic stream speed, implying a fuel consumption benefit.

0 1 2 3 4 5 6 7 0

5

10

15

20

25

30

35

40

45

Normalized Power

Frequency (Cycles per Mile)

Leading Probe Vehicle P0

Following Probe Vehicle P1

Following Probe Vehicle P2

0 1 2 3 4 5 6 7 0

5

10

15

20

25

30

35

40

45

Normalized Power

Frequency (Cycles per Mile)

Leading Probe Vehicle P0

Following Probe Vehicle P1

Following Probe Vehicle P2
36

Oscillations and large variability in traffic stream speed behavior have been associated with 

safety risks. This is often the underlying premise for applications such as queue warning.

On the disbenefit side of the equation, there is the potential for increasing segment travel times 

by applying speed harmonization. In this study, the following probes did not show a significant 

or consistent reduction in travel times compared to leading probe travel times, and thus the travel 

time disbenefit was not observed. That said, the experiment reported here was done on a 

microscopic traffic scale (though repeatedly), and these results are not guaranteed to materialize 

in a macroscopic measurement framework. This linkage of microscopic results to macroscopic 

outcomes for this application of CAVs has yet to be tested.
37

CHAPTER 3. CONCLUSIONS

This project implemented speed harmonization algorithms on an active freeway with recurring 

spatially structured congestion in simulation and field testing using a fleet of CAVs. Due to 

resource constraints, the field experiments could only deploy a maximum of three CAVs. 

Simulation results across three platforms (VISSIM®, INTEGRATION©, and Aimsun®) showed

that the introduction of three CAVs, with a goal of harmonizing overall speeds, would not be 

beneficial on a real-world freeway. 

The simulation results indicated that a field experiment with a limited volume of CAVs was

unlikely to cause a significant negative impact on traffic. The field experiment demonstrated that 

CAVs, with automation in the form of modifications to the OEM-supplied ACC, can be used in 

automated longitudinal control mode to implement V2I-based speed harmonization. The impacts 

on the traffic stream were measured using probe vehicles leading and following the CAVs. 

Furthermore, this project demonstrated that traffic stream trajectories after speed harmonization

reduced oscillatory behavior as characterized using the power spectral densities of the 

measurements. In addition, there was no disbenefit in terms of travel times between the probe 

vehicles before and after speed harmonization.

39

ACKNOWLDGEMENTS

The original maps shown in figure 32 and figure 33 are the copyright property of Google Maps®

and can be accessed from http://maps.google.com. The maps contain overlays of markers, 

shapes, and arrows depicting CMTS trailer locations; vehicles, CMTS trailers, and the server at 

the Saxton lab; and the communication between these items, respectively. These map overlays 

were developed as a result of this research project.

41

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