An Observational Study of Freeway Lane-Changing Behaviour. by M. Rafik Nemeh Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering (Transportation Division) APPROVED: SA. a) Dr. Siamak A. Ardekani (Chairman) LbDW — Cts Dr. Richard Walker VV Dr. Toni Trani December, 1988 Blacksburg, Virginia
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An Observational Study of Freeway Lane-Changing Behaviour.
by
M. Rafik Nemeh
Thesis submitted to the Faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
Master of Science
in
Civil Engineering (Transportation Division)
APPROVED:
SA. a) Dr. Siamak A. Ardekani (Chairman)
Lb DW — Cts Dr. Richard Walker VV Dr. Toni Trani
December, 1988
Blacksburg, Virginia
Yo
LD 5655 V85S 1988 (433
JAN I
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An Observational Study of Freeway Lane-Changing Behaviour. | by
M. Rafik Nemeh
Dr. Siamak A. Ardekani (Chairman)
Civil Engineering (Transportation Division)
(ABSTRACT)
Every one who has driven on a freeway has observed the phenomenon of lane-
changing. This phenomenon is, of course, caused by the desire of most of the drivers not
to be in a slow-moving lane. Therefore, the average driver who finds himself in such a
lane moves into a neighboring faster lane, usually after a certain time-lag. This time-lag
depends on the dynamic characteristics of the vehicle, the availability of acceptable gaps,
and the driver risk, which is the value the driver places on the probability of collision
during a maneuver, i.e. the higher the perceived probability of collision, the higher the
time-lag.
Modelling of the lane-changing phenomenon has been the objective of many inves-
tigators in the past. As will be shown later in this study, lane-changing is a very impor-
tant component in highway traffic flow.
In this study, a mathematical model to describe the lane-changing behaviour is
suggested based on the lane-changing hypothesis that whenever there is a lane-changing
maneuver, the average speed of the neighboring lane is faster than the average speed of
the current lane.
A set of data has been collected by a methodology which involves aerial photo-
graphic technique. The collected data are then used to test the validity of the lane-
changing hypothesis, to calibrate and validate an existing lane-changing model, and to
develop a gap acceptance function for freeway lane-changing maneuvers.
Acknowledgements
I would deeply like to thank Dr. S. Ardekani for his limitless valuable suggestions
and comments. I also appreciate Dr. R. Herman’s valuable discussions with Dr. S.
Ardekani; it proved to be helpful.
Sincere appreciation is expressed to Dr. S.D. Johnson for his kind assistance in us-
ing the Mann Mono-Digital Comparator.
I am grateful to the member of my committe, Dr. R. Walker and Dr. T. Trani, for
their support and guidance.
I am also grateful to my parents for making my education all these years possible.
Gratitude is also expressed to my friends who supported me with thier encourage-
ment.
Acknowledgements iii
Table of Contents
1.0 Background And Study Objectives ....... 0.2 ce cece ee ec ee eee eee eee eeee 1
1.1 Introduction 2.0... cece ee eee ee ee ee eee ee eee eee teens ]
1.2 Study Objectives . 0... ccc ec eee eee eee ee eee ete een eens 2
2.0 Aerial Photographic Observations ........... cc cece ec eee e eee e cree re eeeene 4
7. Number of cases of lane-changes. 2... 0... cece cee eee te ee ees 36
8. Arbitrary data to illustrate the calibration of the model. ............ 38
9, Current lane (Veh No. Sand 6) 2... ce ee ee ees 49
10. Neighboring Lane (Vehs No. 3 and 4) 2... . cee ce eee eee 51
11. Coordinates of the control points 2.6... .... eee eee eee eens 53
12. Coordinates of vehicle number 2. 0... . eee ee ee eee eee 54
13. Concentration data 2... eee eee eee ens 55
14. Gap acceptance distribution data 2... .. .. eee ee ee ee eens 56
List of Tables Vii
1.0 Background And Study Objectives
1.1) Introduction
Modelling of the lane changing phenomenon between lanes of a unidirectional
traffic has been extensively used in simulation of traffic interactions along a roadway as
well as in understanding the dynamic characteristics of a group of vehicles along a
highway section.
The work by D. Gazis, R. Herman and G. Weiss (Ref 1) has been one of the ear-
liest attempts to model lane-changing phenomenon. The model expresses the rate of
change of lane densities as a function of a sensitivity coefficient and the relative lane
density at time t and at equilibrium. The model addresses questions of stability of flow
along a multilane roadway as a function of products of the sensitivity coefficient and the
time lag involved, much like the analysis of car- following models (Ref 2) . A limitation
of Gazis, et al (Ref 1) is the assumption that oscillations in lane densities take place
about an equilibrium density distribution. Munjal and Pipes (Ref 3) relaxed this as-
sumption by incorporating a conservation equation of flow into the Gazis, et al model.
Background And Study Objectives 1
Makigami, et al (Ref 4) adopted Munjal and Pipes work as well as a stochastic de-
scription of lane-changing as a Markov process (Ref 5) to develop a model for uncon-
gested flow conditions. An embedded assumption of stochastic models (Refs 4,5) is the
existence of steady state conditions since the transition probability matrices used in the
Markov process are not time dependent. Michalopoulos and Beskos (Ref 6) continued
the work of Gazis, et al and Munjal and Pipes to develop a set of three macroscopic
continum models. The first model employs a separate conservation equation for each
lane, while the second mode! employs a single equation for all lanes but considers the
street width as well. Finally, the third model considers the street width as well as a
momentum equation to account for exchange of momenta among lanes.
1.2 Study Objectives
A major handicap in the works reviewed in the introduction is the lack of field ob-
servations to validate and calibrate the mentioned models. This limitation arises mainly
due to the structural complexity of the models. Field observations of variables such as
lane density and its oscillations require repeated observations employing elaborate data
collection techniques such as aerial photography taken frequently and under variety of
traffic conditions. Thus, the need exists for a simple macroscopic lane-changing model
which is easy to calibrate based on field observations.
The main objective of this research is the development of a lane changing model
which expresses the number of lane changes per unit distance from one lane to the next
as a function of the speed differential between each pair of lanes.
Background And Study Objectives 2
The lane-changing model, as will be discussed in more details in chapter four, is
suggested based on the observation that the stimulus of the lane-changing maneuver is
the reduction in the speed rather than the increase of concentration of the current lane.
Although higher concentrations imply lower speeds, but there are cases where the drivers
in the current lane perceive reduction in the speed while the concentration has not ac-
tually changed. A case in point is when passenger car drivers change lane simply because
of the presence of a truck in their lane. So such influences on individual perception can
be taken care of through the error terms introduced in the model.
In this work, analysis of aerial phtographs in pursue of the above-mentioned ob-
jective is introduced in chapter two. Review of an existing lane-changing model, statis-
tical analysis of the data collected , and the development of a gap acceptance function
for freeway lane-changing maneuvers are discussed in details in chapter three. The pro-
posed model as well as the calibration procedure is discussed in chapter four. Applica-
tions of the results are given in chapter five. Finally, discussions and recommendations
are presented in chapter six.
Background And Study Objectives 3
2.0 Aerial Photographic Observations
2.1 Introduction
Aerial photographs, although cumbersome and time consuming to reduce, are
means of collecting a very large amount of traffic data in a short period of time. Time-
lapse aerial photography has been used over the years in various traffic studies.
In freeway studies aerial photography has been employed, for example, to determine
the effect of bottlenecks on freeway traffic (Refs 7,8,and 9), to make estimates of travel
time delay and accident experience due to freeway congestion (Ref 10), to study merging
freeway operations (Ref 11) and freeway interchange operations (Ref 12), to determine
the traffic flow characteristics of a facility (Refs 13,14,15 and 16), and to study headway
and speed distributions and their correlation in freeway traffic (Ref 17).
In the arena of non-freeway traffic, aerial photographs have been used, for example,
to measure the vehicular concentration in a network of streets (Ref 18), to conduct
origin-destination surveys (Ref 19), to perform parking studies (Ref 20), and to measure
the effectiveness of traffic control systems in a network (Ref 21).
Aerial Photographic Observations 4
In the present work data have been collected from aerial photographs to calibrate
and validate an existing lane-changing model, to test the validity of the hypothesis that
whenever there is a lane-changing maneuver the average speed of the neighboring lane
is faster than the average speed of the current lane, and to develop a gap acceptance
function for freeway lane-changing maneuvers.
2.2 Specifications
The aerial photographs were taken in 1982 by the Texas State Department of
Highways and Public Transportation along the Interstate Highway 35 through down-
town Austin as well as along the Interstate Highway 30 through downtown Dallas.
A Cessna 206 turbo-engine aircraft, a 153.28 mm RC10 wild Lens cone camera, and
a 9” by 9” diapositive color film were used. The aircraft was flying at 120 mph at an al-
titude of 3000 feet above street level.
2.3 Reduction
The first step in the reduction of the aerial photographs was to locate vehicles in-
volved in a lane-changing maneuver. A light table was used for this purpose. Care was
taken to identify and exclude those lane-changes for the purpose of exiting the freeway.
Vehicles changing-lane were located by visual inspection. Each pair of consecutive
frames were inspected for lane-changing maneuvers at the same time. It should be
Aeria] Photographic Observations 5
pointed out that, at low speeds, vehicles changing-lane could be detected easily due to
the fact that the vehicle changing-lane might be located at the center of the two lanes.
At high speeds, however, extra effort was required to locate a vehicle just having com-
pleted a lane-change since the vehicle would have moved from one normal position on
the first frame to another normal position on the next frame during the photo inter-
exposure time.
The second step in the reduction of the aerial photographs was to assign a scale to
each frame. It must be noted that aerial photographs are perspective projections so that
a location with higher elevation is closer to the camera lens and thus its image has a
greater scale (Ref 22). However, for relatively flat topography one may assume a con-
stant average scale for each photographic frame. As will be discussed later in the section
on sources of errors, this is not an unreasonable assumption for the study areas in
Austin and Dallas.
The scale determination for each frame was made through measuring photo dis-
tances between fixed monuments on the ground (control points) as well as the ground
distances between those points. The control points were selected after the photographs
were taken. The ground measurements were made by Herman et al (Ref 5,10, and 23)
using a Keuffel & Esser Electronics Distance Measurement apparatus. The altitude of
the aircraft has varied with respect to a different set of photographs and that caused the
range of scale to vary from 1” = 471.2’ to 1” = 537.3’. As will be shown later, 1” = 500°
is a reasonable scale to be used in the calculation presented later in chapter 3.
A Mann Mono-Digital comparator was used to determine the cartesian coordinates
of the location of each vehicle shown in Figure 1 as well as to determine the coordinates
of the control points. The comparator was interfaced with an IBM computer to save the
coordinates of vehicles in a data file. The control points were fixed objects shown in both
the master and the conjugate frames. The position of each vehicle was represented by
Aerial Photographic Observations 6
eee —| em Oee aeeaea Se
Figure 1. : Illustration of vehicles positions
Aerial Photographic Observations
the x,y coordinates of its left front corner. Table 9 through 14 in appendix A provide the
data obtained from the photographs. Table 9 shows the coordinates of the two front
vehicles in the current lane, namely, vehicle numbers 5 and 6. Table 10 shows the coor-
dinates of the two front vehicles in the neighboring lane; vehicle numbers 3 and 4. The
average speeds in the current lane and the neighboring lane are computed using the
values in Table 9 and 10, respectively. Table 11 shows the coordinates of the control
points. Table 12 shows the coordinates of vehicle number 2. The duration of gap ac-
ceptance is computed from the speed of vehicle number 2 which is shown in Table 14.
To determine the concentration in the current lane and the neighboring lane, the
group of vehicles infront of the lane-changing vehicle is counted and the distance occu-
pied by that group of vehicles is also measured. The data are shown in Table 13. The
distance between vehicles number 2 and 3 has been measured for the gap acceptance
distribution analysis and is recorded in Table 14.
The determination of the elapsed time between two consecutive photographs, 6dr,
was made by reading the image of a clock on each frame. The close divisions were to
the nearest second and were interpolated to the nearest tenth of a second. It must be
noted that an error of 0.1 seconds in 6f, would only result in a 3 to 5 percent error in the
value of mean speed for the corresponding pair of frames. As can be seen later, since
speed differentials between two neighboring lanes are of primary interest, such small
systematic errors are not critical.
Aerial Photographic Observations 8
2.3.1 Speed Measurement
To determine vehicle speed, the photo displacement of each vehicle, A/ , was
measured as:
Al = [(X,-X,)°+(¥, - ¥,) 1"? (2.1)
where (X,,Y;) and (X,,Y,) are the coordinates of the vehicle on the master and the
conjugate frames , respectively. The above computation assumes that vehicles travel on
a straight line during the elapsed time between two consecutive exposures.
Given the short elapsed time, dt, between successive frames, the above assumption
does not introduce a significant error in the measurements. For example (Ref 23), for a
6t of 2.5 seconds and a scale of 1” = 500’, a vehicle moving at 30 mph would travel only
110 feet corresponding to a displacement of 5588 microns on the photographs. Let us
now assume that the above vehicle has been actually travelling at 30 mph along the
zigzag path ABCDE, rather than the straight path ACE, as shown in Figure 2 (Ref 23)
which schematically depicts a hypothetical case of an extreme lane-changing maneuver.
Then the actual distance travelled in 2.5 seconds in AB+ BC+ CD+ DE= 110’ while the
photographic estimate of the travelled distance is ACE= 108.72’, a discrepancy of only
1.3 percent.
Once a Al is determined in microns using the above procedure, it is converted to the
distance travelled on the ground, AL, through the relation AL = Al x (scale in feet per
microns), However, in measuring, AL , it is, of course, necessary that the coordinates
of a vehicle on the master and the conjugate frames be measured with reference to a
common coordinate system. This was achieved through the transferring of the cartesian
coordinate system of the conjugate frame to that of the master frame, using the fixed
Aerial Photographic Observations 9
SIN (160°) a ———— ‘ « ‘ 27.8' x Soy 1 94-36
—< 2 x $4.36' « 108.72' |
The schematic path of a vehicle conducting an extreme lane- changing maneuver during the 2.5 seconds elapse time between two successive photographs. The hypothetical vehicle has travelled the zigzag path ABCDE (a distance of 110 feet at running speed of 30 mph) while the photo reduction procedure
Figure 2. : has measured the length ACE = 108.72 feet (Ref 23).
Aerial Photographic Observations 10
control points that appeared on both frames. The transfer of coordinates allowed for not
only a shift in X and Y but also a rotation of the conjugate coordinate system relative
to the master coordinate system, as shown schematically in Figure 3 (Ref 23).
Once the three transformation parameters X, ,¥Y,,8 were determined the vehicle co-
ordinates on the conjugate frame, (X’,Y’), were expressed relative to the master frame
coordinate system, namely,
X = X’cos (0) — Y’sin (8) + Xp (2.2)
Y = X'sin (6) + Y’cos (0) + Yo (2.3)
The angles, as shown in Table 1, were computed and found to be very small so the
effect of rotation was not significant in the analysis.
2.3.2 Sources of Errors
The vehicle speeds obtained in the manner decribed in the previous section are
subject to errors from a number of different sources (Ref 24). The more significant of
these sources are the non-level topography of the test area, parallax, relief displacement,
tip and tilt of the airplane, and the operator.
The non-flat topography of the area is a major source of error. Unlike a map which
is an orthographic projection and has a uniform scale, an aerial photograph is a per-
spective view and its scale varies from point to point due to variation in terrain elevation
in addition to parallax, etc. For example, the areas on the photograph with higher
ground elevations are closer to the lens of the camera and thus have a larger scale, since
scale = (focal length of the camera)/(aircraft altitude - ground elevation). As a result
Aerial Photographic Observations 1!
\ _ x!
\ a
\ 0’ — — —
_—— x Xo.Yo)
ae [. \ _ \ — 0 \ xX
\ \
Schematic diagram showing the relative positions of cartesian coordinate systems of a pair of successive aerial photographs. In transferring the coordinates of one frame to the other a shift in origin of (.X,, Y,) as well as a rotation 6 of the conjugate coordinate system relative to the master coordinate
Figure 3. ; System was assumed (Ref 23).
Aerial Photographic Observations 12
Table 1. The angles of rotation between master and conjugate frames.
of variation in terrain elevation, using a constant average scale for an aerial photograph
is bound to produce errors so that a vehicle travelling on top of a hill at speed V appears
to have moved a longer distance during time t than a vehicle travelling at the same speed
V at the bottom of that hill, 1.e. V(bottom) < V < V(top) as shown in Figure 4 (Ref 23).
Parallax is another systematic source of error in photographic reduction. Parallax
is defined as the apparent displacement of the position of an object with respect to a
frame of reference due to a shift in the point of observation (Ref 22). Using the aerial
photographic plane as a reference frame, parallax exists for all images appearing on
successive photographs and is larger the greater the elevation of the point. This apparent
movement between successive exposures takes place parallel to the direction of flight.
The parallax phenomenon affects the transformation of coordinate systems since the
fixed control points used in the transformations are assumed to have the same elevation.
Thus, the control points used in these transformations were chosen to not vary sub-
stantially in elevation and at the same time be widely scattered in the network area.
The relief displacement, while not as major an error source as the parallax, does
generate problems such as the masking due to highrise buildings. The relief displacement
is defined as the shift in position of an image caused by the relief or the height of the
object (Ref 22). In vertical photographs, i.e. those taken when the focal plane of the
camera is parallel to the ground, the relief displacement occurs along radial lines through
the point in the photograph located directly below the camera lens (the principal point).
The relief displacement is greater, the farther the object is from the principal point
and the greater the height of the object. Consequently, the determination of the posi-
tions of vehicles which have greater heights or are further away from the principal point
is subject to greater magnitude of error. However, since the vehicle heights are negligibly
small compared to the flight altitude, the errors due to relief displacement are not con-
siderable.
Aerial Photographic Observations 14
|
\ Comera Focal | y Length
EIT TTT MNT TTT
L
Me 7V7T777T7 TTT
L
Schematic diagram showing the effect of variations in terrain elevation on the scale of an aerial photographs. Note that while ground distance AB and CD are equal, due to variations in terrain elevation their images on the photographic plate abcd are not of equal length, hence (ab/AB) is not equal to (cd/CD). A vehicle travelling the length AB=L during At would appear to have moved a shorter distance on a pair of time-lapse photographs
Figure 4. : than a vehicle travelling the same length CD=L (Ref 23).
Aerial Photographic Observations 15
An assumption in the reduction of the aerial photographs is that they are vertical
photographs. Such is not the case if the aircraft is tipped or tilted with respect to the
plane of its altitude at the time of exposure. Since tips and tilts are usually no greater
than three degrees, the errors due to tip and tilt can be considered neglgible (Ref 25).
The non-systematic operator errors are present in all steps of the photo reduction
process but the two most error-prone steps have been the proper placement of the
comparator reticle on the desired points and the reading of the clock image on each
frame.
To correct for each of the above stated systematic errors individually requires the
lay out of many control points prior to photography as well as a tremendous increase
in the level of effort required for reduction of photographs. Moreover, for the purposes
of these studies, where one often deals exclusively with averages, such tedious efforts to
secure high levels of accuracy are not warranted. The question that arises is whether
or not the directions and magnitudes of errors from these sources are random enough
to yield meaningful averages (Ref 23).
To investigate the above question a study of the apparent speed of parked vehicles
is undertaken. Table 2 shows the coordinates of ten parked vehicles scattered in a pair
of frames. The average velocity of these ten vehicles is 1.28 miles per hour which is rel-
atively small enough i.e. the effect of the mentioned systematic errors can be neglected.
A study by Herman et al (Ref 23) was also undertaken to investigate the above
question. Figure 5 (Ref 23) shows the vector fields of velocities for a three pairs of
frames. Also shown in Figure 5 the speed and drift angles histograms corresponding to
the velocity vectors. As can be seen from the histogram of drift angles in Figure 5, the
angles are rather uniformly distributed i.e. the errors in magnitudes of these velocities
are essentially random and the resulting estimate of the average running speed can be
assur.ied unbiased.
Aerial Photographic Observations 16
Table 2. The coordinates and the apparent velocities of parked vehicles.
30 '=="2 BY: M. Rafik Nemeh sess: &0 'sezze2 =zece:
50 ‘== This program computes the integral of a function f(x) eazs: 60 '=2== between the limit X=a and X=b using Trapezoidal rule. esas: JQ ‘s25= secs:
80 terrae scet srs See terse sess ee stresses eter tresses tstt sere essere sete ere etree ss tseaesresss
90 ''
100 br nr rrr rere tre tene Define function- ------ rrr tr r rte rr errr 110 '' 320 DEF FNFX(X)=(.103474)*(X72.617)%(2.7182381188 > (-X/2.326))} 230 ' 140 CLS 150 ' 160 '---- rrr rrr tren eecn INPUT -------77-7->- Tt te tt et en ne 170 ' 180 PRINT TAB(20); “THIS PROGRAM COMPUTES TH= INTEGRAL OF A FUNCTION"; 190 PRINT TAB(20); "USING TRAPEZOIDAL RULE." 200 PRINT: PRINT 210 220 PRINT TAB(10); "ENTER LOWER LIMIT OF INTEGRAL"; : INPUT A 230 PRINT TAB(10); "ENTER UPPER LIMIT OF INTEGRAL";: INPUT B 240 PRINT TAB(10); “ENTER n SUBINTERVALS";: INPUT N 250 260 ' 270 br nm mrt t rrr ett t tree Computations 280 '' 290 H=(B-A)/N 300 FA=FNFX(A) 310 FB=FNFX(B) 320 SUM = 0 330 FOR I = 1 TO N-1 340 X*A+I*H 350 SUM = SUM + 2 * FNFX(X) 360 NEXT I 370 INTEGRAL * (H/2)* \FA+tFE+SUM) 380 '
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410 PRINT: PRINT &20 PRINT TAB(10);"THE COMPUTED VALUE OF THE INTEGRAL IS: "; INTEGRAL 430 PRINT 440 PRINT TAB(10);"STRIKE 1 TO USE THIS PROGRAM AGAIN" 450 PRINT TAB(10);"OR STRIKE 2 TO QUIT"; &60 INPUT Z 470 IF 2 = 1 GOTO 90 ELSE 480 &80 END &90 '
Appendix B. Computer Program 87
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REFERENCES 60
Vita
Name
Nationality
Date of Birth
Education
Honors
and
Activities
Vita
M. Rafik Nemeh
Syria
November 7,1964
Master of Science in Civil Engineering, (Transportation Division),
Virginia Polytechnic Institute and State University, Blacksburg,
Virginia, December 1988, (GPA: 3.784/4.0)
B.S., Civil Engineering, August 1987, Virginia Tech.
Overall GPA: 3.25/4.0
Minor: Engineering Science And Mechanics, GPA: 3.61/4.0