effect of geometric factors on lateral …docs.trb.org/prp/17-03950.pdf2 vehicles in freeway buffer...
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EFFECT OF GEOMETRIC FACTORS ON LATERAL POSITION OF 1
VEHICLES IN FREEWAY BUFFER SEPARATED MANAGED LANES 2
3
By 4 5
Tomás E. Lindheimer, Ph.D. 6 (Corresponding Author) 7
Associate Transportation Researcher 8
Texas A&M Transportation Institute 3135 TAMU 9
College Station, TX 77843-3135 10
Phone: 979/458-2587, fax 979/845-6006 11
Email: [email protected] 12
13
Kay Fitzpatrick, Ph.D., P.E., P.M.P. 14 Senior Research Engineer 15
Texas A&M Transportation Institute, 3135 TAMU 16
College Station, TX 77843-3135 17
Phone: 979/845-7321, fax: 979/845-6006 18
Email: [email protected] 19
20
Raul Avelar, Ph. D., P.E., P.M.P. 21 Associate Research Engineer 22
Texas A&M Transportation Institute, 3135 TAMU 23
College Station, TX 77843-3135 24
Phone: 979/845-7321, fax: 979/845-6006 25
Email: [email protected] 26
27
Jeffrey D. Miles, P.E., P.T.O.E. 28 Texas Department of Transportation 29
Email: [email protected] 30
31
32
33
Submission Date: August 1, 2016 34
Number of Words in Text: 4,958 35
Number of Tables / Figures: 9x250= 2,250 36
Total Equivalent Number of Words: 7,208 37
38
Lindheimer, Fitzpatrick, Avelar, Miles 1
ABSTRACT 39 Chapter 3 in the 2004 American Association of State Highway and Transportation Officials High 40
Occupancy Vehicle Guidelines includes a prioritized tradeoff table on various design options for 41
high occupancy vehicle lanes (now known as managed lanes). The design tradeoffs include the 42
reduction of lane, shoulder, and/or buffer width. The key measure believed to be affected by 43
lane, shoulder, and buffer width is lateral position. The objective of this study was to identify the 44
relationship between operations and cross-section width, including the type of buffer design 45
separating the managed lanes from the general-purpose lanes. This research study collected 46
lateral position data on existing managed lane facilities with a range of geometric elements 47
within both tangent and horizontal curves and identified potential relationships between the 48
geometric design element values and the measure of effectiveness. The field studies included 49
data collected at 28 sites using fixed video cameras and along 161 centerline miles using an 50
instrumented vehicle that recorded data for the vehicle immediately in front of the instrumented 51
vehicle. The study found that managed lane drivers shifted away from the pylons placed in the 52
buffer. Horizontal alignment (tangent or curve) and the direction of the horizontal curve (left or 53
right) were influential on lateral position. Left shoulder, lane, and buffer width affected lateral 54
position. Modifying a 6.5-ft shoulder to a minimum shoulder (i.e., 1.5 ft) will result in drivers 55
moving to the right about 0.5 ft; however, if a 18.5-ft shoulder is reduced by 5 ft, the impact in 56
operations is negligible (drivers would shift only about 0.11 ft toward the right). 57
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60
Lindheimer, Fitzpatrick, Avelar, Miles 2
INTRODUCTION 61 The 2004 American Association of State Highway and Transportation Officials (AASHTO) 62
High Occupancy Vehicle Guidelines (1) include tradeoff suggestions on various design options 63
for high-occupancy vehicle (HOV) facilities, now called managed lanes. Chapter 3 in the 64
Guidelines contains tables of the prioritized design tradeoffs which include the reduction of lane, 65
shoulder, and/or buffer width. Figure 1 shows the shoulder, lane, and buffer of the managed lane 66
in relation to general purpose traffic. The dimensions of a managed lane could possibly 67
influence driver behavior. Drivers may adjust their position in the managed lane depending on 68
their proximity to a concrete barrier or to traffic in the adjacent general-purpose lane. Those 69
adjustments may be different depending upon the available width for the shoulder, the lane, or 70
the buffer between the managed lane and the general-purpose lane. 71
72
73 FIGURE 1 Managed lane elements. 74
75
Objective 76 The objective of this study was to identify the relationship as revealed through travel data 77
between operations and cross-section width, including the type of buffer design separating the 78
managed lanes from the general-purpose lane. The researchers collected lateral position data on 79
existing managed lane facilities with a range of lane widths, shoulder widths, and buffer widths 80
within both tangent and horizontal curves and identified potential relationships between the 81
geometric design element values and the measures of effectiveness. 82
83
LITERATURE REVIEW 84 Previous studies on lateral position of vehicles within a driving lane mostly investigated two-lane 85
rural roads and curves. When looking at how the application of rumble strips affects the lateral 86
position of vehicles within the lane, researchers used piezoelectric sensors in a 87
Z-configuration (2). The same configuration using road tubes was deployed when investigating 88
lateral position and speed at horizontal curves (3,4). Fitzsimmons et al. analyzed the speed and 89
Lindheimer, Fitzpatrick, Avelar, Miles 3
lateral position data for 23,468 vehicles traveling on two horizontal curves in central Iowa. The 90
tubes were placed in five equally spaced stations along the curve, and the spacing was 91
determined by the distance between the PC and PT points. The study used a linear mixed effects 92
model to attempt to predict speed and lateral position along curves. The researchers found that 93
vehicle type, time of day, and travel direction were significant factors affecting a vehicle’s speed 94
and lateral position. Researchers looked at driver behavior and found that speed entering the 95
curve has a direct impact on lateral position and acceleration near the center of the curve (3). 96
Hallmark et al. (4) performed an odds ratio analysis to correlate speed and lateral position 97
on curves. The study found that the odds of a near lane crossing were 2.37 to 4.47 greater at 98
higher speeds. These results were statistically significant and imply that the higher the speed the 99
greater the odds of a near lane crossing. Odds of a near lane crossing for vehicles traveling more 100
than 5 mph when compared to slower vehicles were not statistically significant. Gates et al. (5) 101
used video footage to gain insight on the impact of centerline and shoulder rumble strips on 102
driver behavior. High-definition cameras were mounted on poles (7 to 20 ft high) to record 103
traffic during daylight hours. Lateral position was measured according to the center of the lane 104
and the center of the vehicle with the license plate being the reference point. The vehicle was 105
considered centered if it was within 6 inches to the left or right of the center of the lane. The 106
study found that rumble strips had a significant impact on lateral position on curve and tangent 107
segments. Variations existed between vehicle types, but overall vehicles tended to travel down 108
the center of the lane when both center and shoulder rumble strips were present. 109
Bunker et al. (6) used video footage to look at lateral position of cars and heavy vehicles 110
on two-lane highways in Queensland, Australia. What was of interest was the interaction of 111
passenger cars with freight vehicles towing two or more trailers. Lateral position was used as a 112
measure to assess driver behavior. For data collection a camera was on an overpass overlooking 113
the road. Lateral position was defined as the distance between the middle of the road and the 114
nearest edge of the vehicle. Lateral position was measured off the video image by using a scaled 115
overlay on the computer screen. The scale divided each lane into eight divisions. Four hours of 116
video was recorded and a total of 3,151 vehicles were observed. The study showed that typically 117
passenger cars do not change their lateral position when heavy trucks travel in the opposite 118
direction. They also found that heavy trucks tend to occupy part of the shoulder, while passenger 119
cars tend to straddle the edgeline marking that separates the shoulder and the lane. 120
Researchers in Sweden investigated the lateral position and lateral wander (i.e. variation 121
of lateral position) of vehicles and the effect they have on pavement surface wear. Lateral 122
position was measured from the edge of the right front tire to the edge of the right hand side. 123
Researchers collected data from 21 different sites by using three coaxial cables placed in a “Z” 124
configuration within the right hand side lane of the roadway. The investigation was carried out in 125
tangent segments of the roadway and not on curved segments. Lateral position data of over 126
271,000 vehicles was gathered and analyzed. The analysis showed that lateral wander is affected 127
by lane width, verge width, total width of the roadway, and proximity to guardrail. Lateral 128
wonder for smaller vehicles had a higher variation (7.5 to 17.9 inches) than commercial vehicles 129
(5.5 to 16.9 inches). The researchers hypothesize that curvature will have an effect on lateral 130
position (7). 131
In summary, the literature review identified two methods of gathering data for lateral 132
position: use of on-pavement sensors or road tubes, and use of video cameras overlooking a 133
roadway segment. Lateral position research has been a concern mainly on curves and tangent 134
Lindheimer, Fitzpatrick, Avelar, Miles 4
segments of two-lane rural highways. Researchers have used lateral placement as a measure to 135
determine driver behavior and have not researched to identify a relationship with crash rates. 136
137
DATA COLLECTION 138 Data were collected during daylight and dry pavement conditions. Video data using a fixed video 139
camera were obtained from San Jose, CA; Houston, TX; within the Minneapolis/St. Paul, MN 140
region; and within the Puget Sound, WA region. These data were retrieved from either 141
contacting the operating agencies directly or having a research team place stationary cameras in 142
the field. Data from the San Jose, Minnesota, and Washington sites were obtained by contacting 143
the Santa Clara Valley Transportation Authority, the Minnesota Department of Transportation, 144
and the Washington State Department of Transportation, respectively. Individuals from all 145
agencies provided the research team with video samples representing either a period or an entire 146
day of operation. The focal point for each camera was centered on the managed lane, with the 147
background capturing traffic conditions from the adjacent general-purpose lanes. Cameras 148
captured either a period of observed traffic (e.g. morning, afternoon), or an entire day or two of 149
operation depending upon what the agency could provide. Data from the Houston, TX, location 150
were obtained from stationary cameras installed on the concrete barrier separating the direction 151
of travel. Cameras in-site recorded traffic for a 24-hour period. 152
An instrumented vehicle was used to obtain in-field data for a selection of sites. For this 153
protocol, an instrumented vehicle followed a vehicle traveling in the managed lane. The 154
instrumented vehicle was outfitted with a still-frame video camera, a LIDAR detector, and a GPS 155
data logger. The still-frame video camera captured single black-and-white images, recording the 156
images once per second. The LIDAR detector measured the distance from the instrumented 157
vehicle to the followed vehicle. The GPS data logger recorded the geographical coordinates 158
(latitude, longitude) and speed of the instrumented vehicle. Data from each instrument were 159
transmitted into an onboard laptop computer. 160
161
SITE SELECTION 162 Sites were chosen based on geographic distribution and variety in design widths. The research 163
team considered sites in California, Minnesota, Texas, and Washington. Only sites with one 164
managed lane per direction and buffer-separated from the general purpose lanes were considered. 165
The geometric characteristics obtained for each site included physical components of the 166
managed lane, adjacent general-purpose lane, and other traits within the corridor. Data on 167
geometric features were gathered through discussion with local agencies responsible for 168
operating the managed lane, measurements from aerial photographs, or measurements taken 169
when installing the fixed video cameras. Specifically, the following geometric features were 170
collected for use in the study: 171
Left shoulder width. 172
Managed lane width. 173
Lane separation type between managed lane and general-purpose lanes (e.g. flush 174
buffer, pylons). 175
Buffer width. 176
Buffer type (described below). 177
Number of general-purpose lanes. 178
Average lane width for the general-purpose lanes. 179
Right shoulder width. 180
Lindheimer, Fitzpatrick, Avelar, Miles 5
The following buffer types were observed during the study: 181
Double white lines (DW), see Figure 2 (a). 182
Single white and four yellow lines (SWFY), see Figure 2 (b). 183
Double white lines with pylons (DWP) see Figure 2 (c). 184
Single white line and single yellow line (SWSY). 185
Single white line and two yellow lines (SWTY) see Figure 2 (d). 186
Single white line (SW). 187
Pylons, where present, were 36 to 39 inched high and were spaced 12 to 14 ft apart. 188
189
(a) (b)
(c) (d)
FIGURE 2 Examples of buffer types observed during the study. 190 191
Data were collected through fixed camera video footage or by an instrumented vehicle 192
outfitted with appropriate sensors and video recorders. For driving data, freeways in and near the 193
city of Dallas were chosen because of the use of pylons serving as a barrier between the managed 194
lane and the general-purpose lanes. In California, freeways were chosen to provide a range of 195
buffer widths. The routes and data collection times for the driving data were selected to increase 196
the number of potential data points while being on segments of interest. The research team 197
gathered driving data from a total of 11 routes; 9 in California and 2 in Texas. The following 198
buffer types (and widths shown in parentheses), lane widths, and shoulder widths were observed 199
during the study: 200
Lane width: managed lane (10.4 – 11.8 ft), general-purpose lane (11 – 12 ft). 201
Shoulder width (1.4 – 14.9 ft). 202
Buffer type: DW (1 – 4.5 ft). 203
Buffer type: SWTY (1.7 – 4.9 ft). 204
Buffer type: SWFY (4.1 – 4.9 ft). 205
Buffer type: SWSY (1.7 – 2.2 ft). 206
Buffer type: DWP (4 – 5 ft). 207
There were a total of 28 sites where data were gathered with fixed video cameras. Seven 208
sites were located in Minnesota, 10 in Texas, 10 in Washington, and one in California. Managed 209
lane facilities in Minnesota, California and Texas had limited access, while Washington facilities 210
Lindheimer, Fitzpatrick, Avelar, Miles 6
have continuous access. The following buffer types (and widths shown in parentheses), lane 211
widths, and shoulder widths were observed during the study: 212
Lane width: managed lane (10 – 13 ft), general-purpose lane (11 – 12 ft). 213
Shoulder width (1.67 – 18.35 ft). 214
Buffer type: DW (1 – 4.67 ft). 215
Buffer type: DWP (5 ft). 216
Buffer type: SW (1 ft). 217
218
DRIVING AND FIXED VIDEO DATA REDUCTION 219 For this research, lateral position was defined as the space between the edge of the back wheel 220
and the inside edge of the pavement marking. Figure 3 illustrates the left lateral position (LP-Lf) 221
and the right lateral position (LP-Rt) for a vehicle in a managed lane. 222
223
224 Source: TTI 225
FIGURE 3 Example of left and right lateral position for vehicle near center of the managed 226
lane 227
228 The following data variables were collected for each vehicle: 229
Time of day. 230
Type of vehicle. 231
Presence of an adjacent vehicle in the general-purpose lane. 232
General-purpose lane traffic was traveling 10 mph slower than the managed lane, in 233
the opinion of the technician. 234
Lateral position of the vehicle within the managed lane. 235
Lateral position data were reduced from the video on desktop computers. To determine 236
lateral position, a transparency sheet was placed over the computer monitor. The pavement 237
marking lines and a perpendicular line across the lane were drawn on the transparency. Road 238
features (such as diamond markings) or vehicle features (i.e. rear bumper) were used to draw a 239
Lindheimer, Fitzpatrick, Avelar, Miles 7
horizontal line across the lane in order to ensure that the horizontal line was perpendicular to the 240
pavement markings, and straight according the plane of the video. A ruler was aligned to the 241
horizontal line and the tick mark “0” was placed along the inside edge of the pavement marking 242
and then the tick marks from the left pavement marking to the wheel were noted. After the lateral 243
position in millimeters was read, the lane width was measured with the ruler. For some videos it 244
was better to measure the right wheel instead of the left wheel. Lane width measurements were 245
taken in the field or using aerial photographs for each site where video footage was recorded. 246
These measurements allowed the research team to scale the lateral position readings from 247
millimeters to feet for each vehicle observed. 248
For the data from the instrumented vehicle each photograph was automatically saved with 249
a time stamp depicting the date and time of day the picture was captured. All LIDAR readings 250
and GPS coordinates were entered into a spreadsheet and matched according to the time stamp of 251
when the data point was recorded. A researcher would enter on the spreadsheet the following 252
information from the picture: 253
Is the vehicle within an access opening or entrance/exit point? Vehicle within an 254
access opening or at entrance/exit points were not reduced. 255
Is the vehicle on a tangent (T), a curve to the left (LC), a curve to the right (RC). 256
Pixel coordinates for the left pavement marking. 257
Pixel coordinates for the edge of the right rear wheel of the car. 258
Pixel coordinates for the right pavement marking. 259
Only pictures with a clear resolution and with all road features visible were used in data 260
reduction. The picture file was opened with Microsoft Paint to obtain the pixel coordinates of the 261
right wheel and the inside edge of the pavement marking. Once all pixel coordinates were 262
entered, the difference between pixel coordinates was calculated. The LIDAR distance was used 263
to determine the reference scale from millimeters on the screen to estimated feet within the 264
managed lane. To ensure data quality, limits for non-realistic outliers were set for lane width. 265
Data were also not used for occurrence when lane readings were below 9 ft or above 13 ft. Both 266
occurrences could be due to an error in LIDAR reading, or due to difficulties in aiming the 267
LIDAR gun. All valid data points where compiled into a main database for analysis. This 268
calibration, and other tests of the procedure, further ensured that lateral position readings were 269
accurate within 6 inches. 270
When reducing the dataset, some data points represented the left lateral position and 271
some represented the right lateral position depending upon which side of the vehicle provided the 272
better view. Because most of the dataset was left lateral position, the right lateral positions were 273
converted to be left lateral position through the use of the following assumed vehicle wheel base 274
widths: 275
Passenger car = 6.0 ft, based on Green Book Figure 2-1 (8). 276
SUV / Van = 6.0 ft, based on Green Book Figure 2-2 (8). 277
Pickup Truck = 6.5 ft, estimated from: http://dodgeram.info/2001/dimensions.html and 278
https://www.fleet.ford.com/truckbbas/topics/2012/12_SD_Pickups_SB.pdf. 279
Transit or school bus = 8.5 ft, based on Green Book Figure 2-4 (8). 280
Emergency vehicle = 8.0 ft, based on following website: 281
http://www.hortonambulance.com/type1.cfm. 282
Motorcycle = 2.3 ft, estimated from: 283
https://www.fleet.ford.com/truckbbas/topics/2012/12_SD_Pickups_SB.pdf. 284
The resulting dataset included over 7000 vehicles. 285
Lindheimer, Fitzpatrick, Avelar, Miles 8
DRIVING AND FIXED VIDEO FINDINGS 286 287
Preliminary Findings 288 The average and standard deviation for lateral position (left) is shown in Table 1 for the driving 289
sites and in Table 2 for the fixed video camera sites. These tables also provide the total number 290
of lateral position readings available for the analysis. Overall, the vehicles in the managed lane 291
were about 2.5 ft from the left edgeline. 292
293
TABLE 1 Average left lateral position by site for driving sites. 294 Site
a SW (ft) LW (ft) BW (ft) Buffer Count Ave Lf_LP StdDev Lf_LP
CA I-10 12.8 11.3 4.9 DW, SWTY 180 2.9 0.9
CA I-105 9.4 11.0 4.9 SWFY 205 2.9 0.8
CA I-210 2.7 11.1 1.9 SWTY 348 2.8 0.8
CA I-405 2.7 10.4 1.7 SWTY 144 2.9 0.8
CA I-605 2.2 10.4 2.2 SWSY 26 2.6 0.8
CA SR-118 2.2 11.7 2.4 SWTY 172 3.3 1.1
CA SR-134 1.8 10.9 1.7 SWSY 142 3.0 0.8
CA SR-210 14.9 11.8 4.1 SWFY 83 2.6 0.8
CA SR-60 1.4 10.5 1.7 SWTY 8 2.9 0.6
CA SR-91 1.8 10.9 2.0 SWTY 13 3.3 1.2
TX I-635 2.0 10.5 5.0 DWP 865 2.4 0.8
TX US-75 2.0 11.0 4.0 DWP 1169 2.0 0.8
All Sites NA b NA NA NA 3355 2.5 0.9
a Column Headings
Site = Name of site consisting of state and highway number.
SW = left shoulder width (ft).
LW = managed lane width (ft).
BW = buffer width (ft).
Buffer = buffer type.
Count = number of vehicles included in dataset.
Ave Lf_LP = average left lateral position.
StdDev Lf_LP = standard deviation for left lateral position. b NA = value not applicable or meaningful for all site totals or averages.
295
296
Lindheimer, Fitzpatrick, Avelar, Miles 9
TABLE 2 Average left lateral position by site for fixed view sites. 297 Site
a Road LA
or
CA
Tan
or
Cur
SW
(ft)
LW
(ft)
BW
(ft)
Buffer Count Ave
Lf_LP
StdDev
Lf_LP
CA 01 SR-237 LA Tan 4.0 11.0 2.0 DW 1097 1.9 1.0
MN 6091 I-35W LA Tan 4.0 10.0 3.0 DW 203 1.2 0.9
MN 6131 I-35W LA Tan 3.0 10.5 2.0 DW 191 1.7 0.9
MN 614 I-35W LA Tan 3.0 10.0 3.0 DW 109 1.7 1.2
MN 6231 I-35W LA Tan 2.0 12.0 0.8 SY 203 3.9 1.3
MN 908 I-394 LA Tan 8.0 11.8 2.0 DW 152 3.0 1.0
MN 909 I-394 LA Tan 8.5 11.5 3.0 DW 132 2.4 1.2
TX 01 US-59 LA Tan 9.8 11.5 1.0 DW 190 1.8 1.5
TX 02 US-59 LA Tan 9.9 11.2 1.0 DW 184 2.2 1.3
TX 03 I-10 LA Tan 18.4 13.0 5.0 DWP 114 3.9 1.5
TX 04 I-10 LA Tan 15.3 13.0 5.0 DWP 100 2.2 0.9
TX 05 US-59 LA Tan 13.3 11.3 4.7 DW 187 3.1 1.2
TX 06 US-59 LA Tan 13.4 11.5 4.5 DW 289 3.0 1.3
TX 07 US-290 LA Tan 1.7 10.5 0.8 DW 179 2.7 0.8
TX 08 US-290 LA Tan 1.7 10.5 0.8 DW 119 2.9 0.8
TX 09 US-290 LA Tan 1.7 10.5 0.8 DW 142 2.8 0.8
TX 10 US-290 LA Tan 1.7 10.5 0.8 DW 107 2.7 0.8
WA-01 SR-167 CA Tan 9.50 11.0 1.00 SW 177 2.3 1.0
WA-02 SR-167 CA Tan 7.77 11.3 1.00 SW 170 2.5 0.9
WA-03 SR-167 CA Tan 8.50 10.2 2.00 DW 108 1.9 0.8
WA-04 SR-167 CA Tan 6.47 12.8 1.00 SW 104 2.7 1.0
WA-05 SR-167 CA Tan 8.35 12.2 1.00 SW 108 3.5 1.0
WA-06 SR-167 CA Tan 11.00 12.2 1.00 SW 111 3.4 1.2
WA-07 SR-167 CA Cur 8.35 12.2 1.00 SW 108 0.8 0.8
WA-08 SR-167 CA Cur 11.00 12.2 1.00 SW 198 1.8 0.8
WA-09 SR-167 CA Cur 9.50 11.0 1.00 SW 107 3.1 1.0
WA-10 SR-167 CA Cur 7.77 11.3 1.00 SW 116 3.1 1.1
All Sites NA b NA NA NA NA NA NA 5005 2.5 1.0
a Column Headings
Site = Name of site.
Road = name of road for site.
LA or CA = Limited access (LA) or continuous access (CA).
Tan or Cur= Tangent (T) segment or curve (C) segment of highway.
SW = left shoulder width (ft).
LW = managed lane width (ft).
BW = buffer width (ft).
Buffer = buffer type.
Count = number of vehicles included in dataset.
Ave Lf_LP = average left lateral position.
StdDev Lf_LP = standard deviation for left lateral position. b NA = value not applicable or meaningful for all site totals or averages.
298 299
Lindheimer, Fitzpatrick, Avelar, Miles 10
STATISTICAL EVALUATIONS 300 301
Variable Selection 302 During preliminary evaluations, characteristics of the dataset that needed to be considered during 303
the evaluation were identified. As expected, narrow lane widths were typically associated with 304
narrow shoulder and buffer widths. If that relationship is always true, then the shoulder, lane, and 305
buffer widths would be correlated, and not all variables would be able to be in the model. By 306
combining the driving and fixed video camera datasets, sufficient variability in shoulder, lane, 307
and buffer widths exists so that all three variables can be uniquely included. 308
In addition to the site characteristics and level of access, conditions present when the 309
lateral position reading was taken could affect a driver’s decision. The type of vehicle, especially 310
motorcycles, has an obvious influence on lateral position. Other conditions measured included 311
whether a vehicle in the neighboring general-purpose lane was near the managed lane vehicle 312
and whether the technician believed the managed lane vehicle’s speed could be 10 mph higher 313
than the general-purpose lanes. While a neighboring general-purpose vehicle could be next to the 314
managed lane vehicle without having the 10-mph speed difference, for this dataset these 315
variables were highly correlated. Therefore, only one of the two variables (vehicle in 316
neighboring lane or managed lane vehicle more than 10 mph higher) could be retained in the 317
model. The team selected the variable for whether a neighboring general-purpose vehicle was 318
present because stronger statistical models resulted. 319
320
Statistical Model 321 A linear mixed-effect model was used to analyze the lateral position data. Initial models did not 322
produce very satisfactory results, so the sites and data were reviewed to identify other variables 323
or other relationships that could help to explain the variations observed. Two changes were 324
identified. The variable pylon (yes or no) was added as it appears that left lateral position is 325
smaller for those sites with pylons. The other change was to model the shoulder, lane, and buffer 326
widths as parabolic curves. An advantage to using the parabolic curve function is that it reflects 327
changes in width having minimal influence when the width is large and having much greater 328
influence when the width is small. A parabolic curve has a portion where the curve is decreasing 329
to a vertex after which it will then be increasing. To improve the ability to easily interpret the 330
results, the vertex of the curves were set to fall outside the available range for the variable. 331
The best fit model is shown in Table 3. This table also shows variable definitions and 332
baseline conditions of the model. The sign of lane width and shoulder width should be 333
interpreted in the opposite direction than the rest of variables because of how these shifted 334
variables were defined. The results demonstrate that in most cases the lateral position for most of 335
the vehicle types is significantly different from a passenger car. As anticipated, larger vehicles 336
(e.g., buses) were closer to the left edgeline while motorcycles are farther from the edgeline. 337
When a general-purpose vehicle is next to the managed lane vehicle, the managed lane vehicle 338
was 0.32 ft closer to the edgeline. 339
340
Lindheimer, Fitzpatrick, Avelar, Miles 11
TABLE 3 Linear mixed-effect model. 341 Variable
a, b Estimate Std. Error DF t-value p-value
Reference c 3.14528 0.22674 8310 13.87173 >0.00001
TpVeh=B -1.23188 0.07862 8310 -15.66793 >0.00001 d
TpVeh=EM -0.39833 0.245064 8310 -1.62546 0.1041 d
TpVeh=MC 1.92241 0.08664 8310 22.18856 >0.00001 d
TpVeh=PT -0.27951 0.03267 8310 -8.55412 >0.00001 d
TpVeh=V 0.092721 0.02188 8310 4.23762 >0.00001 d
Veh_GP=Yes -0.31771 0.02037 8310 -15.59416 >0.00001
Pylons=yes -0.92541 0.37144 34 -2.49143 0.0178
sqBW 0.03180 0.01421 34 2.23837 0.0319
sqLW.r14 -0.13387 0.02738 34 -4.88866 >0.00001
sqSW.r19 0.00361 0.00114 34 3.16544 0.00033
HorAl=LC -1.69920 0.20453 8310 -8.30779 >0.00001
HorAl=RC 0.44487 0.09033 8310 4.92481 >0.00001
sqBW:HorAl=LC 0.03796 0.00548 8310 6.91957 >0.00001
sqBW:HorAl=RC -0.01289 0.00584 8310 -2.20807 0.0273
sqSW.r19:HorAl=LC 0.00357 0.00065 8310 5.50724 >0.00001
Notes:
a Column Headings:
Estimate = natural logarithm of the ratio: Odds (coefficient level) / Odds (reference level). In the case of
reference level, Estimate is the log-odds of the average yielding rate at the reference level.
Std. Error = Standard error of value.
DF = degree of freedom
t-value = conservative estimate of the z-value, which is the standard normal score for estimate, given the
hypothesis that the actual odds ratio equals one.
p-value = Probability that the observed log-odds ratio be at least as extreme as estimate, given the
hypothesis that the actual odds ratio equals one. b Variables included in the statistical evaluation:
TpVeh = Type of vehicle: Passenger Car (PC), Pickup Truck (PT), SUV/Van (V), Transit or
School Bus (B), Emergency Vehicle (EM), Motorcycle (MC)
Veh_GP = was there a general-purpose vehicle next to managed lane vehicle? (yes or no)
Pylons = were pylons present? (yes or no)
sqBW = square of buffer width
sqLW.r14 = square of lane width with a reference point of 14
sqSW.r19 = square of shoulder width with a reference point of 19
HorAl = horizontal alignment, left curve (LC), right curve (RC), or tangent (Tan) c Baseline condition left lateral position in the model is estimated for the following conditions:
TpVeh = PC
Veh_GP = No
Pylons = No
HorAl = Tan d These p-values require an adjustment for multiple comparisons if inferences about different lateral
position values among vehicles are intended.
342
The results of the statistical evaluation can be used to develop a lateral position prediction 343
equation as shown in equation 1. 344
345
LP_Lf = 3.14528 + 0 (TpVeh=PC) – 1.23188(TpVeh=B) – 0.39833 (TpVeh=EM)
Lindheimer, Fitzpatrick, Avelar, Miles 12
+ 1.92241 (TpVeh=MC) – 0.27951 (TpVeh=PT) + 0.09272 (TpVeh=V)
– 0.31771 (Veh_GP=Yes) –0.92541 (Pylons=yes) + 0.03180 (BW)^2
– 0.13387 (14-LW)^2 + 0.00361 (19-SW)^2 + 0 (Hor=Tan) –1.69920 (Hor=LC)
+ 0.44487 (Hor=RC) + 0.03796 (BW)^2 × (Hor=LC) – 0.01289 (BW)^2 × (Hor=LC)
+ 0.00357 (19-SW)^2 × (Hor=LC)
Equation 1 346 Where: 347
LP_Lf = Left lateral position within the managed lane, in other words the 348
distance between the left wheel of the vehicle and the edgeline between the 349
managed lane and the shoulder (ft). 350
TpVeh=PC = 1 when the vehicle type is a passenger car, 0 otherwise. 351
TpVeh=B = 1 when the vehicle type is a bus, 0 otherwise. 352
TpVeh=EM = 1 when the vehicle type is an emergency vehicle, 0 otherwise. 353
TpVeh=MC = 1 when the vehicle type is a motorcycle, 0 otherwise. 354
TpVeh=PT = 1 when the vehicle type is a pickup truck, 0 otherwise. 355
TpVeh=V = 1 when the vehicle type is a van, 0 otherwise. 356
Veh_GP=Yes = 1 when a vehicle is present in the general-purpose lane next to the 357
managed lane vehicle, 0 otherwise. 358
Pylons=yes = 1 when pylons are present in the buffer, 0 otherwise. 359
BW = Buffer width (ft). 360
LW = Lane width (ft). 361
SW = Shoulder width (ft). 362
Hor=Tan = 1 when the horizontal alignment is a tangent, 0 otherwise. 363
Hor=LC = 1 when the horizontal alignment is a curve to the left, 0 otherwise. 364
Hor=RC = 1 when the horizontal alignment is a curve to the right, 0 otherwise. 365
366
According to the model in equation 1 drivers shy away from the pylons. When pylons 367
were present, drivers were 0.93 ft closer to the left edgeline as compared to when the pylons 368
were not present. Horizontal alignment and the direction of the horizontal curve were influential 369
on lateral position. Drivers were closer to the left edgeline by up to 1.7 ft when on a curve to the 370
left and drivers shifted farther from the left edgeline by up to 0.44 ft when on a curve to the right 371
depending upon assumed shoulder, lane, and buffer widths. The model also tested if access to the 372
managed lane (i.e. continuous vs. limited access) had an effect on lateral position. The variable 373
was found not significant; therefore, it was not included in the final model. 374
375
Illustration of Lateral Positions for Key Variables 376 Figure 4 illustrates the relationship between lateral position and shoulder width. Note that the 377
graph is a plot of regression findings showing results for the complete range between the 378
minimum of 1.5 ft and the maximum of 18.5 ft. For some agencies, shoulders more than 4 ft and 379
less than 8 ft are avoided because drivers may believe sufficient width is available for refuge. 380
The plot shows that when the left shoulder of a tangent section or a horizontal curve to the right 381
is at the minimum for the dataset (about 1.5 ft), drivers tend to be 1.11 ft farther to the right of 382
the left edgeline (i.e., left lateral position increases), compared to when shoulder width is 18.5 ft. 383
This curved function also implies that modifying a 6.5 ft shoulder to a minimum shoulder (i.e., 384
1.5 ft) will result in drivers moving to the right about 0.54 ft; however, if a 18.5 ft shoulder is 385
Lindheimer, Fitzpatrick, Avelar, Miles 13
reduced by 5 ft, the impact in operations is negligible (drivers would shift only about 0.11 ft 386
toward the right). The effects were more pronounced for drivers on curves to the left, which limit 387
sight distance more than tangents or curves to the right. Drivers on a section with minimal 388
shoulders appear to be more concerned with avoiding the median barrier when turning left as 389
demonstrated by the larger left lateral position distances. 390
391
392 FIGURE 4 Lateral position relative to changes in shoulder width. 393
394
Smaller lane widths logically result in smaller left lateral positions because the 395
measurement is a reflection of the lane width. As lane width decreases, drivers are closer to the 396
left edgeline as shown in Figure 5. The plot shows that when the lane width is at the minimum 397
for the dataset (10.5 ft), drivers tend to be 1.6 ft closer to the left edgeline (i.e., left lateral 398
position decreases), compared to when lane width is 13.5 ft. A curvilinear relationship implies 399
different effects at different levels of lane width. When reducing a 13-ft lane by 1 ft, the model 400
predicts a shift toward the left of about 0.41 ft. However, when reducing an 11.5-ft lane by 1 ft, 401
the result would be drivers shifting toward the left by about 0.8 ft. 402
403
Lindheimer, Fitzpatrick, Avelar, Miles 14
404 FIGURE 5 Lateral position related to lane width. 405
406
The width of the buffer affects lateral position with larger widths having more influence 407
than smaller widths, as shown in Figure 6. The interaction between buffer width and horizontal 408
alignment also affects lateral position. The presence of a horizontal curve to the left was more 409
influential than a tangent section or a horizontal curve to the right. A difference of about 0.9 ft in 410
lateral position exists between 5 ft and 0.8 ft buffers on tangents, whereas left curves there was a 411
difference of 1.9 ft. The curvilinear relationship for tangents indicates that reducing a 2-ft buffer 412
to a 1-ft buffer will have a negligible effect (a shift to the left of approximately 0.1 ft) compared 413
to reducing a 5-ft buffer to 4 ft (a shift to the left about 0.3 ft). When on a left turning curve, 414
drivers are 0.84 ft closer to the left shoulder with a 2-ft buffer as compared to a 4-ft buffer. 415
416
417 FIGURE 6 Lateral position relative to buffer width. 418
419
420
Lindheimer, Fitzpatrick, Avelar, Miles 15
SUMMARY / CONCLUSION 421 This study identified potential tradeoffs in cross section dimensions by gathering the lateral 422
position of vehicles within existing managed lanes with different shoulder, lane, and buffer 423
widths. The field studies included data collected at 28 sites using fixed video cameras and along 424
161 centerline miles using an instrumented vehicle that recorded data for the vehicle 425
immediately in front of the instrumented vehicle. The key measure was lateral position of the 426
managed lane vehicle measured between the shoulder edgeline and the left rear wheel. A 427
summary of the findings for variables that affect lateral position follow: 428
Vehicle type affects lateral position. Larger vehicles, such as buses, are closer to the 429
shoulder edgeline while smaller vehicles, such as motorcycles, are a greater distance 430
away. 431
Presence of a vehicle in the neighboring general-purpose lane results in the managed 432
lane vehicle shifting closer to the shoulder edgeline. 433
Pylons in the buffer result in managed lane drivers shifting away from the pylons. 434
Horizontal alignment (tangent or curve) and the direction of the horizontal curve (left 435
or right) are influential on lateral position. 436
Left shoulder, lane, and buffer width affect lateral position. The best statistical model 437
used a parabolic curve to model the relationships resulting in smaller values for those 438
elements having greater influence on the lateral position. For example, modifying a 439
6.5-ft shoulder to a minimum shoulder (i.e., 1.5 ft) will result in drivers moving to the 440
right about 0.5 ft; however, if a 18.5-ft shoulder is reduced by 5 ft, the impact in 441
operations is negligible (drivers would shift only about 0.11 ft toward the right). 442
443
The speed of the lead vehicle for the data collected using the instrumented vehicle was 444
also considered; however, it was found to be not significant for this dataset. The variable 445
concerning types of access to the managed lane was considered but found to be not significant. 446
Another variable considered but found to be not significant was an estimate of whether the 447
managed lane vehicle was more than 10 mph faster than the neighboring general-purpose lane 448
vehicles. 449
Based on the findings, the following changes to practice can be considered: 450
The provision of adequate shoulder width is desirable because drivers are shying away 451
from the concrete median barrier. Research findings indicated that lateral position is 452
highly affected for narrow shoulder widths; however, a buffer can offset this impact. 453
Research findings show that the impact on lateral position is greater within the 454
minimal values for shoulder, lane, and buffer widths. For example, a 1-ft reduction in 455
shoulder width results in greater changes in lateral position when the shoulder width is 456
near minimal values (e.g., 2 or 4 ft) as compared to when the shoulder width is near 457
desirable (e.g., 8 ft or 14 ft). 458
If insufficient space is available for a full-width left shoulder, consider splitting the 459
available width between the left shoulder and a buffer. Managed lane vehicles are 460
closer to the center of the lane when these values are similar. 461
The practice of reducing the lane width by 1 ft (from 12 ft to 11 ft) and providing that 462
ft of width to the buffer is appropriate. 463
The use of pylons affects lateral position. Using the pylons within a wider buffer can 464
offset the impacts on lateral position. 465
Lindheimer, Fitzpatrick, Avelar, Miles 16
As expected, driver’s lateral position is affected by horizontal curvature. Consider 466
providing additional buffer or shoulder widths within horizontal curves as drivers are 467
shifting their lateral positions when driving on a horizontal curve, especially horizontal 468
curves to the left. 469
470
ACKNOWLEDGMENTS 471 The material in this paper is from the National Cooperative Highway Research Program 472
(NCHRP) project 15-49, “Guidelines for Implementing Managed Lanes.” The research is 473
sponsored by the American Association of State Highway and Transportation Officials 474
(AASHTO), in cooperation with the Federal Highway Administration (FHWA), and is 475
conducted in the National Cooperative Highway Research Program, which is administered by the 476
Transportation Research Board of the National Research Council. The opinions and conclusions 477
expressed or implied in this paper are those of the authors. They are not necessarily those of the 478
Transportation Research Board, the National Research Council, the Federal Highway 479
Administration, the American Association of State Highway and Transportation Officials, or the 480
individual states participating in the National Cooperative Highway Research Program. The 481
authors appreciate the efforts of the numerous TTI staff and student workers who collected and 482
reduced the NCHRP 15-49 data used in this research or who assisted with other facets of the 483
research, especially Nick Wood and Dan Walker. 484
485
Lindheimer, Fitzpatrick, Avelar, Miles 17
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