Determining the Free-Flow Speeds in a Regional Travel Demand Model Based on the Highway Capacity Manual

1 Determining the Free-Flow Speeds in a Regional Travel Demand Model Based on the Highway Capacity Manual Chao Wang* Senior Research Associate Institute for Transportation Research and Education North Carolina State University 909 Capability Drive, Suite 3600 Research Building IV Raleigh, NC 27606 Phone: (919) 513-7379 Fax: (919) 515-8898 Email: cwang11@ncsu.edu Joseph B. Huegy Director, Travel Behavior Modeling Group Institute for Transportation Research and Education North Carolina State University 909 Capability Drive, Suite 3600 Research Building IV Raleigh, NC 27606 Phone: (919) 513-7378 Fax: (919) 515-8898 Email: jbhuegy@ncsu.edu * Corresponding author Word count 6,202 + 1,250 (1 figure + 4 tables) = 7,452 Submitted for presentation at the 93rd TRB Annual Meeting and publication in the Transportation Research Record January 2014, Washington, DC Submission date: July 31, 2013 Revision date: November 15, 2013

2 Abstract This paper presents the approach to determine the free-flow speeds in the Triangle Regional Travel Demand Model (TRM) in North Carolina. Improvements to free-flow speeds are of particular importance in light of the need for improved network skims and accessibility measures, and reasonable speed outputs to support air quality analyses. Directly using formulas in the Highway Capacity Manual (HCM) has several advantages including: saving additional studies, the consistency of free-flow speeds and capacities, and the consistency of travel demand modeling with traffic operations analysis. With the publication of the HCM 2010, it is of great interest to learn if the new HCM can generate reasonable free-flow speeds in the framework of a regional travel demand model. One of the key challenges is that the HCM requires many link attributes, some of which are not usually available to a regional travel demand model. For such link attributes, default values are used by facility type and area type. As a result, when a link s area type is changed for a future year model run, a different set of default values will be used, which results in different free-flow speeds without manually changing the coded link attributes. The resulting free-flow speeds are validated based on a floating car survey conducted in 2011. The result indicates that the HCM is able to yield reasonable free-flow speeds in a regional travel demand model with adjustments based on local data.

3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 In recent years interest has been growing in estimating reasonable speeds in travel demand models. More and more regions have started to validate the highway assignment results by comparing the speed outputs with the observed speeds, whereas historically validation only focused on the comparison of assigned link trips with traffic counts. This change is prompted by several new demands on the travel demand modeling process such as: air quality analyses, the consistency of accessibility measures in model feedback loops, and nontraditional travel demand management strategies (1). In a travel demand model, speeds are estimated in the highway trip assignment stage based on volume-delay functions (VDFs), which use link capacity, free-flow speed, and trip volume to calculate the speeds under congested conditions. Many studies have been focused on the VDFs, including the development of new functional forms (2) and how to calibrate these functions (3). VDFs account for the effects of congestion on the travel speed, and they are critical to reasonable speed outputs from travel demand models. On the other hand, free-flow speed is the theoretical speed of traffic as density approaches zero, so it is the basis for speed estimation and should also be determined carefully. In addition, free-flow speed is usually the initial speed for the model feedback loops for the peak period, and the initial speed for highway trip assignment in the off-peak period. It is also usually used in practice to calculate the network skims for the off-peak period, which affects trip distribution and mode choice in the off-peak period. The Highway Capacity Manual (HCM) presents the procedures for evaluating the operational characteristics of roadways, including the formulas to determine free-flow speeds. Although the HCM has been used in the determination of free-flow speeds in many regional travel demand models, few of them directly adopt the formulas or procedures in the HCM. However, there are several obvious advantages to directly using the formulas in the HCM: The formulas are readily available and they are the product of substantial research efforts. There are more than six decades of research behind the HCM since its first edition was published in 1950. The latest edition, HCM 2010 (4), is the result of a multiagency effort (including TRB, AASHTO, and FHWA) over many years to meet changing analytic needs, and to provide contemporary evaluation tools. So the HCM is a good choice if local data or studies are not available. The HCM is widely used in the determination of capacities in travel demand models. Using formulas for free-flow speeds in the HCM ensures consistency of the freeflow speeds and capacities. The HCM is also widely used for the analysis of traffic operations, which sometimes uses the output from a travel demand model, or its highway network. Therefore, using formulas in the HCM ensures consistency of the travel demand modeling with traffic operations analysis. With the publication of a new version of the HCM in 2010, it is of great interest to learn if the new HCM can generate reasonable free-flow speeds in the framework of a regional travel demand model. This paper shares the experience of using the free-flow speed formulas in the HCM 2010 for the Triangle Regional Travel Demand Model (TRM), which covers Raleigh, Durham and Chapel Hill in North Carolina. This paper first reviews the current practices in determining free-flow speeds in travel demand models in the United States. Then it summarizes the formulas that calculate the freeflow speeds. These formulas are originally taken from the HCM, but some of them are simplified

4 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 to fit the free-flow condition. This paper then discusses how to implement these formulas, followed by the validation of the free-flow speeds based on a floating car survey. The result indicates that the HCM 2010 is able to yield reasonable free-flow speeds in a regional travel demand model with adjustments based on local data. CURRENT PRACTICES Many regions in the United States determine free-flow speeds based on lookup tables, which are typically stratified by link facility type, area type and other strata. For example, the free-flow speed lookup table used in the Atlanta Regional Commission (ARC) model is stratified by link facility type and area type (5). The values in the table were reviewed by a model panel and validated with two speed studies. Another example is the Southern California Association of Governments (SCAG) Regional Model, whose free-flow lookup table is stratified by facility type, area type and posted speed (6). In the New York Best Practice Model (BPM), Physical Link Type (PLT) and area type are used to look up the free-flow speed for each link (7). Several sources were used to determine the free-flow speed values. For uninterrupted facilities, free-flow speed was basically computed as capacity divided by critical density, which is the density when capacity occurs. For other roadways, free-flow speed was defined in a manner consistent with other similar models and was adjusted based on local knowledge. Due to the unique PLT and area type values being used in the BPM, there were many cells in the speed lookup table that cannot be derived from the literature or from other models. In these cases, judgments were made to apply changes between adjacent rows or columns of the table, based on logical relationships. The lookup table approach is easy to implement, but it has some limitations. The values in the tables are averages that might or might not reflect actual speed conditions for specific links (1). For example, if free-flow speeds are determined from a lookup table stratified by area type and facility type, the underlying assumption is that the free-flow speeds for all links of a specific area type and facility type are the same, even if they have different posted speeds, median types, signal timings or parking restrictions. To address this issue, some regions post-process the values from the lookup table based on link attributes. For example, in the BPM Model, the values in the lookup tables need to be reduced by 5% if on-street parking is allowed, and in the SCAG model, the values should be increased by 4% for divided arterials or collectors. However, such simple post-processing might not be applicable when more link attributes need to be considered. Another approach to determine free-flow speeds for travel demand models is based on formulas that use link attributes as inputs to calculate free-flow speeds. For example, the Florida Southeast Regional Planning Model VI (SERPM6) uses two types of formulas to calculate freeflow speeds: one for uninterrupted facilities, and another for interrupted facilities (8). The formula for uninterrupted facilities is a revision of the equation presented in NCHRP 387 (9). The formula for interrupted facilities is a function of posted speed and signal information, such as signal locations, the ratio of effective green time and cycle length, and the cycle length. The basic idea is to add the intersection delay to a link s free-flow travel time to obtain the total travel time, and distance divided by the total travel time yields the free-flow speeds. Similar formulas are used for interrupted facilities in the Dallas-Fort Worth Regional Travel Model (DFWRTM) (10) and the Indiana Statewide Travel Demand Model (ISTDM) (11).There are two major differences among these three models. First, SERPM6 and ISTDM use a function of posted speed as a link s free-flow speed. In detail, SERPM6 uses the linear function from NCHRP 387 and ISTDM develops non-linear regression models based on speed surveys. However, DFWRTM uses a link s posted speed directly as a link s free flow speed. Second, SERPM6 and

5 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 ISTDM use formulas in the Highway Capacity Manual 2000 (12) to calculate the delay at signalized intersections, and the delay used in DFWRTM is the sum of intervening control delay and end-node control delay. Intervening control delay is the delay experienced at the intersection of a coded link with streets that have not been coded in the travel demand model network. It is assumed to be 12 seconds for each intervening control. End-node control delay is the delay experienced at the downstream intersection (i.e., end node) of a link. It is determined based on a set of lookup tables that consider end node traffic control types, functional classifications and area types. Compared to the lookup table approach, the formula approach is more flexible in incorporating different factors in the determination of free-flow speeds. It can yield more reasonable free-flow speed for a link since it is calculated based on the characteristics of that specific link. However, it requires more input data and the formulas need to be carefully determined. The six models reviewed above indicate that free-flow speed lookup tables and formulas are developed based on different methods, including speed surveys (ISTDM), previous studies (SERPM6), other models (BPM), and professional judgment (ARC). However, the HCM is involved in most models. The SERPM6 model starts with the formulas in NCHRP 387, which results in the HCM 2000. The BPM model develops free-flow speeds based on capacities, which are obtained following the HCM procedures. Both the ISTDM and the SERPM6 models use the formulas in the HCM 2000 to calculate the signalized intersection delay. But none of the models directly use the formulas in the HCM. DETERMINING THE FREE-FLOW SPEEDS BASED ON THE HIGHWAY CAPACITY MANUAL The formulas to calculate the free-flow speeds based on the HCM 2010 are summarized below. These formulas are originally taken from the HCM, but some of them are simplified to fit the free-flow condition. Free-flow Speeds for Freeways Chapter 11 of the HCM 2010 describes the procedures to analyze basic freeway segments. The formula to estimate the free-flow speed on a basic freeway segment is shown below (Equation 11-1 from the HCM 2010). 75.4 3.22. (1) is the free-flow speed (mph); is the adjustment for lane width (mph); is the adjustment for right-side lateral clearance (mph); and is the total ramp density (ramps/mile). Adjustment for lane width ( ) can be found in Exhibit 11-8 from the HCM 2010, and adjustment for right-side lateral clearance ( ) is in Exhibit 11-9. Lane width, right-side lateral clearance and the number of lanes are needed for these two adjustments. The first two terms are not usually collected for a regional travel demand model. When they are not available, default

6 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 values of 12 feet and 6 feet can be used for lane width and right-side lateral clearance, respectively. With these two default values, 0. Total ramp density is defined as the average number of ramps (including on-ramps, offramps, major merges, and major diverge junctions) per mile over a 6-mile freeway segment, 3- mile upstream and 3-mile downstream of the midpoint of the study segment. Posted speed is not included in Equation 1 as a factor to affect free-flow speeds on freeways. A possible reason is that posted speed is highly correlated with total ramp density. Free-flow Speeds for Multilane Highways Chapter 14 of the HCM 2010 describes the procedures to analyze multilane highways. In general, uninterrupted flow exists on a multilane highway since there are two miles or more between traffic signals. Where signals are more closely spaced, the facility should be analyzed as an urban street. The formula to estimate the free-flow speed on a multilane highway is shown below (Equation 14-1 from the HCM 2010). (2) is the free-flow speed (mph); is the base free-flow speed (mph); is the adjustment for lane width (mph); is the adjustment for total lateral clearance (mph); is the adjustment for median type (mph); and is the adjustment for access point density (mph). The base free-flow speed ( ) is like the design speed it represents the potential free-flow speed based only upon the horizontal and vertical alignment of the highway. While speed limits are not always uniformly set, the base free-flow speed may be estimated as the posted speed plus 5 mph for posted speed of 50 mph and higher, and the posted speed plus 7 mph for posted speed less than 50 mph. The adjustment for lane width ( ) and total lateral clearance ( ) are shown in Exhibits 14-8 and 14-9 of the HCM 2010, respectively. The adjustment for median type ( ) is -1.6 mph for undivided multilane highways, and 0 mph if the median is divided or is a two-way left-turn lane. The adjustment for access point density ( ) is -0.25 mph for each access point per mile. The number of access points per mile is determined by dividing the total number of access points (i.e., driveways and unsignalized intersections) on the right side of the highway in the direction of travel, by the length of the segment in miles. An intersection or driveway should only be included in the count if it influences traffic flow. Access points that go unnoticed by drivers, or with little activity, should not be used to determine access-point density. Free-flow Speeds for Two-Lane Highways Chapter 15 of the HCM 2010 describes the procedures to analyze two-lane highways. The principal characteristic that separates two-lane and multilane highways is that passing maneuvers have to take place in the opposing lane of traffic for two-lane highways. The formula to estimate the free-flow speed on a two-lane highway is shown below (Equation 15-2 from the HCM 2010).

7 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 (3) is the free-flow speed (mph); is the base free-flow speed (mph); is the adjustment for lane and shoulder width (mph); and is the adjustment for access point density (mph). The design speed might be an acceptable estimator of base free-flow speed ( ), as it is based primarily on horizontal and vertical alignment. Posted speed may not reflect current conditions or driver desires. A very rough estimate of might be taken as the posted speed plus 10 mph. The adjustment for lane and shoulder width ( ) is shown in Exhibit 15-7 of the HCM 2010. The adjustment for access point density ( ) is -0.25 mph for each access point per mile. The access-point density is computed by dividing the total number of unsignalized intersections and driveways on both sides of the roadway segment by the length of the segment in miles. Free-flow Speeds for Urban Streets Traffic flow on urban streets is interrupted flow, because of the existence of traffic signals or other traffic control devices. Therefore, free-flow speeds on urban streets depend on two principal factors: running time over urban street segments, and control delay at signalized intersections. The formula is shown below (Equation 17-12 from the HCM 2010). This formula is the same as the formulas used in the SERPM6, DFWRTM, and ISTDM models. 3600 (4) 5280 is the free-flow speed that includes the impact of intersection delay (mph); is the segment length (feet); is the segment running time (seconds), that is, the time to traverse a segment; and is the control delay at the downstream intersection (seconds/veh). Running Time on Urban Streets In Equation 4, the running time ( ) can be calculated based on the formula shown below (a revision of Equation 17-1 from the HCM 2010). 6.0 3600 (5) 0.0025 5280 is the start-up lost time, which is 2.0 for signalized intersections (seconds); and is the segment free-flow speed, which does not include the impact of intersection delay (mph). Equation 5 is a revision of Equation 17-1 in the HCM 2010 to fit the free-flow condition when the traffic volume is low. It assumes that the impact of traffic density on travel speed can

8 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 be ignored, therefore the vehicle proximity adjustment factor ( ) is equal to one. It also assumes the delay due to turning vehicles or other factors is zero. The first term in Equation 5 accounts for the time required to accelerate to the running speed, less the start-up lost time used to compute the through movement delay. The divisor in this term is an empirical adjustment that minimizes the contribution of this term for longer segments. in Equation 5 is calculated based on the formula shown below (a consolidation of Equations 17-2 and 17-3 from the HCM 2010). (6) is the speed constant (mph); is the adjustment for cross section, that is, median and curb (mph); is the adjustment for access point (mph); and is the signal spacing adjustment factor. The speed constant ( ) in Equation 6 is a linear function of posted speed, as shown below. 25.6 0.47 (7) The adjustment for cross section ( ) in Equation 6 reflects the impact of median type and presence of curb, and the formula is shown below. 1.5 0.47 3.7 (8) is the proportion of link length with restrictive median (decimal); and is the proportion of segment with curb on the right-hand side (decimal). The adjustment for access point ( ) in Equation 6 is a function of access point density and the number of through lanes, as shown below. 0.078 / (9) 5280,, / (10) is the access point density on segment (points/mile); is the number of through lanes in the subject direction of travel;, is the number of access points on the right side in the subject direction of travel;, is the number of access points on the right side in the opposing direction of travel; is the segment length (feet); and is the width of signalized intersection (feet). The signal spacing adjustment factor ( ) in Equation 6 accounts for the observation that drivers tend to choose slower free-flow speed on shorter segments, all other factors being the

9 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 same. The formula is shown below. If in Equation 11 is less than 400 feet, it should be set to 400 feet. 1.02 4.7 19.5 Control Delay at Signalized Intersections 1.0 (11) Chapter 18 of the HCM 2010 describes the procedures to analyze signalized intersections, which can be used to determine the control delay ( ) in Equation 4. Equations 18-19 from the HCM 2010 show that the control delay is the sum of uniform delay, incremental delay and initial queue delay. Uniform delay is the delay when arrivals are random throughout the cycle (uniform arrivals). Incremental delay accounts for the delays caused by random or sustained oversaturation. Initial queue delay accounts for the additional delay incurred due to an initial queue. For the purpose of calculating delays in free-flow conditions, incremental delay and initial queue delay can be assumed to be zero. Compared to the HCM 2000, the HCM 2010 adopted a new procedure to calculate uniform delay. This new procedure is called incremental queue accumulation. It requires detailed data that are difficult for a travel demand model to collect, such as saturation flow rate and arrival rate, and no formulas are available for this procedure. Therefore, it was decided to continue using the procedure described in the HCM 2000, which was also adopted in the SERPM6 and ISTDM models. The formula is shown below (a compilation of Equations 16-9 to 16-11 in the HCM 2000). 0.5 1 (12) is the cycle length (seconds); is the effective green time (seconds); and is the progression adjustment factor. Progression adjustment factor ( ) in Equation 12 is used to account for the quality of signal progression, and can be calculated using the formula shown below (Equation 16-10 from the HCM 2000). 1 1 1 1 (13) is the proportion of vehicles arriving on green; is the supplemental adjustment factor for a platoon arriving during green, and its default value for each arrival type is listed in Exhibit 16-12 in the HCM 2000; and is the platoon ratio, and its default value for each arrival type is listed in Exhibit 16-12 in the HCM 2000.

10 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 IMPLEMENTATION How to Get the Link Attributes Required by the Formulas As shown in the above section, the free-flow speed formulas in the HCM 2010 require many link attributes as inputs. Some of them are not typically available to a regional travel demand model. According to how difficult it is to collect them, these link attributes are classified into two groups in the TRM, as shown in Table 1. TABLE 1 Classification of Link Attributes in the TRM Link Attributes that are Easier to Collect Link Attributes that are More Difficult to Collect 1) Number of lanes 1) Access point density (for freeways, it is called 2) Median/left turn lane total ramp density) 3) Posted speed 2) Signal spacing (distance between two adjacent 4) Lane width signals, used as the segment length ) 5) Shoulder width 3) Signal cycle length 6) Lateral clearance 4) G/C ratio (the ratio of green time and cycle length) 5) Vehicle arrival type at intersections Link attributes in the first column of Table 1 are easier to collect for the model base year. Most of them are links physical attributes. They are also usually specified for new projects in future plans, such as the Metropolitan Transportation Plan (MTP), therefore they are available for future year model runs. Compared to the link attributes in the first column of Table 1, the attributes in the second column are more difficult to collect, especially for future year model runs. They are mostly attributes related to traffic operations, and could change frequently. For example, signal timing at intersections ( Signal cycle length and G/C ratio ) is usually adjusted frequently to accommodate new traffic patterns. Different signal timings could even be set up at the same intersection for different time periods during a day. It is even more difficult to obtain these link attributes for future years. Most of the attributes in the second column of Table 1 have strong correlations with area type. For example, when an urban street s area type changes from rural in the base year to urban in a future year, usually more access points will be created to access this urban street and the access point density will increase. At the same time, signal timing will usually be adjusted to accommodate new traffic patterns. In a travel demand model, economic development will induce the change of area type, and therefore some of the link attributes in the second column of Table 1. Unfortunately, these link attributes are not usually specified in future plans. Based on the characteristics of the link attributes in the second column of Table 1, lookup tables are used to determine their values in the TRM. In detail, default values for these link attributes are developed by facility type and area type, and all links with the same facility type and area type use the same default values. As a result, when a link s area type is changed due to future economic development, its free-flow speeds could change even if its link attributes in the first column of Table 1 remain the same. Obviously, using default value lookup tables yield less accurate free-flow speeds for each specific link in the highway network. However, it should have limited negative impacts on the performance of a regional model, and it makes it possible to change free-flow speeds automatically when a link s area type is changed.

11 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 In summary, the link attributes in the first column of Table 1 should be collected for the model base year and coded in the network. For a future year model run, they should be updated manually if any future year project changes their values. On the other hand, the link attributes in the second column of Table 1 use default values by facility type and area type, and there is no need to collect these link attributes for the model base year or future years. When a link s area type is changed for a future year model run, a different set of default values will be used, which results in different free-flow speeds without manually changing the coded link attributes. The classification of link attributes shown in Table 1 is used by the TRM. If the same method is used in other regions, link attributes can be classified differently to fit their own data availability. For example, lane width, shoulder width and lateral clearance can be classified into the second column if they are not available. Major Facility Types In order to make it easier to use the free-flow speed formulas from the HCM, the facility type defined in the TRM follows the chapters in the HCM, as shown in Table 2. TABLE 2 Major Facility Types in the TRM Facility Type Description HCM 2010 Equation Freeway Uninterrupted facility with full control of access Chapter 11 Equation 1 Multilane Uninterrupted facility without full control of Highway access, more than one lane in each direction Chapter 14 Equation 2 Two-lane Uninterrupted facility without full control of Highway access, only one lane in each direction Chapter 15 Equation 3 Major Arterial Interrupted facility whose major function is to provide high-speed movement Minor Arterial Interrupted facility that is not a major arterial or Chapters Equations 4 collector/local street 17, 18 to 13 Collector/Local Interrupted facility whose major function is to Street provide accessibility Table 2 shows that three facility types are defined for urban streets. The motivation is to provide appropriate default values. The link attributes could be quite different for different urban streets with the same area type. For example, two intersecting urban streets could have different signal timings: one has much longer green time or much better progression than the other. Therefore it is not appropriate to use the same default values for these two urban streets. If they are defined as two different facility types, different default values can then be applied. How to Develop the Default Values Several sources are used to develop the default values. The HCM 2010 suggests some default values, such as access point density, which are directly used in the TRM. A study on the Level of Service (LOS) in North Carolina (13) is used to develop the default signal cycle length, G/C ratio, and vehicle arrival type at intersections. Default signal spacing is determined based on the average of samples by facility type and area type collected from the field.

12 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 RESULTS AND VALIDATION Free-flow speeds in the TRM were calculated based on the approach described in this paper. Only free-flow speeds on freeways were calibrated due to the limitations of available speed data. The free-flow speeds were then validated based on the travel time data from a floating car survey. Calibration of Free-flow Speeds on Freeways There are many ways to collect free-flow speeds on freeways, such as using sensors installed on freeways, GPS-based devices, and cell phones or probe vehicles. In the TRM, a cell phone location based data set is selected to calibrate the free-flow speeds on freeways. TRM sampled several freeway segments in the model area and calculated their average observed speeds in the off-peak time period by area type and posted speed. The results indicate that the observed free-flow speeds are significantly different for freeway segments with the same area type but with different posted speeds. The modeled free-flow speeds on freeways are calculated based on Equation 1. This equation shows that the free-flow speeds on freeways are only affected by lane width, right-side lateral clearance, and total ramp density, but not by posted speed. Since all freeway segments in the TRM use the same lane width and right-side lateral clearance, and use the default value for total ramp density based on area type, all freeway segments with the same area type have the same free-flow speeds, despite their posted speeds. This is not consistent with the observed freeflow speeds. One of the reasons for this inconsistency is that default total ramp density, instead of the real total ramp density, is used. However, it is difficult to collect the total ramp density for each highway link in a regional travel demand model. To address this inconsistency issue, an additive term is developed based on a regression analysis. The basic idea is to take the free-flow speed from Equation 1 as the free-flow speed for freeway segments with posted speed of 65 mph, which is the most popular posted speed for freeways in the TRM model area. If a freeway segment has a posted speed different from 65 mph, a term is added to Equation 1 to adjust its free-flow speed. In this regression analysis, the dependent variable is calculated as the observed free-flow speed by area type and posted speed minus the observed free-flow speed for freeway segments with the same area type and posted speed of 65 mph. The independent variable is the posted speed minus 65 mph. This term is shown below. 0.0086 0.051 0.5223 (14) is the additive term to reflect the impact of posted speeds on free-flow speeds; and is the posted speed minus 65 mph, and should not be greater than 5 mph or smaller than -10 mph. Equation 14 is added to Equation 1 to calculate the free-flow speeds on freeways. Since the posted speed for freeways in the TRM model area is in the range of 55 mph to 70 mph, in Equation 14 should be in the range of -10 mph and 5 mph. The calculated free-flow speed based on Equations 1 and 14 is further calibrated using a multiplicative factor to match the observed speeds.

13 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 Validation The free-flow speeds are validated based on the speed data from a floating car survey. The major reason to select a floating car survey is that it can provide reasonable free-flow speeds on urban streets. Intersection delay is an important component of free-flow speeds on urban streets. Therefore, the observed free-flow speeds for an urban street should come from a long urban street segment that includes several signals. In a floating car survey, a GPS-quipped probe vehicle is driven along a preselected route and the elapsed time and distance traversed are measured. Therefore, intersection delay is a part of the probe vehicle s travel time. The floating car survey was conducted in 2011. It selected 48 routes in Durham, Chapel Hill and Hillsborough. There are two directions for each route, and nine vehicle runs for each direction. Table 3 summarizes the surveyed roadway length by facility type and area type. The length of a two-way roadway is counted twice in Table 3, and the length of a one-way roadway is counted only once. TABLE 3 Surveyed Roadway Length by Facility Type and Area Type (miles) Facility Type CBD Urban Suburb Rural Freeway 3 54 44 24 Multilane Highway 0 7 2 0 Two-lane Highway 0 0 22 9 Major Arterial 11 123 49 0 Minor Arterial 3 75 42 0 Collector/Local Street 1 3 0 0 Table 3 shows that the 48 routes in the floating car survey cover almost 480 miles of roadways in the model area. They provide good coverage of major facility types, such as freeway, major arterial and minor arterial. Unfortunately, not enough multilane highways, two-lane highways and collector/local streets were surveyed. For each route and direction, the vehicle runs that were conducted when the traffic was light are selected, and their average travel time is used as the observed free-flow travel time. The observed free-flow speeds are then calculated as route length divided by observed free-flow travel time. They are compared to the modeled free-flow speeds. Since the roadway segments in a route could have different facility types and area types, therefore different free-flow speeds, the modeled free-flow speed is the average speed over a route, calculated as route length divided by the sum of modeled free-flow travel times over each of the roadway segments. Table 4 shows samples of the observed and modeled free-flow speeds.

14 430 431 432 433 434 435 436 437 438 439 Table 4 Samples of Observed and Modeled Free-flow Speeds from the Floating Car Survey Major Route Observed Modeled Route (direction) Major Facility Type Area Length Free-flow Free-flow Type (miles) Speed (mph) Speed (mph) I-85 (EB) Freeway Suburb 21.2 65.4 68.7 I-40 (EB) Freeway Suburb 24.1 67.2 68.0 NC 147 (WB) Freeway Urban 13.0 61.6 61.1 Eubanks Rd. (EB) Two-lane Highway Suburb 2.6 37.3 42.8 Fordham Blvd. (EB) Multilane Highway, Major Arterial Urban 7.3 41.0 36.6 MLK Blvd. (EB) Major Arterial Urban 5.3 30.0 32.5 Davis Dr. (NB) Major Arterial Urban 2.8 33.1 32.2 Erwin Rd. (EB) Major Arterial CBD 2.3 23.0 21.9 US 70 (NB) Minor Arterial Suburb 3.1 28.8 35.1 Jones Ferry Rd. (WB) Minor Arterial Urban 1.0 31.8 28.7 Estes Dr. (NB) Minor Arterial Urban 1.7 26.6 28.3 Horton Rd. (WB) Minor Arterial Urban 1.9 29.2 28.3 The samples in Table 4 are selected because most of their roadway segments have the same facility type and area type. However, please notice that each route in Table 4 still could consist of roadway segments with different facility types and area types, and Table 4 only shows the major facility type and area type. Table 4 shows that the observed and the modeled free-flow speeds are close for the sampled routes. To consider all 48 routes in the floating car survey, the observed travel times are compared with the modeled travel times. The results are shown in Figure 1.

15 1400 1200 y = 0.9801x R² = 0.9736 Modeled Travel Time (s) 1000 800 600 400 200 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 0 0 200 400 600 800 1000 1200 1400 Observed Travel Time (s) FIGURE 1 Comparison of the observed travel time and the modeled travel time. There are 48 routes and each has two directions, so 96 data points are plotted in Figure 1. The thin black line is the regression line, and the thick red line is the reference line of. The regression equation is 0.9801, which implies that the modeled travel time is very close to (slightly smaller than) the observed value, or in other words, the modeled free-flow speed is very close to (slightly higher than) the observed value. The R-squared value is as high as 0.9736. So, the modeled travel time matches the observed travel time very well. SUMMARY Free-flow speed is important to a travel demand model. It is the basis for speed estimation. The speed estimation determines the network skims and accessibility measures, which affect almost all steps in a traditional four-step model. Reasonable speed estimation is also needed to validate a travel demand model and support air quality analyses. A review of the current practices in other regions reveals that free-flow speeds are usually determined using lookup tables or formulas. Directly using formulas in the HCM has several advantages, including saving additional studies, the consistency of free-flow speeds and capacities, and the consistency of travel demand modeling with traffic operations analysis. This paper shares the experience in using the formulas in the newest version of the HCM (the HCM 2010) to determine the free-flow speeds in a regional travel demand model. The formulas to calculate the free-flow speeds based on the HCM 2010 are summarized in this paper. They are either directly taken from the HCM 2010 or are modified to fit the freeflow condition. These formulas require many link attributes as inputs, but some of them are not

16 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 typically available to a regional travel demand model. So the link attributes are classified into two groups. In the first group, the link attributes should be collected for the model base year and coded in the network. For a future year model run, they should be updated manually if any future year project changes their values. In the second group, the link attributes use default values by facility type and area type, and there is no need to collect these link attributes for the model base year or future years. When a link s area type is changed for a future year model run, a different set of default values will be used, which results in different free-flow speeds without manually changing the coded link attributes. The free-flow speeds on freeways are calibrated based on a cell phone location based speed data set. An additive term is introduced to consider the impact of posted speed. The freeflow speeds on other facilities are not calibrated due to the limitations of available speed data. A floating car survey is used to validate the free-flow speeds. The observed travel time for each route direction in the floating car survey is compared with the modeled travel time calculated from the modeled free-flow speed. The comparison indicates that the modeled free-flow speeds are reasonable. Appropriate default values are important to the performance of these free-flow speed formulas. They should be carefully determined based on local studies or field data whenever possible. It is also suggested to validate the free-flow speeds based on observed speed data, and to make adjustments to the default values if necessary. ACKNOWLEDGEMENTS The author would like to thank the North Carolina Department of Transportation, the Capital Area Metropolitan Planning Organization, the Durham-Chapel Hill-Carrboro Metropolitan Planning Organization, and Triangle Transit for funding this project. REFERENCES: 1. Kurth, D.L., A. van den Hout, and B. Ives. Implementation of Highway Capacity Manual Based Volume-Delay Functions in Regional Traffic Assignment Process. In Transportation Research Record 1556, TRB, National Research Council, Washington, D.C., 1996, pp. 27-36. 2. Spiess, H. Conical Volume-Delay Functions. Transportation Science, Vol. 24, No. 2, 1990, pp. 153-158. 3. Huntsinger, L. F. and N. M. Rouphail. Bottleneck and Queuing Analysis: Calibrating Volume-Delay Functions of Travel Demand Models. In Transportation Research Record 2255, TRB, National Research Council, Washington, D.C., 2011, pp. 117-124. 4. Highway Capacity Manual 2010. TRB, National Research Council, Washington, D.C., 2010. 5. The Travel Forecasting Model Set for the Atlanta Region: 2009 Documentation, Atlanta Regional Commission, Atlanta, G.A., 2008. 6. 2003 Model Validation and Summary, SCAG Regional Transportation Model, Southern California Association of Governments, Los Angeles, C.A., 2008. 7. Transportation Models and Data Initiative, General Final Report, New York Best Practice Model (NYBPM), New York Metropolitan Transportation Council, New York, N.Y., 2005.

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