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Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets (2020)

Chapter: Appendix F: Freeway Facilities Lane-by-Lane Analysis

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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
×
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
×
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
×
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
×
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
×
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
×
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
×
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
×
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Suggested Citation:"Appendix F: Freeway Facilities Lane-by-Lane Analysis." National Academies of Sciences, Engineering, and Medicine. 2020. Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets. Washington, DC: The National Academies Press. doi: 10.17226/25963.
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351 A P P E N D I X F Freeway Facilities Lane-by-Lane Analysis Data Collection The data collected for this part of the project include speed and flow data from selected detector station sensors in California, Virginia, Utah, Wisconsin, Minnesota, and Florida. These locations represent diverse operational and design conditions across the US. Sites were selected based on the following criteria: • Speed and flow data available for each lane, aggregated in 15-min intervals, for a period of at least one year; • Absence of freeway management strategies, such as express or high-occupancy vehicle (HOV) lanes, ramp metering, speed harmonization, or demand shoulder use; • For merge and diverge and segments, good health detector data available for the upstream, downstream and ramp sections; • Percentages of heavy vehicles were available. The dataset includes 48 locations: 19 basic, 14 merge, 15 diverge and 16 weaving segments with 2, 3 or 4 lanes on each direction. There are no 5-lane segments in the database, as many of the identified locations operate with HOV lanes. The number of required detector stations is different for each segment type ( Figure F-1). Basic segments require only one detector station. Diverge segments require two stations: one at the ramp influence area (upstream of the exit) and one along the ramp. Merge segments require three stations: one at the ramp influence area (downstream the merge), one along the ramp and one upstream of the merge. Figure F-1 – Required detector data positions by segment type The list of data collection locations is provided in Table F-1 (basic segments), Table F-2 (merge segments), Table F-3 (diverge segments) and Table F-4 (weaving segments).

352 Table F-1 – Database used for determination of lane-by-lane flows – Basic freeway segments # lanes State Road Observation Period Detector Station IDs % Grade %HV # adjacent ramps 2L CA HWY 1 NB 2018 500014082 0.5 1.7 2 CA SR-132 EB 2018 10119910 -0.5 0.3 0 MN US-10 2017 - 18 946 0.3 1.4 1 MN I-694 NB 2017 1413 -1.2 8.6 1 UT SR-67 NB 2018 820 -0.3 18 0 VA I-66 WB 2018 19002981 0.5 1 2 VA I-64 EB 2018 64239221 -0.9 9 1 WI I-43 SB 2017 - 18 692 -0.02 6.5 0 3L CA I-205 WB 2018 - 19 1027310 -0.9 4.2 0 CA SR-85 NB 2018 - 19 407336 -0.8 5.6 1 FL I-4 WB 2017 4712 -0.2 10.8 0 MN I-94 NB 2017 - 18 1356 -1.7 11.8 0 UT I-215 SB 2016 - 17 82 -3.1 10.5 0 UT I-15 SB 2018- 19 963 1.45 32.9 1 VA I-64 EB 2017- 18 64055221 0.2 4 3 WI I-43 NB 2017 - 18 659 -0.6 10.2 1 4L CA I-80 2018 - 19 413373 0.4 6.8 1 CA SR-24 EB 2018 - 19 400532 1.7 14.1 0 CA I-80 EB 2018 - 19 413375 1.1 5 1 FL I-295W NB 2017 2220 0 13.6 1 FL I-275 SB 2016 - 17 3829 -1.1 4.4 0 FL I-275 NB 2016 - 17 3408 0 4.4 0 UT I-215 CW 2018 - 19 50 -0.8 28.2 1 VA I-295 EB 2018 - 19 4044741 -0.1 10 1

353 Table F-2 – Database used for determination of lane-by-lane flows – Merge segments # lanes State Road Observation Period Detector Station IDs % Grade %HV # adjacent ramps 2L UT SR-67 S 2018 872, 876, 1872 0 13 0 UT SR-67 N 2018 830, 834, 1830 0.1 17 0 FL I-295E NB 2018 10821, 10852, 10890 2.7 11.8 0 FL I-295E NB 2018 10854, 10841, 10879 1.5 11.8 0 3L CA I-5 SB 2018 - 19 10121110, 10121310, 1083110 -0.9 11.9 0 CA CA-99 WB 2018 10109610, 10109810, 10109710 0.1 11.23 1 MN I-694 2017 174, 172, 753 1.8 8.6 1 UT SR201-W 2018 - 19 348, 350, 1348 0 27.9 1 UT I-215 CCW 2017 173, 175, 1173 1.5 9 1 UT I-215S EB 2017 168, 169, 1168 0.2 11 0 UT I-215 2017 188, 190, 1188 0 10 0 UT I-80 2017 231, 232, 1231 1.32 14 0 4L CA I280 SB 2018 - 19 403908, 403328, 403909 0 1.3 1 CA 1-8 WB 2017 403908, 403328, 403909 2.71 2.1 1 Table F-3 – Database used for determination of lane-by-lane flows – Diverge segments # lanes State Road Observation Period Detector Station IDs % Grade %HV # adjacent ramps 2L CA US-101 SB 2018 – 19 406305, 406303 -0.3 5 1 CA I-8 WB 2016 - 17 1115624, 1122447 0.8 3.4 0 UT SR-67 NB 2017 810, 2810 0 9 0 FL I-295E NB 2017 10829, 10876 0 11.8 0 WI I-94 WB 2017 67663, 67662 -2 7.2 1 3L CA CA-242 2018 – 19 414251, 417124 0 2.43 0 CA I-5 NB 2018 – 19 10121410, 1090210 0 18.1 0 CA CA-73 2018 – 19 1208789, 1208940 -5.4 3.8 0 MN I-694 2017 151, 554 2.5 8.6 2 MN I-694 2017 171, 755 2.5 8.6 2 UT I-215 CCW 2017 112, 2114 0 17 0 UT I-215 CW 2018 – 19 22, 2024 -2.2 61.6 0 UT I-215 CW 2018 – 19 86, 2087 0 8 0 4L CA SR-242 NB 2018 – 19 414252, 418256 1.5 2.21 4 CA I-80 EB 2017 413375, 410766 0.7 5.1 1

354 Table F-4 – Database used for determination of lane-by-lane flows – Weaving segments # lanes State Road Observation Period Detector Station IDs % Grade %HV # adjacent ramps 2L CA CA-56 WB 2018 1125546, 1125575, 1125543, 1126293 0 2.03 0 MN I-694 NB 2018 1027, 1410, 5120, 6226 0.6 14.8 3 MN Lafayette Hwy 2017 S1169, S1170, 5626, 5629 0 8.81 0 MN US 52 2017 S1442, S1444, 6061, 6069 0 8.01 0 MN Lafayette Hwy 2017 S1159, S1160, 5581, 5584 0 8.81 0 MN MN-36 WB 2017 S616, S617, 2361, 2362 0.8 8.81 0 MN MN-36 EB 2017 S591, S592, 2256, 2257 0.8 8.81 0 3 CA I-80 SB 2018-2019 409107, 404408, 409108, 419489 1 15.8 3 UT I-215 CW 2013-2014 320, 322, 1320, 2322 0 14 1 UT I-215 CW 2015-16 344, 346, 1344, 2346 0 14 0 UT Belt Route 2011-2012 162, 165, 1162, 2165 1 14 1 4 CA SR4-EB 2018 416930, 414707, 416931, 414708 -0.5 3.3 2 CA SR4-EB 2018 400049, 405269, 418869, 406635 -0.8 4.8 0 CA I-680 SB 2018 407177, 407179, 409059, 407178 0.51 4.4 4 CA I-880 SB 2018 400949, 400678, 403028, 403030 0.1 6.1 0 UT I-80 EB 2015 228, 240, 1228, 2231 0 16 0 Speed and flow detector data were collected from online sources from the respective state agencies. Data were obtained by lane in 15-min intervals, over a 1-year period for each location. Erroneous speed and flow data and those associated with crashes, lane closures, and work zones were removed. Holidays and weekends were excluded. The heavy vehicle percentage (HV%) was collected from the respective state agencies. Average truck percentages are typically reported on an annual basis by agencies; therefore the speed-flow data from detectors were downloaded only for periods when HV% information was available. The presence of ramps upstream or downstream of a site might cause significant impact on lane flow distribution. Therefore, the analysis included the number of such ramps within a half-mile upstream and downstream of the segment (access point density). Lane-By-Lane Flow Models by Segment Type The lane flow ratio (LFR) model for each lane is estimated as a function of the logarithm of the segment volume-capacity ratio (v/c). This relationship was established empirically after evaluating the performance of logarithmic and polynomial regressions. Although a 4th degree polynomial provided an overall slightly better fit, the number of adjustment factors required to accommodate parameters of geometry (grade and number of accesses) and flow (truck percentile and ramp flow) was considered too high. Thus, a logarithmic model was selected as a balance between model complexity and accuracy. The flow estimation curves for each lane are fitted using the least squares method, except for the leftmost lane, which is estimated as the remaining flow, to ensure the sum of the flow shares from each lane always equals 100%. The equations estimating LFR are as follows: 𝐿𝐹𝑅 = 𝑎 × 𝑙𝑛 + 𝑏 (Equation F-1) 𝐿𝐹𝑅 = 1 − ∑ 𝐿𝐹𝑅 (Equation F-2) Where: LFRi = share of the total flow on lane i, where i ranges from 1 to n-1 (n = total number of segment lanes)

355 LFRn = share of the total flow on the leftmost lane (lane n); fa = adjustment factor for 𝑎 (Equations F-3, F-5, F-7); v/c = volume/capacity ratio (0 ≤ v/c ≤ 1) fc = adjustment factor for 𝑐 (Equations F-4, F-6, F-8) The model proposed in Equation F-1 can be applied for basic, merge, diverge and weaving segments. For merge and diverge segments, the share of flow is estimated at the area upstream of the ramp. For weaving segments, the share of flow is estimated at the mainline upstream the on-ramp. For the proposed methodology, volume and capacity are given in veh/h. The adjustment factors fa and fc applicable in the analysis of basic segments are as follows: 𝑓 = 𝑎 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝑛 ∙ 𝑓 , (Equation F-3) 𝑓 = 𝑐 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝑛 ∙ 𝑓 , (Equation F-4) For merge and diverge segments, the fa and fc factors are as follows, with additional coefficients f , and f , to address ramp demand: 𝑓 = 𝑎 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝑛 ∙ 𝑓 , + ∙ 𝑓 , (Equation F-5) 𝑓 = 𝑐 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝑛 ∙ 𝑓 , + ∙ 𝑓 , (Equation F-6) where: G = grade (%) a = empirical constant fa,G = adjustment factor for a due to impact of grade fc,G = adjustment factor for c due to impact of grade t = truck percentage (%) fa,t = adjustment factor for a due to impact of trucks fc,t = adjustment factor for c due to impact of trucks n = access point density – number of ramps half a mile upstream and half mile downstream fa,n = adjustment factor for a due to impact of access point density c = empirical constant fc,n = adjustment factor for c due to impact of access point density vR = ramp flow (vph) fa,vR = adjustment factor for a due to impact of ramp flow fc,vR = adjustment factor for c due to impact of ramp flow The adjustment factors for the weaving segments address the effect of weaving-specific properties: 𝑓 = 𝑎 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼𝐷 ∙ 𝑓 , + , ∙ 𝑓 , + , ∙ 𝑓 , + ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 , (Equation F-7) 𝑓 = 𝑐 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼𝐷 ∙ 𝑓 , + , ∙ 𝑓 , + , ∙ 𝑓 , + ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 , (Equation F-8) where: ID = interchange density, as defined in HCM Chapter 13 fa,I = adjustment factor for a due to impact of interchange density fc,I = adjustment factor for c due to impact of interchange density vR,m = on-ramp flow (veh/h) fa,vm = adjustment factor for a due to on-ramp flow fc,vm = adjustment factor for c due to on-ramp flow vR,d = off-ramp flow (veh/h) fa,vd = adjustment factor for a due to off-ramp flow fc,vd = adjustment factor for c due to off-ramp flow

356 LS = length of the weaving segment (ft) fa,LS = adjustment factor for a due to length of the weaving segment fc,LS = adjustment factor for c due to length of the weaving segment VR = volume ratio (weaving volume/total volume) fa,VR = adjustment factor for a due to volume ratio fc,VR = adjustment factor for c due to volume ratio The remaining factors have been defined previously. The empirical constants (a, c, and the adjustment factors f) were obtained by regression and are specific for each combination of segment type, lane number and total number of lanes. The obtained values for basic, merge and diverge segments are presented in Table F-5.

357 Table F-5 – Adjustment factors for lane flow distribution on basic, merge and diverge segments Lane # Para- meter Basic segments Diverge segments Merge segments 2 lanes 3 lanes 4 lanes 2 lanes 3 lanes 4 lanes 2 lanes 3 lanes 4 lanes L1 a 0.17991 0.02708 0.06815 0.00969 -0.07503 0.30943 0.01501 0.00290 -0.07664 c 0.51747 0.27040 0.21903 0.44267 0.26667 0.24818 0.58644 0.28248 0.23621 fa,g 0.02397 0.02095 -0.01107 0.00969 0.00768 -0.03381 0.01501 -0.00290 -0.00302 fa,t -0.04821 -0.00364 -0.00209 -0.00928 0.00080 -0.05689 -0.00929 -0.00290 0.01110 fa,n -0.09525 -0.00829 -0.05870 -0.00969 0.01382 -0.02756 -0.00474 -0.00290 0.01449 fc,g 0.00301 0.00969 -0.03378 -0.00976 -0.00810 -0.00016 0.01965 0.03100 0.04041 fc,t 0.00788 -0.00289 0.00243 0.00775 0.00140 -0.01887 -0.01350 -0.00179 -0.02714 fc,n 0.00134 0.03222 -0.03481 0.00057 0.03129 0.00516 -0.03997 -0.04212 -0.04073 fa,vR -0.21359 -0.06664 -0.00871 -0.03477 -0.10409 0.02637 fc,vR -0.12519 0.01324 -0.02112 -0.07032 -0.02982 0.00914 L2 a -0.06337 -0.02491 0.00960 0.28585 -0.00816 -0.08022 c 0.31448 0.28769 0.33948 0.24967 0.37687 0.24498 fa,g -0.00596 0.00150 -0.00960 -0.03465 -0.00816 0.00048 fa,t 0.00113 0.00027 -0.00054 -0.05211 -0.00082 0.01250 fa,n 0.00368 -0.00845 -0.00960 -0.03023 -0.00261 0.01782 fc,g -0.01688 -0.02388 -0.00189 0.00189 0.00791 -0.01938 fc,t 0.00239 -0.00036 0.00089 -0.00408 -0.00048 -0.00670 fc,n 0.01139 -0.04134 0.00520 0.00437 -0.00597 0.00101 fa,vR -0.04766 -0.00652 -0.11832 -0.03270 fc,vR -0.07333 -0.00914 -0.03855 -0.01262 L3 a -0.04510 0.26611 0.02860 c 0.27607 0.25113 0.25373 fa,g -0.00171 -0.03618 -0.00169 fa,t 0.00213 -0.04404 -0.00579 fa,n 0.00808 -0.03444 -0.00678 fc,g 0.01052 0.00344 0.00060 fc,t -0.00112 0.00918 0.01424 fc,n 0.01485 0.00164 0.01764 fa,vR 0.02083 -0.07890 fc,vR -0.00644 -0.04144

358 The weaving LFRs are calculated at two locations: upstream of the on-ramp and within the weaving segment (Figure F-1). The downstream LFRs are calculated as a function of the upstream LFRs. Figure F-2. Notation for LFR estimation at weaving segments The adjustment factors calculated for the upstream LFRs are presented in Table F-6. The number of lanes refer to the freeway section immediately upstream of the weave, and any lanes connecting the on-ramp and off-ramp are not considered as part of the total number of lanes. Table F-6 – Adjustment factors for lane flow distribution on weaving segments Parameter 2-lane segments 3-lane segments 4-lane segments L1 L1 L2 L1 L2 L3 a 0.99465 0.64110 0.47799 -0.13493 0.00483 0.11993 c 0.40000 0.40000 0.33391 0.24344 0.25717 0.27102 fa,g -0.21470 -0.28453 0.11187 0.13490 -0.00483 -0.11991 fa,t -0.11511 -0.05549 -0.03308 -0.01189 -0.00483 0.01851 fa,I 0.13262 0.00370 -0.03519 -0.00252 -0.00483 -0.11993 fa,vm 0.02186 0.07467 -0.09000 0.07183 -0.03130 -0.01135 fa,vd -0.19422 -0.03564 0.01725 -0.12644 0.02999 0.05097 fa,Ls -0.19745 0.09771 -0.03081 0.05588 0.00195 -0.04056 fa,VR 0.00799 0.02427 0.08859 -0.11102 -0.00445 0.11993 fc,g 0.06882 -0.40000 0.03850 -0.03002 0.04479 0.04102 fc,t 0.00318 -0.05137 0.00449 -0.00433 -0.01122 -0.00426 fc,I -0.01613 0.40000 -0.02045 -0.00670 -0.00498 -0.00261 fc,vm -0.04763 -0.13800 0.00474 0.06457 -0.00885 -0.03777 fc,vd 0.03962 0.03917 -0.04740 0.06291 -0.01525 -0.03723 fc,Ls -0.01090 0.14690 0.00495 -0.03030 0.01073 0.01985 fc,VR 0.07777 0.40000 0.01786 -0.14324 0.04014 0.15454 The LFRs within the weave are estimated considering the number of lanes involved in weaving. According to the HCM Chapter 13, the number of weaving lanes (NWL) is the total number of lanes from which a weaving maneuver may be completed with one lane change or no lane changes. The auxiliary lane

359 is included in the NWL. Figure F-3 provides two weaving example configurations with the respective NWL. The number of weaving lanes on the mainline freeway, excluding the auxiliary lane(s) is denoted as NWUP, also shown in Figure F-3 for the two example configurations. Figure F-3. Notation and number of weaving lanes upstream (NWUP) and within the merge (NWL) for two weaving configurations The methodology assumes that all mandatory weaving lane change maneuvers are completed before the midpoint of the short weaving length (LS). This assumption is based on the results reported by (Menendez, and He, 2016; Ahmed at al., 2019). Menendez and He (2016) concluded that about 70% of lane change completion in the weaving segment occurred within 19% of the weaving section length during all times and for all traffic conditions. Another study (Ahmed at al., 2019) related to weaving lane changes at the US- 101 freeway indicated that 50% of all lane changes were completed within 16% of the short length of the weave. The methodology also assumes that for segments with only one weaving lane upstream (NWUP=1) the entire freeway-to-ramp flow (vFR) will be positioned in the rightmost lane (L1,UP). For segments with two upstream weaving lanes (NWUP=2), the methodology assumes that 80% of freeway-to-ramp flow (vFR) will be on the rightmost lane (L1,UP) while the remaining 20% will be on the adjacent lane (L2,UP). This assumption is based on recent work by Menendez, and He, (2016); and Ahmed at al. (2019). The distribution of flows for non-weaving vehicles (freeway-to-freeway) in the middle of the weaving segment is assumed to be equal to that upstream of the weave. Therefore (Figure F-4), flows within the weave are calculated assuming the entire vFR flow will be on the auxiliary lane when it reaches the midpoint of the weave. For traffic that is on the adjacent lane, it is assumed that it will be located on L1 when it reaches the mid-point of the weave, i.e. it will make one lane change toward the exit by the mid-point. If the VFR exceeds the calculated upstream flow in lane 1 v1,UP, then the extra flow is allocated to the adjacent lane when estimating the mid-point lane allocations. Thus, the methodology checks whether there is excess traffic from vFR (vEXFR) that needs to be allocated to L2 at the midpoint of the weave. The sum of lane flows estimated within the weave should be equal to the sum of the upstream lane flows (freeway and merge flows). Figure F-4. Weaving flows lane allocation for two example weaving configurations

360 The calculation steps are as follows: Step 1. Determine the number of upstream freeway weaving lanes (NWUP) based on geometry Step 2. Check whether vFR exceeds the estimated flow in lane 1. These checks are based on the value of NWUP. For NWUP = 1: 𝑣 ≤ 𝑣 (Equation F-9) Set vEXFR1 = 0, if equation F-9 is true. Otherwise: 𝑣 = 𝑣 − 𝑣 , (Equation F-10) For NWUP =2: 0.8 × 𝑣 ≤ 𝑣 , (Equation F-11) Set vEXFR2 =0, if equation F-11 is true. Otherwise: 𝑣 = 0.8 × 𝑣 − 𝑣 , (Equation F-12) 𝑣 + (0.2 × 𝑣 ) ≤ 𝑣 , (Equation F-13) Set vEXFR3 =0, if equation F-13 is true. Otherwise: 𝑣 = 𝑣 + (0.2 × 𝑣 ) − 𝑣 , (Equation F-14) Where: v,FR = freeway to ramp flow (veh/h) v1,UP = upstream weaving lane flow for lane 1 (veh/h) v2,UP = upstream weaving lane flow for lane 2 (veh/h) vEXFR1 = excess of freeway to ramp flow that needs to be accommodated in the lane adjacent to lane 1 upstream of the weaving segment when NWUP =1 vEXFR2 = excess of freeway to ramp flow that needs to be accommodated in the lane adjacent to lane 2 upstream of the weaving segment when NWUP = 2 vEXFR3 = excess of freeway to ramp flow that needs to be accommodated in the lane adjacent to lane 3 upstream of the weaving segment when NWUP = 2 Step 3. Calculate the auxiliary lane flow (v0) 𝑣 = 𝑣 + 𝑣 − 𝑣 (NWUP =1) or (Equation F-15) v = 𝑣 + (0.8 ∗ 𝑣 ) (NWUP =2) 𝑖𝑓 (0.8 × 𝑣 ) ≤ 𝑣 , (Equation F-16) 𝑣 = 𝑣 + 𝑣 , (NWUP =2) 𝑖𝑓 (0.8 × 𝑣 ) > 𝑣 , (Equation F-17) where: v0 = auxiliary lane flow (veh/h) vFR = freeway-to-ramp flow (veh/h) v1,UP = upstream lane 1 flow (veh/h) vRR = ramp-to-ramp flow (veh/h) Step 4. Calculate the rightmost freeway weaving lane flow (v1) 𝑣 = 𝑣 + 𝑣 − (𝑣 − 𝑣 ) + 𝑣 (NWUP =1) or (Equation F-18) 𝑣 = 𝑣 , − (0.8 ∗ 𝑣 ) + (0.2 ∗ 𝑣 ) + 𝑣 (NWUP =2) 𝑖𝑓 (0.8 ∗ 𝑣 ) ≤ 𝑣 , (Equation F-19)

361 𝑣 = (0.2 ∗ 𝑣 ) + 𝑣 + 𝑣 (NWUP =2) 𝑖𝑓 (0.8 ∗ 𝑣 ) > 𝑣 , (Equation F-20) 𝑣 = 𝑣 + 𝑣 , (NWUP =2) 𝑖𝑓 (0.8 ∗ 𝑣 ) > 𝑣 , and 𝑣 + (0.2 ∗ 𝑣 ) > 𝑣 , (Equation F-21) where: v1 = lane 1 flow (veh/h) within the weaving segment v1,UP = upstream weaving lane flow for lane 1 (veh/h) v2,UP = upstream weaving lane flow for lane 2 (veh/h) vRF = ramp-to-freeway flow (veh/h) vEXFR1 = excess of freeway to ramp flow that needs to be accommodated in the lane adjacent to lane 1 upstream of the weaving segment when NWUP =1 vEXFR2 = excess of freeway to ramp flow that needs to be accommodated in the lane adjacent to lane 2 upstream of the weaving segment when NWUP = 2 Step 5. Calculate the freeway weaving lane flow for lane 2 (v2) 𝑣 = 𝑣 , − 𝑣 (NWUP =1) or (Equation F-22) 𝑣 = 𝑣 , − (0.2 ∗ 𝑣 ) − 𝑣 (NWUP =2) 𝑖𝑓 (0.8 ∗ 𝑣 ) < 𝑣 , and (0.8 ∗ 𝑣 ) > 𝑣 , (Equation F-23) 𝑣 = 𝑣 (NWUP =2) 𝑖𝑓 (0.8 ∗ 𝑣 ) > 𝑣 , and (0.2 ∗ 𝑣 ) + 𝑣 > 𝑣 , (Equation F-24) where: v2 = lane 2 flow (veh/h) within the weaving segment Step 6. Calculate the freeway weaving lane flow for lane 3 (v3) This step is only valid with the presence of vEXFR3 . 𝑣 = 𝑣 , − 𝑣 (Equation F-25) where: v3 = lane 3 flow (veh/h) within the weaving segment v3,UP = upstream lane 3 (veh/h) Step 7. Obtain flows for the remaining lanes, which will be equal to the respective upstream flow values. The flows of the remaining lanes will be same as their respective upstream lane flows. Step 8. Check whether there are v/c ratios greater than 1 for each lane. This step checks whether any of the lane v/c ratios are greater than 1. When that occurs, flows should be adjusted based on the procedure described above. Capacity for lane-by-lane flow models The method for estimating the capacity used in Equation F-1 is unique to each segment type. For basic, merge and diverge segments, a segment capacity is a single value, measured in veh/h, obtained through the breakdown method by measuring speed drop occurrences at different detectors within the area of study according to the segment type: • Basic: a mainline detector within the area of study; • Merge: a mainline detector right after the merge location; and • Diverge: a mainline detector right before the diverge location.

362 For the weaving segments, capacity is estimated using the method proposed in HCM 6th Edition – Chapter 13 (Step 5, Equations 13-5 through 13-9) in passenger-cars per hour (pc/h). It should be noticed that capacity in this method is function of the volume ratio (VR). As such, the capacity for weaving segments may vary for different time intervals. Reasonableness checks After lane flow ratios are obtained, a two-step reasonableness check must be performed to ensure the obtained flow distribution remains under feasible constraints. The first step checks for any negative flows that may occur in any segment lane – this issue is more likely to occur in the leftmost lane, as the flows on this lane are obtained by the difference between the total segment flow and the sum of estimated flows in the other lanes. Therefore, if flows on the remaining lanes are overestimated the resulting flow in the leftmost lane may become negative. Figure F-5 illustrates the recommended procedure for the first check. Figure F-5. Reasonableness check for negative flows The second step of the reasonableness check compares the estimated flow by lane with the respective lane capacities to make sure no lane operates with a demand-to-capacity ratio greater than 1.The procedure illustrated in Figure F-5. If any lane is observed to operate above its capacity, the flow in this given lane is constrained by the capacity value and the exceeding demand is rearranged to the adjacent lane.

363 Figure F-6. Reasonableness check for lane capacity Model application examples Diverge segment A practical application of the LFR model is presented next for a 3-lane diverge segment (single period analysis), with the following input data: • Grade (G): 3% • Heavy vehicles (t): 4% • Access point density (n): 2 adjacent ramps • Mainline demand flow rate (v): 5500 veh/h • Off-ramp demand (vR): 850 veh/h • Measured segment capacity (c): 2050 veh/h/ln (6150 veh/h) The flow ratio for lane 1 (right lane) is obtained by the following equation: 𝐿𝐹𝑅 = 𝑓 ∙ ln 𝑣𝑐 + 𝑓 The adjustment factors fa and fc for lane 1 are obtained as follows: 𝑓 = 𝑎 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝑛 ∙ 𝑓 , + ∙ 𝑓 , 𝑓 = −0.07503 + 3 ∙ 0.00768 + 4 ∙ 0.00080 + 2 ∙ 0.01382 + ∙ (−0.06664) 𝑓 = −0.07779 𝑓 = 𝑐 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝑛 ∙ 𝑓 , + ∙ 𝑓 , 𝑓 = 0.26667 + 3 ∙ (−0.00810) + 4 ∙ 0.00140 + 2 ∙ 0.03129 + ∙ (0.01324)

364 𝑓 = 0.3218 The lane flow ratio on lane 1 can then be obtained by: 𝐿𝐹𝑅 = −0.07779 ∙ ln 55003 ∙ 2050 + 0.3218 𝐿𝐹𝑅 = 33.0% The same procedure is applied to obtain the lane flow ratio on lane 2, using the respective coefficients from Table F-5: 𝑓 = 𝑎 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝑛 ∙ 𝑓 , + ∙ 𝑓 , 𝑓 = 0.0096 + 3 ∙ (−0.00960) + 4 ∙ (−0.00054) + 2 ∙ (−0.0096) + ∙ (−0.04766) 𝑓 = −0.08107 𝑓 = 𝑐 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝑛 ∙ 𝑓 , + ∙ 𝑓 , 𝑓 = 0.33948 + 3 ∙ (−0.00189) + 4 ∙ (0.00089) + 2 ∙ 0.00520 + ∙ (−0.07333) 𝑓 = 0.2854 𝐿𝐹𝑅 = −0.08107 ∙ ln 55003 ∙ 2050 + 0.2854 𝐿𝐹𝑅 = 29.4% Finally, the lane flow ratio on the leftmost lane (lane 3) can be obtained as follows: 𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 = 1 − 0.294 − 0.33 𝐿𝐹𝑅 = 37.6% Weaving Segment A practical application of the LFR model is presented next for a weaving segment (Figure F-7), where the lane flow share among 5 lanes is estimated both upstream and within the weave (single period analysis). Figure F-7. Study case on a weaving segment, with four mainline lanes upstream The following input data are provided: • Number of lanes within the weave (N): 5 • Number of upstream lanes (NUP): 4 • Grade (G): -0.5% • Heavy vehicles (t): 3.3% • Interchange density (𝐼𝐷): 0.67 • Weaving length (𝐿 ): 3920 ft • Upstream mainline demand flow rate (vUP): 4512 veh/h

365 • On-ramp demand flow rate (vR,m): 428 veh/h • Freeway-to-freeway demand (vFF): 3912 veh/h • Freeway-to-ramp demand (vFR): 600 veh/h • Ramp-to-freeway demand (vRF): 404 veh/h • Ramp-to-ramp demand (vRR): 24 veh/h • Off-ramp flow rate (vR,d): 624 veh/h • Number of weaving lanes (NWL): 2 • Measured segment free-flow speed (FFS): 70 mi/h • PHF = 1.0 LFRs and lane flows are first calculated for the upstream section of the weaving segment. The heavy- vehicles adjustment factor can be estimated (adopting 𝐸 = 2) as: 𝑓 = 11 + 𝑃 (𝐸 − 1) = 11 + 0.03(2 − 1) = 0.968 The weaving and non-weaving demands can be adjusted to flow rates under ideal conditions. Because the demands are estimated based on 15-minute volumes, PHF is equal to 1. 𝑣 = 𝑉𝑃𝐻𝐹 ∙ 𝑓 𝑣 = 241 ∙ 0.968 = 24.8 𝑝𝑐/ℎ 𝑣 = 4041 ∙ 0.968 = 417.3 𝑝𝑐/ℎ 𝑣 = 6001 ∙ 0.968 = 619.8 𝑝𝑐/ℎ 𝑣 = 3912 1 ∙ 0.968 = 4041.3 𝑝𝑐/ℎ The weaving and non-weaving flows are given by 𝑣 = 𝑣 + 𝑣 = 619.8 + 417.3 = 1037.1 𝑝𝑐/ℎ 𝑣 = 𝑣 + 𝑣 = 24.8 + 4041.3 = 4066.1 𝑝𝑐/ℎ The volume ratio is: 𝑉𝑅 = 𝑣𝑣 = 1037.11037.1 + 4066.1 = 0.203 The capacity of the weaving segment is given by the minimum between the density-capacity (𝑐 ) and weaving-demand-capacity (𝑐 ), which are: 𝑐′ = 𝑐 − 438.2(1 + 𝑉𝑅) . + (0.0765𝐿 ) + (119.8𝑁 ) 𝑐 = 2400 𝑝𝑐/ℎ 𝑐′ = 2400 − 438.2(1 + 0.203) . + (0.0765 ∙ 3920) + (119.8 ∙ 2) = 2351 𝑝𝑐/ℎ/𝑙𝑛 𝑐 = 𝑐′ ∙ 𝑓 = 2350.5 ∙ 0.968 = 2275 𝑣𝑒ℎ/ℎ/𝑙𝑛 𝑐′ = 2400𝑉𝑅 = 24000.203 = 11822 𝑝𝑐/ℎ

366 𝑐 = 𝑐′ ∙ 𝑓𝑁 = 11822.5 . 0.9684 = 2861 𝑣𝑒ℎ/ℎ/𝑙𝑛 𝑐 = min(𝑐 , 𝑐 ) = min(2275.3 ,2861.1 ) = 2275 𝑣𝑒ℎ/ℎ/𝑙𝑛 Therefore, the capacity of the weave is 2275 veh/h/ln. The flow ratio for lane 1 (right lane) is obtained by applying Equation F-1: 𝐿𝐹𝑅 = 𝑓 ∙ ln 𝑣𝑐 + 𝑓 The adjustment factors fa and fc for lane 1 are obtained as follows: 𝑓 , = 𝑎 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼𝐷 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝐿1000 ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 , 𝑓 , = −0.1349 + (−0.5) ∙ 0.1349 + (3.3) ∙ (−0.0119) + 0.67 ∙ (−0.0025) + 4281000 ∙ 0.0718+ 6241000 ∙ (−0.1264) + 39201000 ∙ (0.0558) + 0.203 ∙ (−0.1111) 𝑓 , = −0.0953 𝑓 , = 𝑐 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝐿1000 ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 , 𝑓 , = 0.2434 + (−0.5) ∙ (−0.03) + (3.3) ∙ (−0.004) + 0.67 ∙ (−0.0067) + 4281000 ∙ 0.0645+ 6241000 ∙ (0.0629) + 39201000 ∙ (−0.0303) + 0.203 ∙ (−0.1432) 𝑓 = 0.1606 The lane flow ratio of lane 1 upstream of the weave is: 𝐿𝐹𝑅 = −0.0953 ∙ ln 45124 ∙ 2275.3 + 0.1606 𝐿𝐹𝑅 = 22.8% The same procedure is applied to obtain the lane flow ratio on lane 2, using the respective coefficients from Table F-6: 𝑓 , = 𝑎 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝐿1000 ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 , 𝑓 , = 0.0048 + (−0.5) ∙ (−0.0048) + (3.3) ∙ (−0.00482) + 0.67 ∙ (−0.00482) + 4281000∙ (−0.0313) + 6241000 ∙ (0.03) + 39201000 ∙ (0.0019) + 0.203 ∙ (−0.0044) 𝑓 = −0.00012 𝑓 , = 𝑐 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝐿1000 ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 , 𝑓 , = 0.2571 + (−0.5) ∙ (0.0447) + (3.3) ∙ (−0.0112) + 0.67 ∙ (−0.0049) + 4281000∙ (−0.0088) + 6241000 ∙ (−0.0152) + 39201000 ∙ (0.0107) + 0.203 ∙ (0.0401) 𝑓 , = 0.2310 The LFR of upstream lane 2 can then be obtained by:

367 𝐿𝐹𝑅 = − 0.00012 ∙ ln 45124 ∙ 2275.3 + 0.2310 𝐿𝐹𝑅 = 23.1% The same procedure is applied to obtain the LFR on lane 3, using the respective coefficients from Table F-6: 𝑓 , = 𝑎 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼𝐷 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝐿 ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 , 𝑓 , = 0.12 + (−0.5) ∙ (−0.1199) + (3.3) ∙ (0.0185) + 0.67 ∙ (−0.1199) + 4281000 ∙ (−0.0113)+ 6241000 ∙ (0.0509) + 39201000 ∙ (−0.0405) + 0.203 ∙ (0.1199) 𝑓 , = 0.0524 𝑓 , = 𝑐 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝑣 ,1000 ∙ 𝑓 , + 𝐿 ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 , 𝑓 , = 0.2710 + (−0.5) ∙ (0.0410) + (3.3) ∙ (−0.0042) + 0.67 ∙ (−0.0026) + 4281000∙ (−0.0377) + 6241000 ∙ (−0.0372) + 39201000 ∙ (0.0198) + 0.203 ∙ (0.1545) 𝑓 , = 0.3039 The LFR of lane 3 can then be obtained by: 𝐿𝐹𝑅 = 0.0524 ∙ ln 45124 ∙ 2275.3 + 0.3039 𝐿𝐹𝑅 = 26.7% Finally, the LFR on the leftmost lane (lane 4) can be obtained as follows: 𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 = 1 − 0.228 − 0.231 − 0.267 𝐿𝐹𝑅 = 27.4% In summary, the lane flows upstream of the weave are as follows: 𝑣 , = 4512 ∙ 0.228 = 1029 veh/h 𝑣 , = 4512 ∙ 0.231 = 1043 veh/h 𝑣 , = 4512 ∙ 0.267 = 1204 veh/h 𝑣 , = 4512 ∙ 0.274 = 1236 veh/h Based on these, we calculate the LFRs and lane flows within the weave. Step 1: Determine the number of upstream freeway weaving lanes (NWUP) based on geometry N =1, obtained from Figure F-7 Step 2: Check for VFR 𝑣 , = 1029 veh/h 𝑣 = 600 veh/h Here, v < v ,

368 Hence, the entire freeway-to-ramp flow will be located at the upstream freeway-weaving lane and v =0. Step 3: Calculate auxiliary lane flow (v0) 𝑣 = 𝑣 + 𝑣 − 𝑣 (NWUP =1) 𝑣 = 24 + (600 -0) = 624 veh/h Step 4: Calculate the lane 1 flow (v1) 𝑣 = 𝑣 + 𝑣 − (𝑣 − 𝑣 ) + 𝑣 (NWUP =1) 𝑣 = 404 + {1029 – (600-0)} + 0 = 833 veh/h Step 5: Calculate the lane 2 flow (v2) 𝑣 = 𝑣 , − 𝑣 (NWUP =1) 𝑣 = 1043 – 0 = 1043 veh/h Step 6 Calculate the lane 3 flow (v3) This step does not apply since NWUP =1. Step 7. Obtain flows for the remaining lanes, which will be equal to the respective upstream flow values. 𝑣 = 𝑣 , = 1204 veh/h 𝑣 = 𝑣 , = 1236 veh/h Step 8. Check whether there are v/c ratios greater than 1 for each lane. Given the following flows and capacities for each lane within the weave: 𝑣 = 624 veh/h, 𝑣 = 833 veh/h, 𝑣 = 1043 veh/h, 𝑣 = 1204 veh/h, 𝑣 = 1236 veh/h 𝑐 = 𝑐 = 𝑐 = 𝑐 = 𝑐 = 2275 veh/h Checking v/c ratios for each lane: Lane 1: 624/2275 = 0.27 < 1.0 (OK) Lane 2: 833/2275 = 0.37 < 1.0 (OK) Lane 3:1043/2275 = 0.45 < 1.0 (OK) Lane 4:1204/2275 = 0.59 < 1.0 (OK) Lane 5: 1236/2275 = 0.54 < 1.0 (OK) Speed-Flow Curves by Lane and by Segment Type This section presents the models developed to obtain speed-flow curves for each lane in a freeway segment, as a function of two key inputs: free-flow speed (FFS) and lane capacity. The first part of the section discusses the estimation of lane FFS, while the next part presents models for obtaining lane capacities. The last part provides the speed-flow models obtained as a function of lane FFS and lane capacities.

369 Lane FFS Field observations have shown that operating speeds differ among lanes, and they are typically lower in shoulder lanes and higher in median lanes. Free-flow speeds were measured as the average speed for segment flow rates below 450 veh/h/ln. This criterion is consistent with HCM guidance, which recommends measuring FFS for flows no greater than 500 pc/h/ln. Next, lane FFS were modeled as a function of the segment FFS and as a function of the number of lanes on the segment, as shown in Figure F-8. Due to the ramp influence on traffic flow, merge and diverge segments are likely to have different distributions of FFS. Therefore, distinct models were developed by segment type. Linear regression models were developed with the intercept set to zero. As it can be observed in Figure F-8, there is a good correlation between segment and lane FFS, confirming field observations: shoulder lanes’ FFS are lower than the segment average, while median lanes’ FFS are higher. Center lanes typically have FFS values very close to the segment average. Figure F-8. Segment FFS and lane FFS, by segment type and number of lanes

370 Based on the obtained results, models were developed to estimate individual lane FFS by applying a multiplying factor to the segment FFS. These models are shown in Figure F-8 for each lane. Table F-7 summarizes the recommended multipliers which are provided as a function of the segment type and the number of lanes in the segment. As shown, when the number of lanes increases, the range of FFS multipliers increase as well (i.e. there are lower speeds in the shoulder lanes and higher speeds on the median lanes). For 2-lane segments, merge and diverge segments have a higher difference in FFS between the two lanes when compared to basic segments. For 3-lane segments, basic segments show the highest FFS range, while merge segments have more uniform lane FFS. As for 4-lane segments, merge segments show the highest FFS range, followed by basic and merge segments yield similar results. Table F-7. Multipliers to estimate lane FFS from segment FFS Segment type Number of lanes FFS Multiplier L1 L2 L3 L4 Basic 2 lanes 0.965 1.032 3 lanes 0.934 1.010 1.087 4 lanes 0.924 0.989 1.028 1.079 Merge 2 lanes 0.964 1.044 3 lanes 0.955 1.015 1.045 4 lanes 0.935 0.991 1.036 1.091 Diverge 2 lanes 0.961 1.035 3 lanes 0.943 1.024 1.068 4 lanes 0.933 0.975 1.018 1.074 Weaving 2 lanes 0.969 1.018 3 lanes 0.968 1.023 1.062 4 lanes 0.910 0.988 1.053 1.110 Capacity for speed flow curves by lane Individual lane capacities were obtained through the breakdown observation approach, as previously described. Although the literature shows that lanes may break down at different times, especially on ramp segments, using 15-min aggregated data allows using the assumption that all lanes break down within one time period. The process for measuring lane capacities is illustrated in Figure F-8 based on an example merge segment with 3 lanes. At the 85th percentile, the estimated segment capacity is 1561 veh/h/ln. However, the 85th percentile approach for different lanes yields significantly different flows at breakdown (Figure F-9a): 1132 veh/h/ln (lane 1), 1604 veh/h/ln (lane 2) and 2064 veh/h/ln (lane 3). These values are taken as the estimated capacities of individual lanes. When considered as the relative proportion of total flow, lane capacities can be estimated as 24%, 33% and 43% of total capacity for lanes 1, 2 and 3, respectively. Figure F-9b shows the distribution of LFRs as a function of segment capacity. As observed, at higher volumes the flow distribution is stable at the time of breakdown, showing that lane capacities can be consistently measured using this approach.

371 Figure F-9. Example of lane capacity estimation (French Camp, CA): (a) lane flow distribution at breakdown and (b) LFRs as a function of segment capacity The same rationale was applied to all locations in the database. Figure F-10 shows the relationship between the measured segment capacities and their respective capacities for individual lanes. As it can be observed, capacity typically increases from the rightmost to the leftmost lanes, with center lanes showing capacity values similar to the segment average.

372 Figure F-10. Relationship between segment capacity and individual lane capacity, by segment type and number of lanes For weaving segments, capacity distributions were observed to be significantly more complex and the breakdown observation method was not capable of providing reliable results from the selected dataset. Capacity is assumed uniform for all lanes within a weaving segment, obtained by HCM Equation 13-5 (based on a maximum density of 43 pc/h/ln): 𝑐 = 𝑐 − 438.2 (1 + 𝑉𝑅) . + (0.0765 𝐿 ) + (119.8𝑁 ) (Equation F-27)

373 Next, results were averaged by segment type and number of lanes. Figure F-11 presents the percent distribution of the total segment capacity across lanes (the numbers below the whisker boxes represent the average values of lane capacity). Figure F-11. Capacity of individual lanes as a percentage of segment capacity, by segment type and number of lanes The segment capacities measured from field data may not be equal to the estimated capacities using HCM methodologies. According to the HCM Equation 12-6, base capacity can be estimated as: 𝑐 = 𝑚𝑖𝑛 2200 + 10 𝑥 (𝐹𝐹𝑆 − 50), 2400 (Equation F-28)

374 For each location from the dataset, base capacity was calculated using Equation F-28, as FFS is available from field measurements. Since this equation provides capacity values in passenger-car equivalents, a heavy vehicle factor fHV (as defined in HCM Equation 12-10) was applied to convert the base capacity to veh/h and then make the unit consistent with field data. Figure F-12 shows the comparison of capacity values measured from the field against theoretical estimates using the HCM methods. All observations yielded field measurements smaller than the estimated capacities provided by the HCM. When different segment types are compared, however, no clear conclusions can be drawn on which lanes have higher differences between field and estimated capacities. The field measurements of capacity are, on average, 21.7% smaller than their respective HCM estimations. It is a significant difference that can lead to inaccurate capacity analyses, as the HCM methodologies may overestimate capacity and therefore overestimate the overall segment performance. For this reason, it is recommended that capacity adjustment factors (CAFs) are applied to adjust the estimated capacities to local conditions. Additional research is recommended to further investigate the calibration of CAFs.

375 Figure F-12. Field measured and HCM estimated capacity values, for (a) basic segments, (b) merge segments and (c) diverge segments

376 With flow, capacity and FFS by lane determined, HCM equations can be used to estimate operating speeds on individual lanes. Segment-wise inputs of flow, capacity and FFS are based on the field measurements, and the developed methods previously described are applied to estimate their distribution among individual lanes. For basic segments, average speed is determined as: 𝑆 = 𝐹𝐹𝑆 − ( ) (Equation F-29) This model is applied to individual lanes, as the three key parameters (FFS, c and vp) are input by lane. The breakpoint value (BP) is also determined for each lane (Equation F-30). 𝐵𝑃 = 1000 + 40 𝑥 75 − 𝐹𝐹𝑆 𝑥 𝐶𝐴𝐹 (Equation F-30) It is worth noting that a capacity adjustment factor (CAF) is considered in the estimation of the breakpoint. The HCM method defines the adjusted capacity cadj as the product of the base capacity by a capacity adjustment factor (CAF), which typically reflects impacts of weather, incident, work zone, driver population, and calibration adjustments. 𝑐 = 𝑐 𝑥 𝐶𝐴𝐹 (Equation F-91) As field values of segment capacities were obtained, these can be inserted into Equation F-31 as the value of adjusted capacity. Therefore, CAFs become the single unknown in the equation and can be easily obtained. Practical example A practical example was developed to verify and illustrate the developed methodology. A 2-lane basic segment was modeled and the lane-by-lane performance is compared to field data (CA-1 NB – Santa Cruz, CA). Field measured parameters are as follows: • Free-flow speed: 69.1 mph • Capacity: 3993 veh/h (1996.5 veh/h/ln) • % heavy vehicles: 1.7 • Grade: 3% (rolling) By applying the multiplying factors obtained in Table F-7 to the segment FFS, individual FFS can be obtained as follows: FFS1 = FFS x 0.965 = 69.1 x 0.965 = 66.68 mph FFS2 = FFS x 1.032 = 69.1 x 1.032 = 71.31 mph Next, lane capacities are obtained by applying the multiplying factors obtained in Figure F-11 to the capacity as follows: c1 = c x 44% = 3993 x 44% = 1757 veh/h c2 = c x 56% = 3993 x 56% = 2236 veh/h For comparison purposes, HCM methods would obtain the following theoretical capacity value: c = [2200 + 10 x (FFS – 50)] x fHV = [2200 + 10 x (69.1 - 50) )] x 0.967 = 2312 veh/h/ln Therefore, the recommended CAF for this location is obtained by dividing field measured by theoretical values of capacity: CAF = cadj/c = 1996.5/2312 = 0.864

377 Next, the breakpoint values for each lane can be obtained: BP1 = [1000+ 40 x (75-FFS1)] x CAF2 = [1000+ 40 x (75-66.68)] x 0.8642 = 995 veh/h BP2 = [1000+ 40 x (75-FFS2)] x CAF2 = [1000+ 40 x (75-71.31)] x 0.8642 = 857 veh/h Flows on each lane can be obtained by applying the model described in Equation F-1 to the flow rate entering the segment. Next, speeds on individual lanes using the speed-flow relationship described in Equation F-29. For this location, a sample of 14690 observations (15-min each) was randomly selected, and then predicted values are compared to field data in Figure F-12. Figure F-13. Field vs. predicted speed-flow curve for (a) Lane 1 and (b) Lane 2 (CA-1 NB – Santa Cruz, CA) As observed, the individual speed-flow models can replicate field conditions with good accuracy. Naturally, the oversaturated portion of the curve cannot be addressed by the model, as this is already a limitation of the existing method.

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Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets Get This Book
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The procedures detailed in the 6th Edition of the Highway Capacity Manual (HCM) estimate capacity and several operational measures, including those determining Level of Service, for freeway facilities as well as surface streets.

The TRB National Cooperative Highway Research Program's NCHRP Web-Only Document 290: Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets introduces materials to help modify the freeway analysis methods and the urban street methods so that the effects of operations from one facility to the other can be evaluated.

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