Development of a Machine-Learning-Based Novel Framework for Travel Time Distribution Determination Using Probe Vehicle Data
Abstract
:1. Introduction
2. Study Area and Data Collection
2.1. Study Area
2.2. Data Collection
- Non-Interfering Weather Conditions: Weather conditions such as fair, partly cloudy, mostly cloudy, cloudy, haze, smoke, and blowing dust have no discernible effect on the traffic conditions. Hence, these are grouped into the non-interfering weather conditions class.
- Interfering Weather Conditions: all weather situations, such as drizzle, light rain, rain, heavy rain, thunderstorm, mist, shallow fog, fog, etc., that are expected to have a considerable effect on travel times and speed. Hence, these are grouped into interfering weather conditions class.
2.3. Data Pre-Processing
2.3.1. Data Cleaning
2.3.2. Data Visualization and Trip Extraction
3. Methodology
3.1. Analysis and Classification of Data
3.2. Distribution Fitting
- Bounded Distributions: Distributions that fall into this category include Uniform distributions, Triangular, Reciprocal, Power Functions, PERT, Beta, and Johnson-Simons-Brown (JSB). These distributions are bounded between a range of [a,b].
- Unbounded Distributions: Normal, Logistic, Cauchy, Error, Error Function, Johnson SU, Hyperbolic Secant, Student’s t distribution, and Laplace (Double Exponential) are among the unbounded distributions. These distributions are unbounded and have a range of (−∞, +∞).
- Non-Negative Distributions: The majority of these distributions are defined for the range x > γ, which is equivalent to x − γ ≥ 0, where γ is a continuous location parameter. Log-logistic, Inverse Gaussian, Weibull, Levy’s Log-Gamma, Rayleigh’s Rice, Nakagami’s Lognormal, Pearson V, Pearson VI, Pareto (first kind), and Pareto (second kind) are among the non-negative distributions supported by the EasyFit software. Most of the non-negative distributions supported by EasyFit are available in two versions or forms: a simplified version and a complete version.
- Advanced Distributions: EasyFit’s classification of continuous distributions is based on various definitions. As a result, some of the continuous distributions do not fall into any of the categories listed above. Simultaneously, they frequently represent more valid models than a large number of other distributions. EasyFit supports advanced distributions such as generalized Pareto, generalized extreme value (GEV), Log-Pearson III, Wakeby, generalized logistic, Phased Bi-Exponential, and Phased Bi-Weibull. These distributions are generated by combining two or more basic distributions. For instance, the GEV distribution is generated by combining Weibull, Gumbel, and Frechet distributions.
3.2.1. Kolmogorov–Smirnov Test
3.2.2. Anderson–Darling Test
3.2.3. Chi-Squared Test
3.3. Determination of Distribution Suitable for Travel Time Data
4. Results and Discussion
- Classification xi is a true positive for class c if both the actual and the predicted classes of xi are the same as c.
- Classification xi is a true negative for class c if neither of the actual or predicted classes of xi matches with c.
- Classification xi is a false positive for class c if the predicted class of xi matches c but the actual class does not.
- Classification xi is a false negative for class c if the actual class of xi matches c but the predicted class does not.
5. Conclusions
- Disagreement on the best distribution option for fitting to travel time data among the studies available in the literature is possibly due to differences in the traffic situations prevailing in their study area.
- An RUS Boosted decision-tree-classifier-based novel framework proposed in the study can determine the best-fitted distribution for the travel time data with 91% accuracy.
- Travel time distributions determined by the novel framework proposed in the current study have an acceptance rate of 98.4%, even in heterogeneous disordered traffic conditions. This acceptance rate is expected to increase if the framework is applied to travel time data in developed countries with lane-disciplined homogeneous traffic.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Study | Year | Location | Data Source | Dataset Duration/Size | Types of Vehicles Considered | Recommended Distribution | Limitations |
---|---|---|---|---|---|---|---|
[9] | 1979 | Chicago, USA | Drivers who measured TT on their regular daily trips to and from work | 179 trips on 14 routes | - | Gamma | Considered only 179 trips |
[10] | 2009 | Melbourne, Australia | GPS-equipped buses | 3351 trips | Buses | Normal (peak hour) Lognormal (off-peak) | Considered travel time data of only buses and used a small dataset (only 3351 trips) |
[11] | 2009 | Hirakata City, Japan | Buses operated by Keihan Bus Company | 12 Days | Buses | Lognormal | Considered travel time data of only buses |
[12] | 2013 | Adelaide, Australia | GPS-equipped probe vehicles | 180, 67 runs for Route 1 and Route 2, respectively | N/A | Burr Type XII | Used a very small travel time dataset |
[13] | 2014 | Beijing, China | Historical floating car data | Seven days | N/A | Generalized extreme value (GEV) and generalized Pareto | Used travel time data of one week only |
[14] | 2015 | Brisbane, Australia | Transit Signal Priority (TSP) data | 1 year | Buses | Lognormal | Considered travel time data of only buses |
[15] | 2016 | Brisbane, Australia | TransLink Division, Department of Transport and Major Roads (DTMR) | 6 months | Buses | Gaussian mixture | Considered travel time data of only buses |
[16] | 2018 | Beijing, China | Taxis equipped with GPS devices (Probe Vehicles) | 1 week | Taxis | Lognormal | Used travel time data of one week only, also used only taxis as probe vehicles |
[17] | 2018 | Surat and Ahmedabad City, India | Video graphic survey | 5 h a day for two working days | Two-wheelers, Three wheelers, cars, buses, LCVs, Truck | Burr | Used travel time data of 10 h only |
[18] | 2018 | Surat, Mysore, and Chennai, India | SITILINK Ltd., Metropolitan Transport Corporation (MTC), Karnataka State Road Transport Corporation (KSRTC) | N/A | Buses | GEV | Considered travel time data of only buses |
[19] | 2018 | Calgary, Alberta, Canada, | Calgary Transit | From 6 a.m. to 9 a.m. for six months | Buses | Lognormal (For pseudo horizon range = 7–8 km), Normal (For pseudo horizon range > 8 km) | Considered travel time data of only buses that also for morning peak only |
[20] | 2019 | Nanjing, China | RFID Base Stations | One month | N/A | Gaussian mixture model | Used travel time data of one month only |
[21] | 2020 | Surat, India | Video graphic survey | 5 h | N/A | Burr (2 Lane), Log-logistic (3 Lane) | Used travel time data of 5 h only |
[22] | 2020 | Charlotte, North Carolina, USA | Regional Integrated Transportation Information System (RITIS) | N/A | N/A | Burr | Used aggregated travel time data Dataset description, i.e., dataset duration and types of vehicles considered, is missing |
[23] | 2020 | Mysore, India | KSRTC | 4 months | Buses | Normal (peak hours), GEV (off-peak conditions) | Considered travel time data of only buses and used dataset of only four months |
[24] | 2020 | New York City, USA | Department of Transportation, New York City, USA | 8:00 a.m. to 8:00 p.m. for one week | N/A | Gamma Mixture | Considered travel time data for only one week |
[25] | 2021 | Athens, Greece | Vodafone Innovus S.A | Three months | Passenger cars, taxis, minivans, vans, minibuses, buses, mini trucks | Lognormal | Considered travel time data for three months only |
[26] | 2021 | Mysore, India | KSRTC (public transport) | Two months | Buses | GEV | Considered travel time data of only buses and used dataset of only two months |
[27] | 2022 | Tehran, Iran | Wi-Fi and Bluetooth sensors | Two months | N/A | Lognormal | Considered travel time data for two months only |
Encrypted Device ID | Timestamp | Latitude | Longitude | Altitude | Bearing | Engine Status | Speedometer Reading |
---|---|---|---|---|---|---|---|
8493 | 31-07-2018 03:20:54 | 28.65647095 | 77.43452638 | 204 | 0 | 1 | 0 |
458 | 31-07-2018 03:20:53 | 28.66622667 | 77.32199333 | N/A | 16.34 | 1 | 60.5 |
459 | 31-07-2018 03:20:51 | 28.646855 | 77.41362333 | N/A | 36.6 | 1 | 36.6 |
8487 | 31-07-2018 03:20:50 | 28.64896978 | 77.34511459 | 187 | 0 | 1 | 0 |
12533 | 31-07-2018 03:20:52 | 28.68999299 | 77.35131744 | 196 | 241 | 0 | 0 |
Travel Direction | DOW | TOD | Non-Interfering Weather Conditions | Interfering Weather Conditions | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
N | TMin | TMax | ATT | SD | N | TMin | TMax | ATT | SD | |||
Noida to Delhi | Weekdays | MP | 1625 | 165 | 547 | 441 | 60 | 386 | 170 | 810 | 588 | 137 |
IP | 3722 | 178 | 654 | 255 | 36 | 503 | 140 | 732 | 500 | 100 | ||
EP | 1751 | 159 | 640 | 253 | 42 | 264 | 193 | 705 | 510 | 100 | ||
LE | 2788 | 112 | 1192 | 208 | 63 | 650 | 121 | 591 | 410 | 81 | ||
LN | 1038 | 107 | 958 | 154 | 55 | 332 | 139 | 585 | 414 | 80 | ||
EM | 1311 | 146 | 556 | 189 | 37 | 251 | 101 | 536 | 403 | 78 | ||
Saturdays | MP | 749 | 168 | 489 | 359 | 52 | 58 | 257 | 673 | 499 | 94 | |
IP | 749 | 188 | 529 | 271 | 42 | 101 | 103 | 707 | 480 | 94 | ||
EP | 322 | 173 | 521 | 256 | 41 | 49 | 226 | 695 | 494 | 107 | ||
LE | 369 | 129 | 499 | 218 | 57 | 87 | 187 | 573 | 411 | 79 | ||
LN | 221 | 116 | 681 | 165 | 67 | 55 | 165 | 565 | 433 | 76 | ||
EM | 330 | 160 | 493 | 191 | 28 | 63 | 225 | 569 | 415 | 68 | ||
Sundays | MP | 209 | 145 | 555 | 318 | 65 | 49 | 256 | 669 | 495 | 91 | |
IP | 801 | 175 | 413 | 251 | 38 | 110 | 219 | 649 | 475 | 100 | ||
EP | 354 | 175 | 386 | 258 | 35 | 54 | 154 | 699 | 467 | 113 | ||
LE | 346 | 121 | 536 | 208 | 58 | 81 | 224 | 581 | 417 | 78 | ||
LN | 145 | 120 | 359 | 161 | 37 | 37 | 170 | 559 | 415 | 85 | ||
EM | 305 | 160 | 320 | 188 | 21 | 59 | 133 | 557 | 413 | 85 | ||
Delhi to Noida | Weekdays | MP | 981 | 166 | 972 | 310 | 72 | 230 | 137 | 680 | 516 | 116 |
IP | 2513 | 181 | 740 | 263 | 44 | 343 | 102 | 669 | 491 | 96 | ||
EP | 2019 | 187 | 629 | 270 | 35 | 302 | 200 | 720 | 551 | 112 | ||
LE | 2164 | 124 | 933 | 214 | 57 | 508 | 157 | 582 | 425 | 77 | ||
LN | 966 | 115 | 577 | 161 | 50 | 242 | 165 | 596 | 431 | 81 | ||
EM | 1663 | 153 | 769 | 195 | 42 | 317 | 120 | 588 | 421 | 75 | ||
Saturdays | MP | 168 | 168 | 452 | 318 | 55 | 41 | 104 | 677 | 491 | 117 | |
IP | 463 | 192 | 504 | 263 | 39 | 65 | 291 | 672 | 495 | 81 | ||
EP | 442 | 171 | 559 | 261 | 46 | 65 | 197 | 670 | 493 | 111 | ||
LE | 417 | 125 | 768 | 211 | 59 | 96 | 178 | 584 | 422 | 90 | ||
LN | 202 | 112 | 490 | 163 | 51 | 51 | 121 | 579 | 428 | 83 | ||
EM | 333 | 153 | 500 | 187 | 30 | 62 | 170 | 583 | 413 | 79 | ||
Sundays | MP | 159 | 126 | 481 | 301 | 59 | 36 | 214 | 674 | 497 | 95 | |
IP | 466 | 163 | 427 | 246 | 40 | 64 | 195 | 639 | 474 | 98 | ||
EP | 480 | 166 | 527 | 253 | 43 | 71 | 195 | 662 | 492 | 103 | ||
LE | 410 | 106 | 748 | 205 | 54 | 97 | 212 | 568 | 440 | 73 | ||
LN | 192 | 117 | 493 | 169 | 57 | 49 | 155 | 591 | 438 | 68 | ||
EM | 324 | 166 | 293 | 191 | 18 | 65 | 148 | 575 | 406 | 87 |
Travel Direction | DOW | TOD | Non-Interfering Weather Conditions | Interfering Weather Conditions | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
N | TMin | TMax | ATT | SD | N | TMin | TMax | ATT | SD | |||
UP | Weekdays | MP | 617 | 63 | 200 | 140 | 22 | 145 | 134 | 255 | 213 | 22 |
IP | 1310 | 40 | 220 | 120 | 23 | 179 | 104 | 236 | 183 | 22 | ||
EP | 885 | 82 | 204 | 158 | 18 | 132 | 157 | 270 | 227 | 23 | ||
LE | 1004 | 98 | 195 | 112 | 9 | 235 | 135 | 261 | 219 | 23 | ||
LN | 323 | 70 | 218 | 87 | 18 | 81 | 93 | 215 | 165 | 24 | ||
EM | 649 | 91 | 162 | 104 | 7 | 124 | 137 | 243 | 198 | 22 | ||
Saturdays | MP | 122 | 39 | 192 | 124 | 29 | 29 | 123 | 219 | 184 | 21 | |
IP | 290 | 59 | 177 | 116 | 19 | 38 | 135 | 210 | 177 | 18 | ||
EP | 176 | 77 | 194 | 162 | 18 | 26 | 171 | 256 | 224 | 22 | ||
LE | 190 | 94 | 151 | 108 | 9 | 46 | 150 | 250 | 212 | 28 | ||
LN | 51 | 68 | 148 | 83 | 12 | 14 | 120 | 198 | 168 | 22 | ||
EM | 125 | 92 | 161 | 103 | 9 | 24 | 154 | 236 | 204 | 23 | ||
Sundays | MP | 117 | 57 | 211 | 128 | 28 | 27 | 115 | 206 | 182 | 20 | |
IP | 277 | 68 | 201 | 119 | 19 | 36 | 57 | 217 | 175 | 29 | ||
EP | 167 | 80 | 193 | 162 | 18 | 25 | 158 | 252 | 219 | 25 | ||
LE | 181 | 94 | 167 | 107 | 10 | 36 | 149 | 256 | 220 | 23 | ||
LN | 48 | 67 | 195 | 82 | 18 | 10 | 112 | 192 | 165 | 26 | ||
EM | 119 | 90 | 131 | 100 | 6 | 23 | 147 | 241 | 203 | 25 | ||
DOWN | Weekdays | MP | 558 | 56 | 205 | 143 | 22 | 129 | 126 | 258 | 214 | 23 |
IP | 1184 | 46 | 208 | 122 | 24 | 160 | 97 | 227 | 182 | 24 | ||
EP | 796 | 88 | 205 | 160 | 18 | 122 | 165 | 264 | 225 | 21 | ||
LE | 906 | 97 | 233 | 112 | 10 | 212 | 128 | 271 | 218 | 21 | ||
LN | 291 | 64 | 188 | 80 | 14 | 73 | 82 | 213 | 158 | 25 | ||
EM | 586 | 95 | 173 | 107 | 7 | 112 | 118 | 249 | 196 | 25 | ||
Saturdays | MP | 121 | 70 | 191 | 127 | 25 | 28 | 105 | 208 | 182 | 22 | |
IP | 284 | 83 | 180 | 126 | 17 | 39 | 115 | 216 | 180 | 21 | ||
EP | 172 | 104 | 202 | 164 | 19 | 26 | 184 | 261 | 223 | 20 | ||
LE | 185 | 94 | 186 | 109 | 10 | 44 | 157 | 259 | 220 | 20 | ||
LN | 49 | 65 | 202 | 81 | 20 | 13 | 87 | 190 | 151 | 30 | ||
EM | 122 | 96 | 150 | 105 | 9 | 24 | 137 | 241 | 197 | 22 | ||
Sundays | MP | 110 | 75 | 200 | 127 | 28 | 27 | 135 | 211 | 183 | 20 | |
IP | 262 | 65 | 183 | 118 | 19 | 37 | 89 | 238 | 173 | 29 | ||
EP | 160 | 105 | 199 | 163 | 19 | 23 | 159 | 258 | 222 | 24 | ||
LE | 172 | 93 | 148 | 106 | 8 | 40 | 160 | 264 | 223 | 19 | ||
LN | 46 | 62 | 227 | 80 | 25 | 12 | 114 | 188 | 162 | 22 | ||
EM | 114 | 94 | 133 | 104 | 7 | 21 | 145 | 237 | 203 | 21 |
S. No. | Study | No. of Distributions Considered | Number of Traffic Scenarios Considered | Acceptance Rate |
---|---|---|---|---|
1 | Present study | 60 | 144 | 98.4% |
2 | [25] | 7 | 6 | 91.6% |
3 | [16] | 4 | 16 | 87.5% |
4 | [22] | 4 | 24 | 79.2% |
S. No. | Class | Precision | Sensitivity | F1-Score | Specificity | FPR |
---|---|---|---|---|---|---|
1 | Burr | 90.48 | 95.00 | 92.68 | 98.17 | 1.83 |
2 | GEV | 78.57 | 91.67 | 84.62 | 97.44 | 2.56 |
3 | Johnson SB | 90.00 | 75.00 | 81.82 | 98.10 | 1.90 |
4 | Log Logistic | 97.14 | 91.89 | 94.44 | 98.91 | 1.09 |
5 | Weibull | 89.74 | 97.22 | 93.33 | 95.70 | 4.30 |
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Sihag, G.; Kumar, P.; Parida, M. Development of a Machine-Learning-Based Novel Framework for Travel Time Distribution Determination Using Probe Vehicle Data. Data 2023, 8, 60. https://doi.org/10.3390/data8030060
Sihag G, Kumar P, Parida M. Development of a Machine-Learning-Based Novel Framework for Travel Time Distribution Determination Using Probe Vehicle Data. Data. 2023; 8(3):60. https://doi.org/10.3390/data8030060
Chicago/Turabian StyleSihag, Gurmesh, Praveen Kumar, and Manoranjan Parida. 2023. "Development of a Machine-Learning-Based Novel Framework for Travel Time Distribution Determination Using Probe Vehicle Data" Data 8, no. 3: 60. https://doi.org/10.3390/data8030060