Comparative Traffic Flow Prediction of a Heuristic ANN Model and a Hybrid ANN-PSO Model in the Traffic Flow Modelling of Vehicles at a Four-Way Signalized Road Intersection
Abstract
:1. Introduction
1.1. Motivation and Contribution of the Research
1.2. Organization of the Research
2. Literature Review
2.1. Related Studies
- Traditional statistical techniques.
- Traditional machine learning techniques.
- Deep learning methods.
2.2. Traffic Flow Patterns at a Signalized Road Intersection
- Assumption 1
- Assumption 2
- Assumption 3
- Assumption 4
- Assumption 5
- Assumption 6
- Assumption 7
- Assumption 8
- This is called the “traffic shockwaves” of the queues of vehicles forming at a road intersection when the traffic lights turn red.
- This is a traffic shockwave of vehicles when the traffic lights turn green.
- This is a traffic control delay for each vehicle at the intersection. This is the arrival time when vehicles arrive at a road intersection and when they leave the intersection.
- This is when two vehicles depart at the same time from the road intersection. It is called “saturation headway”.
- This is the speed of the vehicles as they arrived at and departed from the road intersection.
- This is called the time gap. It usually occurs between the departing vehicle and the arriving vehicle.
- Assumption 9
- The driver stopped because the traffic light was red.
- This is the driver driving through the intersection when the traffic light is green.
- This is the driver driving through the intersection when the queue is cleared and no vehicles are waiting at the road intersection.
- This is the driver reducing their speed because the traffic light has turned green.
3. Methodology
3.1. Research Design
3.2. Population of the Research
3.3. Size of Traffic Data
3.4. Method of Traffic Data Collection
3.5. Sample and Sampling Methods
3.6. Location of the Study
3.7. Collection and Extraction of the Traffic Datasets
- Brakfontein 1C N1 SB (Roadsite 1).
- Old Johannesburg Road SB off-ramp (Roadsite 2).
- Samrand Avenue SB off-ramp (Roadsite 3).
- Olifantsfnt SB off-ramp (Roadsite 4).
3.8. Traffic Control Delay at Four-Way Signalized Road Intersections
Model Notation and Formulation
3.9. Development of the ANN-PSO Model
- Take into consideration the number of hidden neurons in the hidden layers and develop a neural network model using the initial weights and biases.
- The reformation of the weights and biases, where there can be a representation of the location of a particle in a D-dimensional space of the problem, and D is the number of weights and biases.
- During the iteration of each of the particles, the output values can be predicted and then mathematically calculated for the value of the cost function in Equation (18).
- Update the location of particles in the PSO algorithm for a number of populations and iterations until the target output is fulfilled. In summary, there will be a minimization of the cost function.
- A maximum iteration of 1000.
- The training run will be terminated if the objective function is not up to a specific fixed parameter.
3.10. Development of the ANN Model
4. Results and Discussions
4.1. Four-Way Signalized Road Intersection Vehicular Traffic Flow
4.2. Artificial Neural Network Model
- Network inputs: The traffic density, number of light vehicles, average speed of light vehicles, time of day of light vehicles, the average speed of long trucks, time of day of long trucks, number of long trucks, the average speed of medium trucks, time of day of medium trucks, number of medium trucks, number of short trucks, the average speed of short trucks and time of day of short trucks.
- Network Output: Traffic volume.
4.3. Artificial Neural Network—Particle Swarm Optimization Model
5. Conclusions and Future work
- One of the most significant findings to emerge from this study is that the comparison of the ANN-PSO model and ANN model has shown that the ANN-PSO model is far more accurate, easy to use, and efficient than the ANN model, with a testing performance of 0.9971, compared to the ANN model’s testing performance of 0.99169.
- This study also suggests that a Neural Network comprising five (5) neurons is the best-performing neural network during the ANN-PSO model training of the traffic datasets.
- The investigation of the use of the ANN model to model self-driving vehicles at four-way signalized road intersections has shown that the best training performance of the traffic datasets was achieved when the number of hidden neurons is 6, which leads to training (R) 0.96086, testing (R) 0.99169, validation (R) 0.97258, and All (R) 0.96722.
- The most apparent findings from this research study are that the efficiency of the traffic dataset’s prediction performance depends on the total number of input variables. Further observation also showed that the number of parameters of the input variables determined the predictor model’s accuracy (ANN and ANN-PSO model).
- The evidence from this study suggests that ANN and ANN-PSO are reliable predictors of the traffic flow of vehicles at a signalized road intersection.
- An implication of the results of this research study is the possibility that transportation researchers and civil engineers could apply the ANN and ANN-PSO model used in this research study in the development of ways to improve road transportation mobility through technologically advanced traffic management techniques.
- This research study extends our knowledge of traffic flow modelling and the application of soft computing techniques in vehicular traffic flow at a signalized road intersection.
- A natural progression of this work is to determine whether transportation researchers can use expanded and robust real-time traffic data to achieve a more profound impact of these traffic variables on traffic flow prediction and thus improve the traffic flow prediction efficiency and reliability.
- A possible area of research is the application of statistical analysis in the validation of the ANN and ANN-PSO model results of this study.
- Another possible area of future research would be to investigate the possibility that, due to traffic data’s sequential nature irrespective of whether it is traffic data from developing or developed countries, it would be possible to conduct research by following the deep learning methods explained by [37], such as artificial bee colony optimization, grasshopper optimization algorithm, and bat algorithm. These methods can all be tested and compared with the results obtained from this paper to determine which one has a better testing performance (R2).
- Further research regarding the prediction performance of ANN and ANN-PSO (using convergent plots) in the modelling of the vehicular traffic flow at an un-signalized road intersection would be interesting.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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Input Variables | Output Variables |
---|---|
Traffic density | Traffic Volume |
The Number of light vehicles | |
The average speed of light vehicles | |
Time of day of light vehicles | |
The average speed of a long truck | |
Time of day of long truck | |
Number of long trucks | |
The average speed of a medium truck | |
Time of day of medium truck | |
The Number of medium trucks | |
The Number of short trucks | |
The average speed of a short truck | |
Time of day of short truck |
Road Intersections | Date | Distance (m) | Direction | Number of Lanes | Speed Limit (Km/h) | Number of Vehicles (Vehicles/h) |
---|---|---|---|---|---|---|
Roadsite 1 | 15 July 2019–27 July 2019 | 12.5 | Southbound | 7 | 120 | 1,097,152 |
Roadsite 2 | 15 July 2019–29 July 2019 | 9.40 | Southbound | 5 | 120 | 17,240,260 |
Roadsite 3 | 15 July 2019–29 July 2019 | 7.0 | Southbound | 7 | 120 | 12,448,023 |
Roadsite 4 | 15 July 2019–29 July 2019 | 3.70 | Southbound | 5 | 120 | 18,051,124 |
Light Vehicle | Long Truck | Medium Truck | Short Truck | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Speed (m/s) | Number of Light Vehicles | Time (s) | Speed (m/s) | Number of Long Trucks | Time (s) | Speed (m/s) | Number of Medium Trucks | Time (s) | Speed (m/s) | Number of Light Vehicles | Time (s) |
115 | 1438 | 230 | 87 | 44 | 298 | 92 | 29 | 282 | 97 | 51 | 276 |
65 | 29,934 | 489 | 49 | 197 | 960 | 59 | 188 | 591 | 70 | 625 | 542 |
106 | 18,213 | 245 | 81 | 308 | 321 | 85 | 277 | 315 | 95 | 1056 | 278 |
103 | 223,44 | 255 | 82 | 321 | 316 | 85 | 263 | 308 | 97 | 865 | 271 |
109 | 3071 | 244 | 81 | 140 | 319 | 83 | 70 | 349 | 93 | 96 | 285 |
111 | 1234 | 237 | 82 | 115 | 313 | 84 | 35 | 306 | 95 | 54 | 277 |
60 | 28,844 | 565 | 52 | 258 | 833 | 52 | 206 | 750 | 65 | 635 | 586 |
107 | 24,793 | 241 | 83 | 338 | 310 | 88 | 332 | 298 | 99 | 1437 | 264 |
103 | 22,577 | 254 | 81 | 269 | 318 | 86 | 258 | 302 | 98 | 919 | 270 |
110 | 3432 | 241 | 81 | 162 | 320 | 84 | 91 | 315 | 95 | 94 | 278 |
113 | 1005 | 233 | 85 | 84 | 305 | 91 | 43 | 286 | 103 | 56 | 256 |
76 | 31,392 | 422 | 67 | 225 | 540 | 70 | 234 | 520 | 84 | 758 | 378 |
106 | 25,480 | 243 | 82 | 376 | 313 | 87 | 331 | 297 | 99 | 1503 | 266 |
Roadsites. | Training | Validation | Testing | Total |
---|---|---|---|---|
Brakfontein 1C N1 SB (Roadsite 1) | 36 | 15 | 10 | 61 |
Old Johannesburg Road SB off-ramp (Roadsite 2). | 48 | 16 | 10 | 74 |
Samrand Avenue SB off-ramp (Roadsite 3). | 41 | 13 | 10 | 64 |
Olifantsfnt SB off-ramp (Roadsite 4). | 35 | 15 | 10 | 60 |
Total | 160 | 59 | 40 | 259 |
Roadsites | Training | Testing | Total |
---|---|---|---|
Brakfontein 1C N1 SB (Roadsite 1) | 51 | 10 | 61 |
Old Johannesburg Road SB off-ramp (Roadsite 2). | 64 | 10 | 74 |
Samrand Avenue SB off-ramp (Roadsite 3). | 54 | 10 | 64 |
Olifantsfnt SB off-ramp (Roadsite 4). | 50 | 10 | 60 |
259 |
Number of Neurons | Swarm Population Size | MSE | ||||
---|---|---|---|---|---|---|
5 | 10 | 2.25 | 2 | 0.99600 | 22.228 | 0.9387 |
5 | 20 | 2.25 | 2 | 0.99392 | 27.429 | 0.9404 |
5 | 50 | 1.5 | 2.25 | 0.99966 | 19.522 | 0.7170 |
5 | 100 | 1 | 2.75 | 0.99863 | 15.463 | 0.9298 |
5 | 200 | 1.5 | 2 | 0.99951 | 23.388 | 0.9791 |
5 | 400 | 1.5 | 2 | 0.99952 | 23.161 | 0.9971 |
6 | 10 | 1 | 3 | 0.99127 | 34.088 | 0.8157 |
6 | 20 | 2 | 2.25 | 0.99629 | 21.404 | 0.8634 |
6 | 50 | 1 | 2.5 | 0.99948 | 24.253 | 0.9839 |
6 | 100 | 1 | 2.5 | 0.99917 | 32.025 | 0.9491 |
6 | 200 | 1 | 2.75 | 0.99769 | 17.855 | 0.8562 |
6 | 400 | 1 | 2.25 | 0.99961 | 20.907 | 0.9856 |
7 | 10 | 1.5 | 2.5 | 0.99324 | 29.150 | 0.4626 |
7 | 20 | 1 | 2.75 | 0.99807 | 16.893 | 0.9237 |
7 | 50 | 1 | 2.5 | 0.99939 | 26.448 | 0.2374 |
7 | 100 | 1 | 2.5 | 0.99906 | 34.934 | 0.9650 |
7 | 200 | 1.5 | 2.25 | 0.99893 | 38.076 | 0.9429 |
7 | 400 | 2 | 2 | 0.99847 | 15.881 | 0.8008 |
8 | 10 | 1 | 2.75 | 0.99697 | 19.679 | 0.7347 |
8 | 20 | 1 | 2.5 | 0.99944 | 25.211 | 0.9881 |
8 | 50 | 1.5 | 2.25 | 0.99955 | 22.507 | 0.9898 |
8 | 100 | 1 | 2.5 | 0.99974 | 17.675 | 0.9818 |
8 | 200 | 1 | 2.75 | 0.99943 | 25.388 | 0.9708 |
8 | 400 | 1 | 2.25 | 0.99974 | 17.496 | 0.9138 |
9 | 10 | 1 | 2.75 | 0.99307 | 29.775 | 0.3029 |
9 | 20 | 1 | 3 | 0.99206 | 32.091 | 0.9139 |
9 | 50 | 1.5 | 2.25 | 0.99895 | 37.571 | 0.7646 |
9 | 100 | 2 | 2 | 0.99911 | 33.780 | 0.9468 |
9 | 200 | 1.5 | 2.25 | 0.99807 | 16.890 | 0.8633 |
9 | 400 | 1 | 2.5 | 0.99973 | 17.962 | 0.9816 |
10 | 10 | 1 | 2.75 | 0.99900 | 36.389 | 0.7529 |
10 | 20 | 1.5 | 2.5 | 0.99871 | 15.261 | 0.8945 |
10 | 50 | 1.5 | 2.5 | 0.99896 | 37.306 | 0.6819 |
10 | 100 | 1 | 2.75 | 0.99741 | 18.641 | 0.8663 |
10 | 200 | 1 | 2.75 | 0.99920 | 31.178 | 0.9282 |
10 | 400 | 1.5 | 2.5 | 0.99799 | 17.088 | 0.9135 |
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Olayode, I.O.; Tartibu, L.K.; Okwu, M.O.; Severino, A. Comparative Traffic Flow Prediction of a Heuristic ANN Model and a Hybrid ANN-PSO Model in the Traffic Flow Modelling of Vehicles at a Four-Way Signalized Road Intersection. Sustainability 2021, 13, 10704. https://doi.org/10.3390/su131910704
Olayode IO, Tartibu LK, Okwu MO, Severino A. Comparative Traffic Flow Prediction of a Heuristic ANN Model and a Hybrid ANN-PSO Model in the Traffic Flow Modelling of Vehicles at a Four-Way Signalized Road Intersection. Sustainability. 2021; 13(19):10704. https://doi.org/10.3390/su131910704
Chicago/Turabian StyleOlayode, Isaac Oyeyemi, Lagouge Kwanda Tartibu, Modestus O. Okwu, and Alessandro Severino. 2021. "Comparative Traffic Flow Prediction of a Heuristic ANN Model and a Hybrid ANN-PSO Model in the Traffic Flow Modelling of Vehicles at a Four-Way Signalized Road Intersection" Sustainability 13, no. 19: 10704. https://doi.org/10.3390/su131910704