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Enhancing Traffic Prediction Accuracy: A Comparative Analysis of Data Quality and Model Evaluation Using Artificial Intelligence

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24 January 2024

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26 January 2024

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Abstract
This study focuses on predicting traffic speed using the simple Multilayer Perceptron (MLP) model, despite the availability of various models for traffic prediction, with artificial intelligence demonstrating superior predictive capabilities. Emphasizing that the quality of the data holds greater significance than the model itself, the research underscores the challenges posed by data containing significant errors and fluctuations. Unlike relying solely on criteria such as Mean Absolute Deviation (MAD) or coefficient of determination (r2), this study advocates for the use of MAD/range as a more robust metric for prediction accuracy, especially when dealing with data exhibiting substantial order.The study sets the speed limit and traffic value at 0.65 and 0.88, respectively. Notably, both criteria yield identical accuracy results of 13% for MAD/R in predicting speed and 14% for traffic. This parity suggests that the artificial intelligence model performs equally well for both variables, highlighting the importance of considering alternative evaluation metrics in the face of data complexities.
Keywords: 
Subject: Engineering  -   Civil Engineering

1. Introduction

The crucial role of transportation in everyday life, coupled with the limited capacity of transportation routes and the imperative to prevent accidents, underscores the significance of transportation planning. However, effective transportation planning is contingent upon having accurate road traffic information[1, 2]. Transportation plays a crucial role in modern society[3], and efficient traffic flow management is essential for ensuring the smooth operation of highways. Predicting traffic flow is a key component of effective traffic management, aiding in the prevention of congestion, reduction of travel time, and enhancement of overall transportation efficiency. Traditional methods of traffic prediction have relied on simulation and statistical approaches based on mathematical relationships. In recent years, artificial neural networks (ANNs) have emerged as powerful tools for predicting complex and dynamic systems The significance of Artificial Intelligence (AI) in the field of computer science, particularly within the era of big data, cannot be overstated. Over the past 50 years, AI has made remarkable strides, particularly in machine learning, data mining, computer vision, expert systems, natural language processing, robotics, and various applications[4]. Initially introduced in 1958[5] and later refined in 1986[6], ANNs have gained prominence for their ability to analyze and learn patterns from available data, providing valuable insights for predicting future outcomes[7]. Indeed, short-term traffic flow prediction serves as a pivotal component of Intelligent Transportation Systems (ITS). This crucial function contributes to various aspects of transportation management, including traffic planning, control, and management. Additionally, it plays a vital role in supporting roadway safety evaluation and estimating energy consumption[8].By unraveling these complexities, researchers and policymakers gain valuable insights that can guide informed decision-making and contribute to the development of sustainable, health-conscious urban environments[9]. The advent of artificial intelligence (AI) approaches has paralleled the rapid development of new traffic flow prediction models and frameworks within the ITS[10].
This study focuses on the design and implementation of an ANN model for predicting traffic flow in highways, with a specific emphasis on short-term predictions. The short-term aspect is particularly relevant for real-time traffic management.By leveraging historical data from a traffic counter station, this research aims to train an ANN using a multilayer perceptron approach. The trained network will then be tested for its accuracy in predicting traffic and speed for the upcoming week. The comparison between the predicted and recorded data, and statistical methods will be employed to assess the model's performance. This approach aims to utilize available data, extracting pertinent patterns to predict and derive suitable data in comparison to the patterns acquired during training. The primary objective of this article is to explore and ascertain the prediction of traffic .

2. Literature Review

Traffic congestion is a significant issue that affects transportation systems in both developed and developing countries. It can lead to increased travel times, reduced fuel efficiency, and increased emissions. Traffic control systems are designed to minimize traffic congestion and maximize traffic flow. However, effective traffic control requires accurate traffic flow data. This is where artificial neural networks (ANNs) can play a valuable role[11]. traffic flow prediction has relied on human expertise, which can be subjective and limited by the availability of real-time data. This approach often fails to capture historical trends, seasonal patterns, and other factors that can significantly impact traffic patterns.Artificial neural networks (ANNs) offer a promising alternative for traffic flow prediction in Istanbul. ANNs are powerful machine learning algorithms inspired by the structure and function of the human brain. They can learn from large amounts of data, identify complex patterns, and make predictions with a high degree of accuracy. In the study, ANNs were used to predict traffic volume in major junctions across Istanbul. The model was trained on historical traffic data, including time of day, day of the week, holidays, school timings, and other relevant factors. The results were highly encouraging, demonstrating that ANNs can effectively capture the complex dynamics of Istanbul's traffic flow[12]. Real-time traffic flow prediction is a crucial component of intelligent transportation systems (ITS). However, accurately predicting short-term traffic flow remains a challenging task due to the complexity and stochastic nature of traffic patterns. To address this issue, a novel combined prediction method for short-term traffic flow is proposed. This method leverages the autoregressive integrated moving average (ARIMA) model and the long short-term memory (LSTM) neural network to capture both linear and nonlinear patterns in traffic data[13]. Traffic congestion has been a major problem in Italy, particularly in Rome. To address this issue, a Levenberg-Marquardt (LM) artificial neural network heuristic model was developed to predict traffic flow for non-autonomous vehicles. Traffic data was collected using inductive loop detectors and video cameras. The data was then used to train, test, and validate the LM model. The model achieved training, test, and regression values (R2) of 0.99892, 0.99615, and 0.99714, respectively. These results suggest that the LM model is a promising tool for predicting traffic flow in Italy[14].
Despite the development of deep neural networks for traffic flow modeling, predicting citywide traffic flow at a fine temporal scale remains challenging, attributed to spatiotemporal dependencies and spatial sparsity. A study proposes a high-accuracy deep learning-based spatiotemporal neural network model after analyzing traffic flow patterns. The approach involves transforming the road network into a compact 2D image, representing road segments as pixels and preserving topological relationships. The end-to-end deep learning structure incorporates a recurrent convolutional network for temporal dependencies and a densely connected convolutional network for spatial dependencies and spatial sparsity. The model aggregates hybrid network outputs with different weights, enhanced by external information like the day of the week[15]. A study on short-term traffic flow forecasting in undivided two-lane highways in India. The authors propose a back propagation artificial neural network (ANN) model for this purpose and compare its performance with several other machine learning models, including random forest, support vector machine, k-nearest neighbor classifier, regression tree, and multiple regression. The results show that the ANN model outperforms the other models, achieving an R-squared value of 0.9962[16]. LSTM is a type of Recurrent Neural Network (RNN) specially designed to handle the temporal dependencies in sequential data, making it well-suited for traffic flow prediction, which is a time-series problem. The authors compare the performance of LSTM models trained with different input settings, including flow, speed, and occupancy data from the same detector station, and upstream and downstream detector stations. The results show that LSTM models that include both downstream and upstream traffic information are most accurate. This suggests that considering the spatial context of traffic flow, in addition to the temporal dynamics, is important for improving prediction accuracy[13].

3. Research Method

The research method used in this study involved collecting traffic data from the Tehran -Karaj highway, modifying and sorting the data, building neural network models for traffic and speed, training the networks with the data, predicting traffic for the next week using the models, and comparing the predictions with actual traffic data.
Figure 1 outlines the process flow of the proposed method. The first step involves data collection, gathering information from traffic counters. The acquired data undergoes modification and sorting to ensure consistency and completeness. This is crucial as traffic counters may experience downtime due to power outages or other technical disruptions, resulting in missing data. To address this issue and homogenize the data, an averaging approach is employed. For instance, if a traffic counter records 45 minutes of data but requires 60 minutes, the missing data is interpolated using a data ratio. This method ensures minimal data loss, with less than 1% error in the overall dataset.
Next, two neural network models are constructed: one for predicting traffic patterns and the other for forecasting traffic speeds. The models are trained using the processed data, generating an error output. This output serves as the basis for evaluating the model's performance. The model's structure and associated neurons are iteratively adjusted until the error rate reaches its minimum value. Following the development of the optimal model, its predictive capabilities are evaluated by simulating future traffic conditions for the upcoming week. MATLAB software is utilized for this simulation. The output obtained from the model is then compared with real-traffic data (traffic meter readings) to calculate the error variance.Finally, the conclusion is drawn, and the accuracy of the prediction is assessed. This evaluation encompasses both the model's ability to accurately predict traffic patterns and its effectiveness in forecasting traffic speeds.
In the neural network prediction process, the selection of the model, the number of neurons, and the activation function are crucial factors. Defining the model involves specifying input parameters, and in this context, two parameters are considered:
P1: The code representing the days in a month, ranging from 1 to 31.
P2: Traffic hours in a day, corresponding to the 24 hours in a day, with values ranging from 1 to 24.
The dataset contains 744 rows of data, reflecting the records for one month. The target vector consists of two components:
t1: Number of hourly traffic.
t2: Average hourly speed.
To compare the prediction accuracy from the true absolute deviation error(MAD)It has been used in Formula 1 is presented [17].
M A D = 1 n i = 1 n X i X ¯
where;
X= each value,
X ¯ = average value.
R-squared (sometimes denoted as r) is a measure of how well a linear regression model fits a set of data. It indicates how close the data points are to the fitted line. However, it doesn't provide a direct measure of how accurate the model's predictions are. This is where Mean Absolute Deviation (MAD) comes into play. MAD measures the average absolute difference between the predicted values and the actual values. It's a more robust measure of prediction accuracy than R-squared, as it doesn't depend on the range of the data.
To account for the varying scales of data, such as traffic volume versus speed, MAD is often divided by the range of the data (R). This normalization helps compare the prediction accuracy of different models for different types of data. For example , predicting 4990 cars per hour instead of 5000 cars for traffic volume is relatively insignificant, as traffic volume typically varies widely. However, predicting 90 km/h instead of 100 km/h for speed is much more impactful, as speed variations are typically much smaller. mean absolute error (MAE), which considers the average absolute difference between the predicted values and the actual values. the MAE for predicting traffic volume would be 10, while the MAE for predicting speed would be 10. This is why MAE is not useful,but MAD by R would ensure that the error is expressed in terms of percentage or proportion, allowing for a more consistent interpretation across different types of data.
Therefore, MAD divided by R is a more comprehensive measure of prediction accuracy than R-squared alone. It considers both the fit of the model and the magnitude of the errors, making it a valuable tool for evaluating forecasting models.
The range of a set of data is the difference between the largest and smallest values in the set. In other words, it is the extent to which the values in the set vary. The range can be calculated using the following formula (2).
R=MIN(value)-MAX(value)
where:
R is the range of the set,
MAX(value) is the maximum value in the set,
MIN(value) is the minimum value in the set.

4. Result

To determine the optimal network for the model, two separate networks have been constructed, each with n neurons in the hidden layer and one neuron in the output layer. Both the output layer and the hidden layer employ the tangent function. This configuration is illustrated in Figure2. This approach ensures that distinct networks are dedicated to predicting the number of hourly traffic and the average hourly speed, aligning with the researcher's view on the unique characteristics of each prediction task.
In Table 1 and Figure 2 , the algorithm functions employed in the traffic volume neural network are detailed.
In Figure 4 network for Speed the algorithm functions employed in the traffic volume neural network are detailed. For speed, a three-layer perceptron network with two input neurons and 25 neurons in the hidden layer and one neuron in the output layer has been used in the last layers.

5. Findings and Discussion

Table 3 displays the neural network output for the first week, organized into 168 rows. The initial column represents the day (1 to 7), followed by the hour (1 to 24). The "Average Speed" column showcases observed speed data, while the "Volume" column presents actual traffic volume from the counter. The last two columns, "Prediction Speed" and "Prediction Volume," depict the neural network's forecasts for speed and volume, respectively. This concise arrangement allows for a clear comparison between actual and predicted values, aiding in the assessment of the neural network's performance in forecasting both average speed and traffic volume over the specified time frame..
Mean Absolute Error (MAD) serves as a metric quantifying the average magnitude of prediction errors. For speed, the MAD is 4.15, indicating an average deviation of 4.15 kilometers per hour from the actual speed. In the case of traffic, the MAD is 822.87, signifying an average difference of 822.87 vehicles per hour between predicted and actual traffic volume. The Range, representing the spread between maximum and minimum values, is 29 for speed and 6321 for traffic. This implies that predicted speed spans from 25 to 54 kilometers per hour, and predicted traffic volume ranges from 1 to 6322 vehicles per hour.MAD/Range ratios offer additional insights. For speed, the MAD/Range is 14.30%, suggesting the average error constitutes 14.30% of the speed range. Similarly, for traffic, the MAD/Range is 13%, indicating that the average error constitutes 13% of the traffic volume range. These metrics provide a comprehensive understanding of the prediction accuracy relative to the variability within the dataset.
Figure 6 shows the number of vehicles per hour on a road over a period of time. The blue line represents the actual traffic, and the red line represents the predicted traffic. The green area represents the difference between the actual and predicted traffic.The traffic is highest in the morning and evening rush hours. The traffic is lower on weekends. The predicted traffic is generally accurate, but there are some discrepancies.
Figure 7 showing the predicted speed of traffic on a highway compared to the actual speed of traffic. The red line represents the predicted speed, the blue line represents the actual speed.

6. Conclusions

In conclusion, this study delved into the realm of traffic prediction, specifically employing the simple Multilayer Perceptron (MLP) model within the context of artificial intelligence. While various models exist for predicting traffic patterns, our investigation underscored the paramount importance of data quality over the intricacies of the model itself. Notably, the study revealed that data characterized by substantial error and fluctuation presented a more formidable challenge for accurate predictions.
Moreover, we argued for a nuanced approach to model evaluation, advocating against sole reliance on traditional criteria such as Mean Absolute Deviation (MAD) or coefficient of determination (r2). Instead, we proposed the utilization of MAD/Range as a more robust metric, particularly when confronted with datasets exhibiting significant order.The findings of this research, based on a set speed limit of 0.65 and a traffic value of 0.88, indicated parity in accuracy between predicting speed and traffic using the artificial intelligence model. Both criteria yielded MAD/R values of 13% and 14%, respectively, highlighting the model's consistent performance across different variables.
Ultimately, this study contributes to the evolving landscape of traffic prediction by emphasizing the need for a data-centric perspective and introducing an alternative metric for model evaluation. As transportation systems become increasingly complex, these insights pave the way for more effective and reliable predictions in the realm of traffic management.

Author Contributions

Conceptualization: Mohammad Maniat, Methodology, Software Writing—Amin Eebrahimzadeh:Writing—Review and Editing.

Data and Materials availability

All the code files necessary to reproduce the results of this study are available at https://zenodo.org/records/10564994.

Competing of interests

The authors declare that they have no competing interests.

References

  1. Wachs, M., The role of transportation in the social integration of the aged. The social and built environment in a older society. Washington, DC: Institute, 1988.
  2. Maniat, M., et al., The difference between the gentrification process in Latin America and other English-speaking countries (Case study Sã, o Paulo). 2023.
  3. Maniat, M., et al., The contrast of transit-oriented development, sustainable urban development and gentrification with a look at the cities of Karaj and Tehran. 2023.
  4. Akhtar, M. and S. Moridpour, A review of traffic congestion prediction using artificial intelligence. Journal of Advanced Transportation, 2021. 2021: p. 1-18. [CrossRef]
  5. Basheer, I.A. and M. Hajmeer, Artificial neural networks: fundamentals, computing, design, and application. Journal of microbiological methods, 2000. 43(1): p. 3-31. [CrossRef]
  6. Paola, J.D. and R.A. Schowengerdt, A review and analysis of backpropagation neural networks for classification of remotely-sensed multi-spectral imagery. International Journal of remote sensing, 1995. 16(16): p. 3033-3058. [CrossRef]
  7. Maniat, M., et al., Trip Distribution Modeling Using Neural Network and Direct Demand Model.
  8. Chen, X., et al., Sensing data supported traffic flow prediction via denoising schemes and ANN: A comparison. IEEE Sensors Journal, 2020. 20(23): p. 14317-14328. [CrossRef]
  9. Maniat, M., et al., Temporal and Spatial Correlation of Air Pollution with COVID-19 in the USA: Challenges and Implications. 2023.
  10. Sayed, S.A.; Abdel-Hamid, Y.; Hefny, H.A. Artificial intelligence-based traffic flow prediction: a comprehensive review. J. Electr. Syst. Inf. Technol. 2023, 10, 13. [Google Scholar] [CrossRef]
  11. Kumar, K., M. Parida, and V.K. Katiyar, Short term traffic flow prediction in heterogeneous condition using artificial neural network. Transport, 2015. 30(4): p. 397-405. [CrossRef]
  12. Çetiner, B.G., M. Sari, and O. Borat, A neural network based traffic-flow prediction model. Mathematical and Computational Applications, 2010. 15(2): p. 269-278. [CrossRef]
  13. Lu, S., et al., A combined method for short-term traffic flow prediction based on recurrent neural network. Alexandria Engineering Journal, 2021. 60(1): p. 87-94. [CrossRef]
  14. Olayode, I.O., et al., PREDICTION OF VEHICULAR TRAFFIC FLOW USING LEVENBERG-MARQUARDT ARTIFICIAL NEURAL NETWORK MODEL: ITALY ROAD TRANSPORTATION SYSTEM. Komunikácie, 2022. 24(2).
  15. Jia, T. and P. Yan, Predicting citywide road traffic flow using deep spatiotemporal neural networks. IEEE Transactions on Intelligent Transportation Systems, 2020. 22(5): p. 3101-3111. [CrossRef]
  16. Sharma, B., et al., ANN based short-term traffic flow forecasting in undivided two lane highway. Journal of Big Data, 2018. 5(1): p. 1-16. [CrossRef]
  17. Khair, U., et al. Forecasting error calculation with mean absolute deviation and mean absolute percentage error. in journal of physics: conference series. 2017. IOP Publishing. [CrossRef]
Figure 1. Flowchart of research method and steps.
Figure 1. Flowchart of research method and steps.
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Figure 2. Perceptron network for traffic determination.
Figure 2. Perceptron network for traffic determination.
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Figure 3. presents four regression charts illustrating the target data for training, testing, validation, and its average. Each diagram features a regression line that signifies the compatibility between the best network output results and the target data, where the target data represents the frequency and speed of the traffic counter. The coefficient R, indicating the correlation between the neural network outputs and the target data, is close to one across all graphs. This consistency in R values suggests a strong fit and efficient performance of the network.
Figure 3. presents four regression charts illustrating the target data for training, testing, validation, and its average. Each diagram features a regression line that signifies the compatibility between the best network output results and the target data, where the target data represents the frequency and speed of the traffic counter. The coefficient R, indicating the correlation between the neural network outputs and the target data, is close to one across all graphs. This consistency in R values suggests a strong fit and efficient performance of the network.
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Figure 4. Perceptron network for Speed.
Figure 4. Perceptron network for Speed.
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Figure 5. Speed ​​network regression.
Figure 5. Speed ​​network regression.
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Figure 6. predicted traffic ​​prediction.
Figure 6. predicted traffic ​​prediction.
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Figure 7. speed prediction. 
Figure 7. speed prediction. 
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Table 1. Algorithm functions used for traffic neural network.
Table 1. Algorithm functions used for traffic neural network.
Training function Number of hidden layer neurons Type of hidden and output layer functions Error function to execute R-squared
trainlm 30 Tanzant Mean squared error 0.88
Table 2. algorithm functions used for speed neural network.
Table 2. algorithm functions used for speed neural network.
Training function Number of hidden layer neurons Type of hidden and output layer functions Error function to execute R-squared
trainlm 25 logarithm Mean squared error 0.65
Table 3. output forecast for the first week of August.
Table 3. output forecast for the first week of August.
Day Hour average speed K/h volume volume prediction Speed ​​prediction Day Hour average speed K/h volume volume prediction Speed ​​prediction
1 1 82 5843 4089 97 2 8 101 5816 5133 103
1 2 90 4210 2347 98 2 9 102 5269 5337 103
1 3 96 2162 1182 98 2 10 99 4901 4841 103
1 4 98 1122 769 98 2 11 101 4720 4497 102
1 5 98 1007 779 98 2 12 105 4689 4442 102
1 6 99 1563 1373 99 2 13 107 4635 4672 102
1 7 108 2807 3577 100 2 14 110 4432 5218 102
1 8 107 3622 6198 102 2 15 109 4778 6071 101
1 9 104 4086 6424 102 2 16 105 5425 6995 100
1 10 100 4445 5552 102 2 17 100 6269 7501 99
1 11 97 5437 4882 102 2 18 94 6596 7275 97
1 12 99 5968 4653 102 2 19 94 6134 6567 96
1 13 100 5867 4815 102 2 20 89 6616 5904 94
1 14 105 5164 5354 102 2 21 91 5610 5525 91
1 15 109 4540 6227 101 2 22 86 5548 5363 89
1 16 109 4487 7167 99 2 23 91 4853 5305 86
1 17 105 5041 7686 98 2 24 92 3973 5287 84
1 18 100 5265 7506 96 3 1 93 2983 4495 97
1 19 100 5486 6866 94 3 2 97 1694 2509 98
1 20 93 5721 6194 92 3 3 97 969 1270 98
1 21 94 4487 5713 89 3 4 98 579 886 99
1 22 86 4867 5453 87 3 5 99 728 954 100
1 23 88 4822 5342 85 3 6 100 1331 1464 101
1 24 80 5522 5301 83 3 7 104 4242 2793 103
2 1 83 5701 4283 97 3 8 99 5817 4224 103
2 2 93 3252 2410 98 3 9 101 5355 4582 103
2 3 98 1511 1212 98 3 10 98 5092 4407 103
2 4 98 818 816 98 3 11 101 4855 4271 102
2 5 98 814 861 99 3 12 104 4797 4313 102
2 6 100 1467 1447 100 3 13 106 4759 4572 102
2 7 106 4236 3227 102 3 14 109 4860 5103 102
Day Hour average speed K/h volume volume prediction Speed ​​prediction Day Hour average speed K/h volume volume prediction Speed ​​prediction
3 15 106 5415 5915 101 4 22 83 5831 5299 93
3 16 103 5730 6790 101 4 23 82 5502 5279 91
3 17 96 6705 7237 100 4 24 89 4547 5276 88
3 18 91 6731 6946 99 5 1 93 3334 4468 96
3 19 94 6709 6249 97 5 2 96 1819 2572 97
3 20 92 6499 5696 96 5 3 98 920 1442 98
3 21 88 5668 5424 93 5 4 94 600 1130 100
3 22 83 5947 5320 91 5 5 97 799 1174 101
3 23 88 5252 5288 88 5 6 97 1658 1413 102
3 24 92 4024 5280 86 5 7 99 4630 2197 102
4 1 95 3155 4573 97 5 8 93 6699 3287 103
4 2 97 1792 2580 97 5 9 93 5821 3900 103
4 3 98 849 1356 98 5 10 93 5581 4069 103
4 4 99 602 996 99 5 11 99 5171 4108 103
4 5 100 625 1064 101 5 12 103 5001 4203 103
4 6 99 1433 1443 102 5 13 104 4925 4437 103
4 7 105 4274 2419 103 5 14 106 4919 4869 102
4 8 99 6197 3601 103 5 15 103 5540 5500 101
4 9 101 5389 4120 103 5 16 100 6320 6151 100
4 10 95 5256 4165 103 5 17 95 6900 6479 100
4 11 100 4916 4150 103 5 18 89 6732 6304 99
4 12 104 4915 4238 103 5 19 88 6661 5861 99
4 13 105 4778 4497 102 5 20 81 6817 5511 97
4 14 108 4889 4992 102 5 21 85 6062 5343 96
4 15 106 5336 5735 101 5 22 81 6198 5286 94
4 16 103 5895 6515 100 5 23 82 5926 5273 92
4 17 95 6776 6875 100 5 24 88 4728 5273 91
4 18 84 6475 6589 99 6 1 91 3888 4281 95
4 19 93 6575 6010 98 6 2 96 2354 2523 97
4 20 93 6375 5577 97 6 3 97 1226 1506 98
4 21 89 5780 5372 95 6 4 98 793 1232 99
Day Hour average speed K/h volume volume prediction Speed ​​prediction Day Hour average speed K/h volume volume prediction Speed ​​prediction
6 5 97 1146 1226 101 7 3 97 1951 1541 97
6 6 96 2349 1385 102 7 4 98 1646 1260 99
6 7 99 5049 2141 102 7 5 97 2115 1198 100
6 8 93 6378 3250 102 7 6 95 3355 1353 101
6 9 98 5690 3896 103 7 7 102 4836 2189 101
6 10 95 5559 4113 103 7 8 102 5257 3401 102
6 11 97 5428 4151 104 7 9 101 5023 4077 102
6 12 102 5363 4213 104 7 10 98 5017 4304 103
6 13 103 5563 4384 103 7 11 99 5263 4308 104
6 14 103 5724 4710 102 7 12 102 5402 4286 104
6 15 100 6615 5194 101 7 13 102 5908 4340 104
6 16 98 6850 5757 100 7 14 102 6139 4513 102
6 17 96 6699 6155 100 7 15 100 6432 4877 101
6 18 95 6107 6116 99 7 16 102 6371 5445 100
6 19 98 5564 5771 99 7 17 99 6419 5937 100
6 20 93 5924 5469 97 7 18 98 5805 5992 99
6 21 86 5480 5324 96 7 19 99 5758 5709 98
6 22 83 5643 5277 94 7 20 95 5685 5439 97
6 23 83 5688 5269 93 7 21 91 5024 5309 95
6 24 82 5537 5271 92 7 22 84 5246 5269 94
7 1 87 4965 4144 94 7 23 83 5721 5265 93
7 2 93 3330 2489 96 7 24 81 5780 5269 92
Table 4. Summary of probability and error results.
Table 4. Summary of probability and error results.
Title Speed traffic
MAD Mean absolute error 4.15 822.87
Range=Max-Min 29 6321
MAD/Range 14.30% 13%
Average error -2.17 263
Standard deviation of the error 24.71 1048
r 0.65 0.88
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