This paper focuses on the problems of short-term traffic flow forecasting. The main goal is to put forward traffic correlation model and real-time correction algorithm for traffic flow forecasting. Traffic correlation model is established based on the temporal-spatial-historical correlation characteristic of traffic big data. In order to simplify the traffic correlation model, this paper presents correction coefficients optimization algorithm. Considering multistate characteristic of traffic big data, a dynamic part is added to traffic correlation model. Real-time correction algorithm based on Fuzzy Neural Network is presented to overcome the nonlinear mapping problems. A case study based on a real-world road network in Beijing, China, is implemented to test the efficiency and applicability of the proposed modeling methods.
It is of practical significance to predict traffic flow quickly, precisely, and timely. Short-term traffic flow forecasting provides an important basis for traffic guidance and control. Existing studies of short-term traffic flow forecasting can be classified into six categories in transportation literature: linear system theory based models, such as Autoregressive Integrated Moving Average (ARIMA) [ data mining based models, such as Neural Network [ nonlinear system theory based models, such as Wavelet Analysis [ simulation based models [ combination model based models [ the other models.
In the era of big data, it brings both opportunities and challenges to short-term traffic flow forecasting. During data processing, traffic big data meets the same difficulties with the general big data, such as capture, storage, search, sharing, analytics, and visualization. Therefore, short-term traffic flow forecasting method needs to have the capacity to deal with traffic big data. Traffic big data holds several characteristics, such as temporal correlation, spatial correlation, historical correlation, and multistate. Considering the advantages of traffic big data, data-driven based mathematical models can be set up. The physical meaning of these models can by described clearly. In addition, we can put forward real-time correction algorithm to improve the accuracy of traffic flow forecasting.
However, taking into account all the present researches in this field, there is still a lack of consideration of traffic big data and real-time correction for traffic flow forecasting. Further researches remain to be conducted on the direction of traffic big data analysis. In this paper, the method of short-term traffic flow forecasting is proposed in detail. The remainder of this paper is organized as follows. Section
Traffic big data has a strong temporal-spatial-historical correlation as follows. In the temporal series, the traffic flow of last moment can be regarded as a continuation of current traffic flow. Dynamic traffic flow data continuously change over time with a certain trend. In the spatial series, the traffic flow of downstream sections can be seen as a continuation of the upstream traffic flow. There exists a spatial association between traffic flow data of neighboring junctions or sections and that of target junctions or sections. In the historical series, the traffic demand characteristics determine that traffic flow characteristics of the same day in the same period are similar. The law of traffic flow cycle is especially evident.
Therefore, the basic form of traffic correlation model [
Thus, simplified equation of traffic correlation model is obtained:
It is found that the speed and accuracy of data processing are both important for big data driven method. To improve the speed of traffic correlation model, the number of unknown variables in formulation (
Therefore, this paper defines a threshold of computing speed and derives the maximum of acceptable number of variables. Thus, the number of unknown variable
In addition, for
If the value of
Variables reduction makes
Since the alternative process will bring some errors, which are likely to be systematic, a linear correction algorithm is present. Two correction variables
Basic mathematical model can be used for traffic flow forecasting. The error of traffic flow forecasting is written as
Therefore,
The variation range of
For different traffic state, the propagation of traffic congestion is different. So, the temporal-spatial-historical correlation variables are dynamic. As shown in Section
Effective analysis of traffic correlation model is shown in Figure
Effective analysis of traffic correlation model.
It assumes that
The main goal of real-time correction algorithm is to calculate the error term (
The structure of Fuzzy Neural Network.
Every input unit in Fuzzy Neural Network is corresponding to certain fuzzy subset of the input variables, which are
Every output unit in Fuzzy Neural Network is corresponding to certain fuzzy subset of the output variable, which is
To get membership degree model of
Historical date is applied to train the Fuzzy Neural Network. Input signal is corresponding to target output. After training, the network can be seen as a container of fuzzy relations and if we want to get other conclusions from the network, the only thing that needs to be done is to input the real value after defuzzification, as shown in
Real-time corrected traffic correlation model, which is seen as the improved traffic correlation model, is composed of static part and dynamic part. The static part is “
Traffic flow forecasting framework.
The steps of traffic flow forecasting are as follows.
Based on historical data, temporal data, and spatial data, basic traffic correlation model, as shown in formulation (
Simplified traffic correlation model, as shown in formulation (
Based on Fuzzy Neural Network, real-time correction algorithm is put forward. Thus, “
Real-time corrected traffic correlation model, as shown in formulation (
Based on system knowledge, real-time data is processed to calculate the forecasting results.
Taking a section of the Second Ring Road (Section 1, as shown in Figure
Spatial location of research object.
Based on historical data, basic mathematical model, including traffic correlation model and simplified traffic correlation model, is built. The static part of real-time corrected traffic correlation model, which is “
Goodness of Fit is shown in Table
Goodness of Fit.
Parameter of traffic flow | Flow | Speed | Occupancy |
---|---|---|---|
|
0.8885 | 0.9655 | 0.9664 |
Real-time correction algorithm is presented to obtain the dynamic part of real-time corrected traffic correlation model, which is “
Based on SAGA-FCM,
Clustering centers of LOS.
|
Speed (km/h) | Occupancy (%) |
---|---|---|
|
68.1 | 2.1 |
|
58.3 | 3.1 |
|
51.2 | 11.4 |
|
46.0 | 14.9 |
|
38.0 | 20.5 |
|
23.4 | 35.1 |
Clustering centers of
|
Flow (pcu/h) | Speed (km/h) | Occupancy (%) |
---|---|---|---|
|
−1043 | −9.7998 | −7.4513 |
|
−498 | −2.5634 | −2.2416 |
|
−2.9 | 0.2030 | −0.2448 |
|
291.6 | 2.3692 | 1.6348 |
|
812.2 | 9.9043 | 7.0243 |
Formulations are shown is Section
Input layer has 11 nodes; the transmission function of the nerve cells in the hidden layer is transig; the output layer has 5 nodes and the transmission function of the nerve cells in the output layer is logsig, while the training function is traingdx. Historical data is used to train Fuzzy Neural Network.
Making one day as an example, the result is shown in Figure
Effective analysis of real-time correction algorithm.
Mean Absolute Percentage Error (
Evaluation result is shown in Table
Evaluation result of proposed models.
Model | MAPE of flow (%) | MAPE of speed (%) | MAPE of occupancy (%) |
---|---|---|---|
Basic mathematical model | 13.14% | 9.18% | 14.48% |
Model improvement | 10.93% | 7.17% | 10.54% |
Traffic big data strongly shows temporal-spatial-historical correlation and multistate characteristic. Traffic correlation model is established based on temporal-spatial-historical correlation. Correction coefficients optimization algorithm is put forward to reduce parameters and ensure calculation accuracy. In order to improve the effectiveness of short-term traffic flow forecasting, real-time correction algorithm is presented based on multistate characteristic. Fuzzy Neural Network is used to overcome the problem of nonlinear mapping. Case study shows that real-time correction algorithm can improve the effectiveness of traffic correlation model.
The core of this paper is to present a short-term traffic flow forecasting based on traffic big data analysis. The advantages of real-time corrected traffic correlation model for traffic flow forecasting are as follows. The temporal-spatial-historical correlation, which is considered in the static part of model, explains the physical meaning of traffic flow forecasting by mathematical model. The multistate, which is considered in the dynamic part of model, explains the dynamic characteristic of traffic flow. Real-time correction algorithm improves the accuracy of traffic flow forecasting. Case study shows the high efficiency and applicability of the proposed methods.
Moreover, the proposed methods can be extended to 15- or 30-minute-ahead forecasting. The next steps of this work are to study traffic incident and its influence for short-term traffic flow forecasting. In addition, how to deal with the long period traffic flow forecasting like one hour or even longer can also be focused on.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors are grateful to the editor and anonymous reviewers for their valuable suggestions. This research was funded by the “Twelfth Five-Year” National Science & Technology Pillar Program (2014BAG01-B04) and Beijing Science and Technology Plan (no. Z121100000312101).