Journal of Control Science and Engineering

Volume 2018, Article ID 4570493, 8 pages

https://doi.org/10.1155/2018/4570493

## A New Synergistic Forecasting Method for Short-Term Traffic Flow with Event-Triggered Strong Fluctuation

Institute of Information Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, China

Correspondence should be addressed to Darong Huang; nc.ude.utjqc@gnauhrd

Received 22 December 2017; Accepted 12 February 2018; Published 19 March 2018

Academic Editor: Zhijie Zhou

Copyright © 2018 Darong Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Directing against the shortcoming of low accuracy in short-term traffic flow prediction caused by strong traffic flow fluctuation, a novel method for short-term traffic forecasting based on the combination of improved grey Verhulst prediction algorithm and first-order difference exponential smoothing is proposed. Firstly, we constructed an improved grey Verhulst prediction model by introducing the Markov chain to its traditional version. Then, based on an introduced dynamic weighting factor, the improved grey Verhulst prediction method, and the first-order difference exponential smoothing technique, the new method for short-term traffic forecasting is completed in an efficient way. Finally, experiment and analysis are carried out in the light of actual data gathered from strong fluctuation environment to verify the effectiveness and rationality of our proposed scheme.

#### 1. Introduction

In recent years, the popularization of seamless links among heterogeneous traffic equipment brought about higher requirements on the real-time and reliability of short-term traffic flow prediction. With continuous improvement of traffic information processing, how to predict the short-term traffic flow accurately and effectively has aroused wide attention of scholars domestically and abroad [1–3], whereupon numerous of prominent research results have emerged. So far, relevant academic circles mainly focus on the construction and optimization of prediction models in terms of time series, linear regression, historical average model, Kalman filtering, grey theory, chaos theory, nonparametric regression, neural network, support vector machine, dynamic traffic assignment model, and so forth [4–9]. These algorithms and models mentioned above are relatively mature, and their prediction effects are acceptable under the environment of favorable traffic flow stability. However, once the traffic data are seriously fluctuated, one single model can neither guarantee the prediction accuracy nor break through certain limitations of operations to predict short-term traffic flow under the environments of heterogeneous traffic equipment transmission.

In order to solve the aforementioned problems, domestic and foreign scholars have contrived an improved model to realize fusion prediction with the advantages of different models integrated of short-term traffic flow. For example, Xie et al. [10] improved the search efficiency of -nearest neighbor algorithm by cooperating the multivariate statistical regression model and the pattern distance search method based on the analysis of original -nearest neighbor algorithm for short-term traffic flow prediction. Their experimental results indicated that the prediction effect is better when the values are reasonable. Fan et al. [4] exploited the characteristics of time-varying and nonlinearity of traffic flow and proposed a new hybrid forecasting model based on the nonparametric regression model and the BP neural network model; they also employed fuzzy control to determine the weight of each single model. However, the basic support platform of the hybrid model is the traffic flow database, so the demand of data volume is large. Once the data volume is insufficient, the prediction accuracy will be depressed. Xiao et al. [11] proposed an improved binding cycle truncation accumulated generating operation seasonal grey rolling forecasting model based on the properties of similar seasonality within intraday and weekly trends. The model weakens the random disturbance and highlights the intrinsic grey exponent rule after accumulating the sequence, so that the model has better performance under different traffic flow conditions. Lin-chao et al. [12] proposed a short-term traffic flow prediction model based on support vector regression which is suitable for real-time monitoring and then analyzed the model parameters by grid search under the premise of considering the influence of space-time factors. The model can achieve ideal prediction effect even if the real-time traffic data are insufficient. Nevertheless, the accuracy of the model will decrease when the traffic status changes. In order to solve such problem, Ma et al. [13] proposed a two-dimensional prediction method by using the Kalman filtering theory based on historical data. The advantage of this method is that the two predicted values are fused by using an equation with weight coefficients where the weight coefficients can be generated in real time in the process of prediction. Experimental results show that the model has an admirable predictive effect. Chan et al. [14] used exponential smoothing to preprocess traffic data that is taken as the input of network and then used Levenberg Marquardt (LM) variant algorithm to train the network weights, making the generalization ability of network enhanced.

However, thanks to the diversified developments of traffic information processing and data transmission techniques within heterogeneous traffic network, as well as the impact caused by dynamic changes of road topology, traffic accidents, severe weather, driving styles, and so forth, short-term traffic data are instantaneous and the irregular volatility is always changing [15, 16]. In this case, the above combinational algorithm can just solve the short-term traffic prediction problem in certain circumstance, and the prediction effect can hardly be achieved in the light of the real-time requirement. Hence, it is urgent to construct new models and algorithms to deal with the short-term traffic forecasting problem aiming at the strong fluctuation triggered by events. Thus, in this paper, we intend to propose a novel method for short-term traffic prediction based on the energetically grey Verhulst prediction algorithm and the first-order difference exponential smoothing technique to solve the problem of low prediction accuracy caused by traffic event-triggering strong fluctuation.

The layout of this paper is arranged as follows. Firstly, based on the introduction of the traditional grey Verhulst model, an improved grey Markov forecasting model is devised by introducing Markov chain. Secondly, combining the advantages of forecasting by utilizing first-order difference exponential smoothing algorithm and introducing a dynamic weighting factor, a new method for short-term traffic forecasting is concretely constructed according to the afore contrived models. Finally, comparative analysis of the examples illustrated that our proposed model and algorithm are more effective.

#### 2. Short-Term Traffic Flow Prediction Model Based on Grey Difference Exponential Smoothing

##### 2.1. Short-Term Traffic Flow Prediction Model Based on Grey Markov Theory

###### 2.1.1. Introduction of Grey Verhulst Model

The grey system theory was first put forward by Professor Deng Julong, a Chinese scholar, in 1980s [17]. Its quantitative model is mainly based on the structure of number generating, which makes the prediction effect no longer affected by the empirical statistical law gained from the analysis of mass data. At the same time, it surmounted the limitation of white system and the black system relying solely on the probability and statistics method. Therefore, the grey system theory has been widely used in the fields of agricultural production, industrial control, traffic management, and so forth [18].

Classical grey system theory mainly includes GM model, GM model, grey Verhulst model, and so forth [19]. Considering the strong randomness and nonlinearity of traffic flow with strong fluctuation in heterogeneous information model, the data sequence significantly gives expression to the characteristics of nonmonotonic oscillatory development or the S-shaped property of saturation trend, which makes the grey GM prediction model unsuitable. Therefore, we choose the grey Verhulst model in this paper to forecast short-term traffic. The basic modeling process is described as follows.

The nonnegative data sequence is defined aswhile stands for the one-time accumulation sequence (1-Ago):

Then, assuming that represents the consecutive neighbor sequence of ,

The grey Verhulst model and its whitening equation can be defined as follows.

*Definition 1 (see [20, 21]). *The grey Verhulst model iswhere and are the parameters of the equation.

*Definition 2 (see [20, 21]). *The whitening equation of the grey Verhulst model iswhere , , and are the parameters of the whitening equation.

As deduced in [20, 21], the following conclusions are drawn.

Theorem 3. *If the grey Verhulst model is defined as formula (4) and represents the parameter column, let**The least squares estimator of the parameter column satisfies*

Theorem 4. *If the grey Verhulst model is defined as definition (2), the solution of the whitening equation can be deduced as**According to Theorems 3 and 4, the following conclusions are drawn.*

*Inference 5. *The time response sequence of grey Verhulst model can be defined asLet ; we iterate formula (9) to beThe reduction formula can then be defined as

Pointing at the traffic flow with the trend of increasing saturation, numerous traffic prediction algorithms have been proposed taking advantage of the grey Verhulst model to achieve preferable prediction effects. However, as a complicated nonlinear system involving multitudinous uncertainties, the probability of fortuitous events on urban roads is highly fluctuant, which leads to the deviation of forecasting results. Therefore, it is necessary to take the nonlinearity and time-varying characteristics of overall interactions into account in line with various influential factors. So, we improve the algorithm aiming at the accuracy of prediction model next.

###### 2.1.2. Short-Term Traffic Flow Prediction Model Based on Grey Markov Theory

During the process of traffic data aggregation, which is coordinated by complex human-vehicle-environment interaction, the current traffic flow is often affected by previous moments. Therefore, in order to improve the prediction accuracy of grey Verhulst model, mathematical description of traffic flow aggregation is given in advance by constructing the Markov state transition probability matrix [22].

It is obvious that the state transition probability matrix should be updated over time when Markov is used to optimize the grey model. That is to say, at time point , the state transition probability of Markov chain should be recalculated according to real-time traffic data along with the state transition probability matrix updated synchronously. Therefore, at time point , the probability of traffic flow aggregation from state to can be described asAnd the updated Markov transition probability matrix is formulated to bewhere each element is constrained as , , and , .

The grey Markov forecasting model is shown in Figure 1. According to the flow chart of this model, the value of grey Verhulst model to be predicted is at time point . In order to make the predicted value as close to the true value as possible, the true value at the time point is utilized and represented as , and the transition probability from the true value of time point to the predictive value is denoted by . Thus, the cumulative sum of the product of the traffic flow average value and its corresponding probability from the current state to other states can be taken as the predicted value of the grey Markov model:where is the adjustment factor and .