Abstract
The mathematical models for traffic flow have been widely investigated for a lot of application, like planning transportation and easing traffic pressure by using statistics and machine learning methods. However, there remains a lot of challenging problems for various reasons. In this research, we mainly focused on three issues: (a) the data of traffic flow are nonnegative, and hereby, finding a proper probability distribution is essential; (b) the complex stochastic property of the traffic flow leads to the nonstationary variance, i.e., heteroscedasticity; and (c) the multistep-ahead prediction of the traffic flow is often of poor performance. To this end, we developed a Gamma distribution-based time series (GaTS) model. First, we transformed the original traffic flow observations into nonnegative real-valued data by using the Box-Cox transformation. Then, by specifying the generalized linear model with the Gamma distribution, the mean and variance of the distribution are regressed by the past data and homochronous terms, respectively. A Bayesian information criterion is used to select the proper Box-Cox transformation coefficients and the optimal model structures. Finally, the proposed model is applied to the urban traffic flow data achieved from Dalian city in China. The results show that the proposed GaTS has an excellent prediction performance and can represent the nonstationary stochastic property well.
Highlights
As the main driving force of development, traffic has significant effects on the flow of production factors and the daily life of the urban system
The control operations, like variable speed limits (VSLs), are always embedded into intelligent transportation system (ITS) [7]. This fact suggests that the prediction models in ITS should be of concise structures natural to conduct the control and operation design
Because the above two criteria cannot be used to evaluate the models crossing the data sets, the coefficient of determination R2 calculated from the observation yt and estimated valueyt is used as the following: R2
Summary
As the main driving force of development, traffic has significant effects on the flow of production factors and the daily life of the urban system. As we illustrate in the latter, the urban traffic flow data is a nonstationary stochastic process with heterogeneous variance. The time series models are preferred for the prediction of traffic flow. The control operations, like variable speed limits (VSLs), are always embedded into ITS [7]. This fact suggests that the prediction models in ITS should be of concise structures natural to conduct the control and operation design. Our studies focus on developing the data-driven time series model, which can predict the nonstationary distribution of the traffic flow and is of concise structures for the stochastic control design for ITS
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