Distribution Analysis and Forecast of Traffic Flow of an Expressway Electronic Toll Collection Lane

With the rapid increase of vehicle ownership in China, toll collection stations on expressways have become some of the most congested areas. Compared with a manual toll collection system (MTC), the electronic toll collection (ETC) system has advantages of rapidness and convenience. This paper comprehensively explored characteristics of the traffic flow of an ETC lane of the study area located on the Guizhou Expressway, China. The short-term traffic flows of ETC lanes are divided into low, moderate, and high volumes. In case of the low volume, this paper found that it is more reasonable to use Poisson distribution to predict the probability of ETC arrivals than to predict the ETC traffic flow. In case of the high volume, vehicles queue to pass the ETC lane, and ETC throughputs turn into a uniform distribution. This paper mainly focused on the moderate volume, discussed distribution of the ETC traffic flow, and predicted the ETC short-term traffic flow. Firstly, this paper applied the multiple Gaussians to fit the ETC traffic flow, and then used a Gaussian mixture model (GMM) to calculate the probability distribution of different Gaussian components. To verify the rationality of the distribution, Gaussian mixture regression (GMR) was utilized to predict short-term ETC traffic flow. The theoretical and experimental analyses demonstrated that when the ETC traffic volume is low, the prediction error of GMR is large, and with the ETC traffic volume increasing, GMM effectively can fit the distribution of the ETC short-term traffic flow and GMR can make accurate predictions. With the same parameters, GMM and GMR are capable of predicting about 74% of expressway toll stations’ ETC traffic flows in the study area. Moreover, the experimental results indicated that when the ETC traffic volume is greater than 15 passenger car units (pcu)/5 min, the GMR achieves a better forecasting performance than that of long short-term memory (LSTM) and the autoregressive integrated moving average (ARIMA). This in turn verified that the ETC traffic volumes will satisfy a GMM distribution, and GMR will be a better choice for forecasting short-term traffic flow.