# Prediction of Vacant Parking Spaces in Multiple Parking Lots: A DWT-ConvGRU-BRC Model
## 2 Literature Review  
Access to VPS data has become easier with breakthroughs in sensor technology. However, the VPS data obtained in practical applications are often subject to different degrees of noise pollution. How to effectively process the data collected by sensors and improve the accuracy of algorithms is a thorny problem that many existing prediction methods still face. To solve this problem, wavelet analysis has been applied in some recent studies and has proven to be effective. For example, [PERSON] et al. [15] used the wavelet function for multiscale wavelet decomposition and reconstruction of VPS data using the hidden layer function of a wavelet neural network to improve prediction accuracy. [PERSON] et al. [16] proposed a multistep prediction study of impacted parking spaces based on a WT in combination with a multistep prediction strategy using threshold noise reduction to further improve the prediction accuracy. Therefore, effective noise removal helps to improve the efficiency and accuracy of prediction. Predicting the occupancy rate of multiple parking lots is one of the necessary links to solve the \"difficult parking\" problem. In recent years, VPS prediction has been divided into two categories: one is based on a statistical prediction model, and the other is based on machine learning (ML) and deep learning (DL). For statistical prediction models, [PERSON] et al. [17] combined continuous Markov and queuing theory models to predict the occupancy status of parking lots in the destination area. On this basis, [PERSON] et al. [18]proposed a continuous-time Markov M\(\backslash\)M\(\backslash\)C\(\backslash\)C model for predicting available parking spaces. [PERSON] et al. [19] proposed a real-time available dynamic algorithm using historical information to predict the availability of each parking lot. In addition, [PERSON] et al. [20] developed a vector spatiotemporal autoregressive model that can be used to predict the availability of parking spaces at a driver's estimated arrival time at both on-street and off-street parking locations. [PERSON] et al. [21] modelled the discrete occupancy rate of a parking lot as a nonstationary Poisson process and proposed a cost-effective method for searching for parking spaces. [PERSON] et al. [22] proposed a smart parking algorithm that varied the weights of five factors (availability, gate wait time, parking cost, traffic congestion, and driving distance to the parking lot) to achieve balanced traffic allocation and parking best use of the field. In fact, these statistical prediction models are highly dependent on assumptions about the arrival and departure process and therefore have difficulty adapting to the dramatic fluctuations in parking traffic flow. For ML/DP prediction models, researchers have applied models such as regression trees, support vector machines (SVMs), support vector regression (SVR), neural networks, K-nearest neighbour (KNN), and random forests models to predict parking availability [23; 24; 25; 26; 27]. [PERSON] et al. [28] combined support vector regression (SVR) and the fruit fly optimization algorithm (FOA) to predict the number of vacant parking spaces. [PERSON] et al. [29] optimized a multi-step long short-term memory recurrent neural network (LSTM-NN) model with a grid search method to predict the number of vacant parking spaces. Moreover, many scholars have combined nonlinear system theory and optimization algorithms with neural networks to improve prediction accuracy. For example, [PERSON] et al. [30] used a genetic algorithm-optimized multilayer perception (MLP) to predict the occupancy rate of a regional parking lot over the subsequent 30 min. [PERSON] et al. [31] used a genetic algorithm (GA) combined with a recurrent neural network (RNN) to predict parking occupancy in Birmingham. [PERSON] et al. [32] combined a wavelet transform (WT) with bi-directional LSTM (Bi-LSTM) to further improve the prediction accuracy using threshold noise reduction.