# A Spatio-Temporal Schedule-Based Neural Network for Urban Taxi Waiting Time Prediction
## 2 Related Work  
Nowadays, most urban taxis have GPS positioning systems make massive taxi trajectory data easily available. Massive taxi trajectory data contains valuable data on urban transportation patterns as well as driving behaviors, and then useful references for studying urban residents' activities and giving a global picture of an urban transportation system. This led to the concept of \"urban computing\" that offers new computerized models of the city and further opportunities for mining and discovering urban trajectory patterns [4]. Indeed, before the emergence of smart cities, modelling and simulating urban taxi behaviors was, for instance, modelled using online algorithms and linear programming, taking into account taxi availabilities, pricing, number of passengers and waiting times [5]. Passenger flows between large urban areas were modelled using a demand-supply equilibrium of taxi services under competition and regulation and minimizing passenger waiting times [6]. With the development of IoT data, data-driven smart city computing has become an alternative promising resource for urban traffic flow analysis [7; 8]. Incremental approaches based on historical taxi trajectory data can be applied to approximate both taxi demands and allocations to passengers [9]. Neural networks are also used to predict the demand for taxis to serve the drivers. In order to predict the demand of taxis to help drivers plan their routes, the CNN-BiLSTM attention neural network has been introduced to predict taxis demand [10]. Overall, it was shown that urban spatial-temporal flow prediction is of great importance to traffic management, land use, public safety, etc. Urban flows are affected by several complex and dynamic factors, such as patterns of human activities, weathers, events and holidays [11]. Modeling this type of data can be enhanced by deep learning approaches [12]. An attention-based convolutional recursive network was applied to predict taxi demands and correlate times and places [13]. Unlike demand forecasting, neural networks were hardly applied with multi-source data to forecast passengers' waiting time. Nowadays, the most widely used method is to repair and analyze a taxi path based on GPS trajectory to predict taxi waiting times. For instance, a bus route map can be constructed and segmented, based on real-time bus GPS data to derive a path-based waiting time prediction [14]. A similar idea is used by applying three models to predict upstream bus routes separately to provide short-term forecasts for public transportation [15]. Large GPS trajectory data are empirically processed to derive taxi waiting time probabilities at some given locations and times [16]. Similarly, routing protocols and path-finding models are used as references for also deriving taxi waiting times at some given locations [17]. Elsewhere, the XGBoost algorithm is applied to predict static waiting times of taxis [18]. A crossroad network-based Markov decision process scheme is suggested to recommend taxi waiting place [19]. Recently, the importance of spatio-temporal features in traffic flow predictions is receiving more and more attention. The spatio-temporal features of the trajectory images are used in the prediction while the influence of space and weather are ignored [20]. GPS data is used to discover the impact of weather on human flow patterns [21]. The spatio-temporal semantics of the area are inferred to improve the accuracy [22]. Considering that a certain sequence may exist when people pass through the different geographic regions, time and space factors are utilized in learning the sequence rules of vehicles passing through different geographic functional regions [22]. Overall, while there has been valuable progress in the way historical taxi trajectory data are combined with city traffic flow calculation, it appears that the accuracy of urban taxi waiting time prediction models still needs to be further improved.