## 1 Introduction  
Effective real-time and future-planned timetable monitoring and control has long been recognized as a critical requirement for the maintenance of high-quality service on high-frequency, high-ridership public transport (PT) rail systems in urban environments. The key input for the creation of light rail, metro, or tram line timetables is travel speed. For the existing system, this speed is the result of transport supply and demand effects. It is calculated as the ratio of two measurable variables: the distance traveled and the total vehicle travel time on the track section (considering the time in which the vehicle is not moving, regardless of the reason). When planning a new system, or in the case of changes in the public or individual transport demand and/or supply (because of social, economic, land use, or travel habits changes), timetabling is carried out using mechanical-empirical methods. Using the estimated running speed, an initial timetable is calculated and then corrected depending on the traffic characteristics during exploitation. Regarding rail systems, the estimation of the running speed along the track section is based on design speed reduction due to track and vehicle resistance. The resistance values depend on the constructional and exploitation characteristics of these two elements of the rail system. Design speed is reduced to the value of the travel speed, according to the planned or anticipated exploitation conditions. The speed reduction is a direct consequence of additional resistances occasionally occurring along the track section: stop resistance (expressed as dwell time on the rail, metro, and tram stops) and intersection resistance (expressed as delay time at tram traffic regulation signal). With increasing computing and communication means, numerous new approaches to the prediction of urban PT speed and travel time, relying on various statistical models or machine learning techniques, are being developed. These approaches can be divided into three main groups [1]:  
1. Simple models are based on historical data, i.e., on the observation that travel times are repeatable between days, at the same time of the day, and the same day of the week. These models rely on average travel time or average speed (usually calculated from the GPS data) in previous days as a prediction factor, and therefore, are only reliable when the traffic patterns are relatively stable. 2. Statistical models use several identified factors, i.e., influential factors (classified as internal or external [2]) as independent variables, and make a prediction based on their statistic distributions and correlations. The precision of these models depends on all the variables that need to be recognized and incorporated as resistances in the model, which is a tough procedure. Time series models and regression models are the most common examples in this group. 3. Machine learning models perform the learning process on existing travel time data to find an answer for unknown input data. The most popular techniques are Artificial Neural Networks, Support Vector Machines, and hybrid models (a combination of the models mentioned above). Recent research focused on methodologies regarding signal priority strategies, bunching control, and schedule optimization, identified the uncertainty of stop dwell time as a major cause of issues regarding rail PT trip progression modeling [3]. The stop dwell time is defined as the difference between the PT vehicle departure and arrival times. The arrival time is defined as the time when the vehicle changes its state from moving to standing still and vice versa for the departure time. There are at least five processes between the arrival time and the departure time: door unlocking, door opening, passengers alighting and boarding, door closing, and vehicle dispatching [4].