*2.1. Predictive Framework for ATIS Subsystem*

The principle of information is defined as one of the foundations of the city's transport policy. The Advanced Traveler Information System (ATIS) is a way to implement the information principle and is an integral part of the Intelligent Transport Systems (ITS) [1,2]. ATIS systems can use all transport data, including the tra ffic volume, journey times, and restrictions on selected sections, timetables, vehicles locations in the network, interchanges, tra ffic events, and weather conditions. The information can come both from the vehicles and tra ffic managemen<sup>t</sup> centres [3,4].

Access to information from ATIS systems can be public or limited. Restrictions may result from the paymen<sup>t</sup> of access to the system or from the fact that the system is dedicated to selected users [5]. Research [6] shows that mobile phone users with Internet access are most likely to use information from ATIS systems, and the interest of travelers in accessing travel information is directly related to the usefulness of the presented data by ATIS systems [4].

The considered issue in the paper is one of the crucial problems, mainly when bus congestion results in the resignation of some passengers from travelling with public transport. Well-prepared forecasts make it possible to make good use of rolling stock, to plan a journey, and to manage urban public transport. Figure 1 presents a diagram of the information flow and relevance of a forecasting module within ATIS. The data based on which the model was created and tested came from buses operating in Cracow.

**Figure 1.** Diagram of the created Advanced Traveler Information System system.

The development of information technology has a significant impact on the functioning of cities and urban public transport. This has enabled the development in a short time of many mobile applications aimed at facilitating travel. They relate to trip planning, checking timetables, or information about the location of the exact vehicle based on the GPS signal. Common access to such extensive information has led to an increase in passenger requirements.

Moreover, information about the current or predicted passenger demand in public transport vehicles is becoming critical. The automatic passenger counting systems using buses do not provide the utilization of data in real time. However, the data will be sufficiently accurate to be used to produce a forecast. Such predictions will enable the optimization of the allocation of buses to public transport lines and the creation of applications for passengers (in the framework of ATIS).

The problem connected with bus allocations to public transport lines is important for carriers. The increasing number of rolling stocks types makes it more challenging to obtain an optimal solution. A large number of urban bus manufacturers and the choice of the cheapest offers by carriers make it difficult to maintain a uniform fleet of vehicles. Vehicles of the same dimensions may differ in travel comfort with the same number of passengers. That is why, in order to achieve a high level of comfort for passengers with a maximum use of rolling stock, it is necessary to optimise the allocation of buses to public transport lines. The solutions that emerged within this topic are described in articles, the most important of which are presented in the table below (Table 1).


**Table 1.** Articles on the optimization of the allocation of rolling stock to public transport lines.

The optimisation of bus allocations to urban public transport lines is presented in different ways in scientific publications. First, the allocation of rolling stock to public transport lines is taken as the queuing of vehicles at depots [7]. However, this solution does not take into account the possibility of a rolling stock rotation between different depots. When there is more than one depot, it is impossible to obtain an optimal solution. Other articles define the allocation of rolling stock as scheduling that reduces costs and the number of vehicles that are needed [8,17,18]. This approach is characterised by the use of various optimisation methods, both traditional linear programming methods and heuristics [9]. However, it should be noted that the analysed models do not use data on the forecast of demand for transport services. In [13], the problem of a model that is resistant to fluctuations in parameters was noted (the issue of planning the allocation of rolling stock for each day). The solutions presented in the publication are based on the example of railway transport. Another type of criterion which is becoming more and more important due to the growing social awareness of environmental protection is the optimization of the allocation of rolling stock as a means of minimising the environmental impact. This topic is described extensively in [10–12,19]. Finally, there are publications that describe the existing tools to support decision-making when scheduling the allocation of rolling stock to public transport lines [10,14,16,20].
