# A Formal Model of the Exploitation Process for Railway Signalling Devices
## 7 Conclusions  
Mathematical modelling is a particularly useful tool in technical applications for controlling a system, particularly in real-time systems and for analysing the behaviours of such systems. A mathematical model corresponds to a group of functions that relate different variables to each other and thus describe the relationships between selected quantities in the system. This type of modelling can be used to model the exploitation process for railway signalling devices.  
Modelling the exploitation process for railway signalling systems has many advantages. Such modelling represents one alternative route to improving the safety and reliability of the railway signalling system. It becomes possible to forecast the exploitation parameters and reliability indicators of railway signalling objects, which have an impact on shaping the exploitation process of the system. A model of the exploitation process for railway signalling systems can fulfil many functions, such as mapping the variability of the processes of usage and service, providing a tool for determining the values of qualitative indicators of the modelled process (coefficient of simultaneity of train runs, probability of damage between train runs, etc.), providing a tool for shaping the exploitation strategy, and assessing exploitation decisions.  
Railway signalling equipment should be exploited in a manner that minimises, e.g., service costs to the greatest extent possible. This means that both the service process itself and any maintenance or modernisation work should be thought through in terms of financial efficiency. That can be conducted using the exploitation process model shown. One of the consequences of designing and constructing railway signalling devices in this way is, among other things, that they can be repaired noninvasively, without having to dismantle the devices, thus, significantly reducing downtime for railway traffic. Most of this type of device are built using modular technology, which allows individual components of the technical object to be easily connected, replaced, and modified. The idea behind this is that the modules are mutually compatible and can be used in different configurations. That is one of the many ways to ensure the safety and smoothness of rail traffic while minimising maintenance costs.  
The exploitation indicators presented in this paper, which characterise the properties of the exploitation process for railway signalling systems, should be included in a decision-making model useful for planning the costly exploitation process of this system.  
Conceptualisation, M.K. and T.C.; methodology, M.K. and W.N.; validation, T.C. and R.P.; formal analysis, M.K.; investigation, T.C.; resources, M.K.; data curation, W.N. and R.P.; writing--original draft preparation, M.K. and T.C.; writing--review and editing, W.N.; visualisation, W.N.; supervision, T.C.; project administration, T.C.; funding acquisition, W.N. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.