Application of Selected Mathematical Models for Analysis and Evaluation of the Functioning of Transport Processes in Crisis Situations
Purpose: This article aimed to identify the possibilities of using mathematical modeling to analyze and evaluate the functioning of transport processes in crisis situations. The study responds to the need for analytical approaches that enhance transport management under disruptions caused by economic, environmental, health, social, and military crises. Design/Methodology/Approach: The study is based on a classification of crisis types and a systematic overview of mathematical modeling methods that can be applied to the analysis and evaluation of transport processes. It combines theoretical and empirical approaches, drawing on data from international statistical sources, public agencies, and national transport authorities. The models were applied to several case studies, including public transport in Warsaw, seaport passenger traffic following the COVID-19 outbreak, road safety analysis and the assessment of transport–energy–emission relationships in Poland. Findings: The analysis's results indicate that mathematical models can be used as valuable tools for analysing and evaluating the functioning of transport processes in specific crisis situations. Their application allows for the identification of disruptions, prediction of changes, and assessment of relations between selected indicators. Classical statistical and econometric models make it possible to identify structural changes and long-term dependencies, while machine learning models demonstrate particular strength in detecting complex interrelations and predicting risk patterns. The results show that the proper selection of mathematical models, depending on the type of crisis, data availability, and the nature of the analysed process, supports decision-making in transport and contributes to improving the safety, sustainability and shaping a resilience of transport systems, which is especially significant in the context of potential crises. Practical Implications: The study’s results provide a solid basis for applying mathematical modeling methods in the analysis and assessment of transport processes under crisis conditions. The findings can support policymakers, public institutions and transport authorities in identifying potential disruptions, forecasting their effects, and planning response strategies as well as strengthening overall resilience. They also indicate that the proper use of modeling tools facilitates informed decision-making and contributes to improving the safety and stability of the transport sector in challenging and dynamic environments. Originality/Value: Previous studies have focused mainly on the impacts of individual crises or the use of single modeling techniques. This research introduces an interdisciplinary and comprehensive approach that combines the typology of crisis situations with the classification and application of mathematical modeling methods with examples. It contributes to the development of a coherent analytical framework for modelling transport processes and supporting their functioning in the event of disruptions of diverse origin.