Ticket tariffs modelling in urban and regional public transport

Ticket tariff is an important factor influencing the demand for public transport. Among basic problematics regarding ticket tariffs are designing new fare systems and optimization of current systems. The task of optimization is influenced by two main factors: ticket prices and the structure of the tariff. Both elements were researched in this article, based on eleven public transport organizers fare systems in Poland – metropolitan areas and cities of a different scale. The purpose of this article was to define basic tariff types used in urban and regional public transport with a presentation of their function models. Ticket tariffs split into two main groups: flat and differential. Differential group of tariffs covers: distance (usually are encountered fares based on a number of kilometres or stops travelled), quality (e.g. different fares on basic and express lines), time (minutes, hours or days of ticket validity, but also different tariff during on-peak and off-peak hours), sections (between which passenger travel on a transit route) and zones (transport network divided into areas, e.g. designated by municipalities boundaries) tariffs. The concept of this study was to transform as many tariffs as possible from tabular form to the mathematical function. Five types of functions were considered for each tariff schematic: linear, power, polynomial, logarithmic and exponential. Functions and associated with them R-squared parameters were obtained as a result of re-gression analysis. The paper indicates that for time, distance and flat tariffs conformity (R2) was in most cases very high and above 0,90. The results indicate that the power function best describes time tariffs. In the case of distance tariffs, different kind of functions can be used: logarithmic, power or polynomial. The proposed function form of tariffs may speed up the process of creating new fare systems or upgrading existing ones. With general knowledge about the structure of tariffs and their function forms, it would be easier to determine the price of different kinds of tickets. New fare integration solutions could be also proposed in the future by using Big Data analysis.