Piecewise linear production function of loading in railway transport
The paper presents a brief review of publications on the application of mathematical modeling methods for the study of railway transport: for the problem of compiling a cyclic train schedule on a double-track railway corridor, assessing the impact of projected emissions from the US transport sector on air quality in a changing climate, analyzing and improving a freight transportation plan with taking into account multimodal transportation with sea, road and rail transport, studies of dynamic characteristics of car bodies during their transportation by rail ferries in the Black Sea water area, supporting decision-making on redirecting vehicles from other lines of the system to a disturbed line in various emergency situations. Linear and piecewise linear (with constant proportions) production functions of the volume of loading on the Krasnoyarsk railway are constructed, while the average weight of a freight train and the reception of empty cars act as independent factors. When evaluating the quality of the models, the criteria of multiple determination and Fisher were used, as well as the average relative approximation error, the values of which indicate a high adequacy of production functions. The vector of operations for a function with constant proportions is calculated, which makes it possible to establish that in 2001-2008, the limiting factor was the acceptance of empty wagons - so there was a shortage of them, and in 2009-2019, this was the average weight of a freight train, which, in order to eliminate the existing disproportion, should be somewhat increased.