Formulation of the problem of random completion of the OD-matrix

Abstract

The main focus of the article is to formalize the process of random generation of elements of the passenger correspondence matrix within the framework of the interval concept of modeling transport demand for passenger movement. To achieve the main goal, the paper analyzes the existing methods of modeling passenger correspondence matrices, based on the results of which the expediency of developing a new method of modeling the passenger correspondence matrix within the interval concept of forming transport demand for passenger movement is substantiated, and its formalization is made. The advantage of using the interval concept of modeling the demand for passenger transportation is the possibility of forming a set of passenger correspondence matrices that cover possible demand states as widely as possible within known constraints. The proposed algorithm for completing in a random matrix of passenger correspondences is based on the method of stepwise generation of correspondences, which, when supplemented with the possibility of taking into account group constraints, can overcome the problem of deadlocks in the process of modeling the matrix of passenger correspondences. The results of the study should become the main basis for the implementation of the matrix generation method, which, in the presence of consistent additional constraints, allows to guarantee a given number of random matrices sufficient for the practical implementation of the interval concept of modeling transport demand for passenger movement, and at the same time to maximize the degree of randomness of the elements of the generated matrices. Further research in this area is aimed at developing a methodology for evaluating the results of generating correspondences using the proposed method.

Key words: passenger correspondence matrix, modeling, passenger transportation, demand, transport planning.