Theoretical justification of the results of passenger correspondence matrix generation using a random method

Abstract

This article presents a theoretical justification for the results of generating passenger correspondence matrices using a random method. An analysis of the basic random method for forming the correspondence matrix has been conducted, in which a uniform distribution of random variables is used to determine correspondences. It has been established that this method ensures maximum randomness, which can be both an advantage (reflecting demand variability) and a disadvantage (lack of structure in the formed matrix). The methods for forming correspondence matrices are based on random variables, and their distributions differ significantly, affecting the results of transport modeling. An analytical expression for the distribution law of correspondences generated by the basic method has been derived, reflecting the relationship between the random capacities of transport zones and the resulting correspondences. The influence of the minimum capacity of transport zones on the distribution of values in the correspondence matrix has been determined. It has been found that this parameter does not have a strict theoretical description and can only be estimated empirically based on field observations and real transport demand data. The research results confirmed that the basic method of random generation of correspondence matrices leads to a monotonically decreasing distribution of correspondences, which should be considered when applying this approach. Additionally, the necessity of verifying the obtained models against real data to adjust generation parameters has been substantiated. Further research development involves the empirical determination of the characteristics of the minimum capacity of transport zones and the assessment of the effectiveness of a new method for the random generation of passenger correspondence matrices within the framework of the interval-based concept of transport demand modeling.

Key words: random variable, distribution law, passenger correspondence matrix, modelling, transport demand.