Analysis of properties of passenger traffic gravity model for linear network

For the description of spatial distribution of passenger traffic in transport network a correspondence matrix is usually used. The elements of the matrix are the volumes of passenger traffic between each pair of network vertices. The elements of the matrix can be calculated with the use of mathematical apparatus based on the transport gravity model. The correspondence matrix gained by the above mentioned method depends on network structure, model parameters and initial data on the number of incoming and departing passengers for each network vertex. Moreover, the dependence has significantly non-linear character and can’t be presented in explicit form. This complicates the research of common properties of correspondence matrix and forecasting its change at modification of transport network, shift in transport behaviour of passengers (it affects the gravity model parameters) and at random fluctuations of number of incoming and departing passengers for network vertices. At the investigation of the mentioned dependence scientists use various approaches on the basis of both analytical apparatus and approximate methods. The paper presents classic simulation modeling for the analysis of the correspondence matrix and the volume of passenger traffic for the linear transport network calculated on its basis. The use of the proposed approach allowed determining that at random distribution of volumes of incoming and departing passengers the passenger traffic is also a random value distributed according to the normal law. Moreover, the authors gained the dependence between the passenger traffic and the parameter of gravity model connected with the average trip length. Besides, the authors studied the dependence of passenger traffic from the network scale.