Adequacy of the Gravity Model of Railway Passenger Flows

The most accurate modelling of spatial distribution of passenger flows is a prerequisite for successful planning of development of the transport system. It is the basis for calculation of a predictive trip matrix. An approach based on the gravity model is among main modelling methods.

The work investigates the issue of the adequacy of the gravity model with a double constraint and an exponential-power function of gravitation. It is this specification of the model and its particular cases with exponential and power functions of gravitation that are most often used to estimate spatial distribution of passenger flows both in theoretical and applied research.

Calibration and validation of the specified model is shown on the observed (actual) matrix of railway passenger origin­destination matrix. It was built with the help of the data of Express [railway ticketing] ADB ACS: the number of tickets sold for long-distance trains for all the pairs of directly linked stations.

Since calibration of the gravity model can be carried out by different methods (depending on how the model incorporates stochasticity, which is responsible for differences between the modelled and observed data), after a detailed analysis of the most common methods for calibrating the gravity model, the approach was chosen based on the maximum likelihood estimation. The work also analyses the gravity model validation tools used to estimate the proximity between the observed and modelled trip matrices.

Comparison of the modelled and observed trip matrices resulted in the conclusion that the gravity model under consideration predicts several aggregate indicators with a high degree of accuracy: total passenger turnover, average travel distance, and travel distance distribution. At the same time, it is shown that the error in the forecast of passenger flow for most individual origin-destination trips is quite large. This circumstance significantly reduces the possibility of practical application of the gravity model or the analysis and modelling of passenger flows in long-distance railway passenger traffic.

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