Synchronization of Inbound and Outbound Flows at Stations in the Model of Freight Transportation Organization

Abstract

This article presents a model for organizing railway freight transportation between two node stations based on the interaction of neighboring stations depending on their technical capabilities and the demand for freight transportation. The main objective of such interaction is to synchronize the inbound and outbound flow at the stations, specifically reducing the degree of inconsistency between the receipt and dispatch of goods at the stations. This characteristic represents the imbalance between the volume of incoming and outgoing goods at the stations per unit of time and is described by a nonnegative function bounded above by unity. Its dynamics are described by a system of differential equations containing a set of parameters characterizing the infrastructure of the stations, the mode of distribution of goods from the final node station, and the demand for freight transportation. The range of parameter variations for which the specified system has a solution has been determined, as well as such a set of these parameters for which the task of synchronizing the inbound and outbound flow at the stations is best solved. It has been found that regardless of the initial value, starting from a certain point in time, the degree of inconsistency between the receipt and dispatch of goods at all stations except the initial node station becomes zero.