The article deals with a model for organizing railway transportation on a long stretch of road between two node stations connected by a large number of intermediate stations. Between two arbitrary neighboring stations, there is a railway track for temporary storage of cargo. The movement of cargo is carried out in one direction. To ensure the smooth movement of cargo, two technologies are used which are common for all stations. The first technology is based on the procedure of interaction of a station with both neighboring stations and adjacent railway tracks. The second technology uses the technical capabilities of the station itself and is based on the interaction of the station with neighboring railway tracks. For cargo transportation, a simple control system is used which provides for measuring the volume of transported goods at neighboring stations with a single time lag.
      This work is devoted to describing and studying the dynamics of the number of roads involved in the railway tracks. For this purpose, a system of differential equations is formed, the right parts of which are functions of variables describing the dynamics of the number of roads involved in the stations. The starting point for this study is previously obtained results from studying the dynamics of the number of tracks involved in the stations (a brief description of these results is given in the Introduction). What follows is the description of the dynamics of the number of roads involved in the railway tracks. Possible variants of the dynamics (growth of the number of the roads involved on one railway tracks and falling on others) and their dependence on parameters of the model are investigated. We also study the dependence of the rate of change in the number of involved roads on the railway tracks on the model parameters. We then find the parameter of control by which it is possible to provide arbitrarily small speed of growth (fall) of the number of the roads involved on all railway tracks.