Dynamic Models of Cargo Flow Organization on Railway Transport

Abstract

This article is devoted to mathematical modeling of the process of organization of railway transportation on the transport network, which is a long section of the road with a large number of intermediate stations and located between them railway tracks for temporary storage of cargo. We investigate a model that predicts dynamics of congestion of stations and streams arising in the transportation network, under a given procedure traffic that uses the two technologies, the same for all stations. The first technology is based on the normative rules of interaction of neighboring stations. According to it, the intensity of the reception and dispatch of goods at an arbitrary station should depend on the workload of neighboring stations. The second technology uses the technical capabilities of the stations, and is based on the interaction of the station with neighboring railway tracks. An integral part of the organization of cargo transportation is a control system. This model uses a simple control system, which is that the volume of goods at neighboring stations must coincide with the time lag common to all stations. This model is described by a system of differential equations satisfying nonlocal linear restrictions. For this model the modes of cargo transportation satisfying the given control system are investigated. Such modes are described by solutions of the traveling wave type and two types of their expansions. One type of expansion is associated with the adjustment of transportation technologies and allows discontinuous solutions, the second type of expansion is associated with the weakening of the control system and allows the feasibility of nonlocal linear constraints with a given error. Stationary modes of transportation are investigated for stability.