Nerses K. Khachatryan - Senior Researcher, Laboratory of Dynamic Models of Economy and Optimization, Central Economics and Mathematics Institute, Russian Academy of Sciences; Associate Professor, Department of Business Analytics, National Research University Higher School of Economics
Address: 47, Nakhimovsky Prospect, Moscow, 117418, Russian Federation
E-mail: nerses@cemi.rssi.ru; nkhachatryan@hse.ru

Andranik S. Akopov - Professor, Department of Business Analytics, National Research University Higher School of Economics; Leading Researcher, Laboratory of Dynamic Models of Economy and Optimization, Central Economics and Mathematics Institute, Russian Academy of Sciences 
Address: 20, Myasnitskaya Street, Moscow, 101000, Russian Federation
E-mail: aakopov@hse.ru

Fedor A. Belousov - Researcher, Laboratory of Dynamic Models of Economy and Optimization, Central Economics and Mathematics Institute, Russian Academy of Sciences; Associate Professor, Department of Business Analytics, National Research University Higher School of Economics
Address: 47, Nakhimovsky Prospect, Moscow, 117418, Russian Federation
E-mail: sky_tt@list.ru; fbelousov@hse.ru

      This article is devoted to the construction and research of a model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations. The organization of freight traffic is facilitated by a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the final node stations. The process of cargo transportation is accompanied by the set rule of control consisting in measuring the volumes of goods transported at neighboring stations with a single time lag. For such a model, one must determine possible modes of cargo transportation and describe their properties. Traffic flow is described by a finite-difference analog of the nonlinear parabolic equation. The control system is set by nonlocal restrictions, which distinguishes the solutions of traveling wave type. The class of such solutions is extremely narrow. This results in the need for the “correct” extension of a class of solutions of the traveling wave type to a class of quasi-solutions of the traveling wave type. One type of expansion presupposes assumptions of discontinuous solutions of the traveling wave type; the second type allows for violations in a small control system. An essential lack of discontinuous solutions is their limitlessness. In this work, we investigate quasi-solutions obtained with the help of a second type of extension. The distinctive feature of such quasi-solutions is the assumption of feasibility of not local restrictions with the set error. The question of the limitation of such quasi-solutions is investigated. Using computer model implementation we investigate the dependence of the error in the performance of nonlocal restrictions on model parameters, which are the characteristics of the technologies used to carry out the cargo flow.

This work was partially supported by the Russian Foundation for Basic Research (project No. 16-01-00110)