ISSN 2587-814X (print),
ISSN 2587-8158 (online)

Russian version: ISSN 1998-0663 (print),
ISSN 2587-8166 (online)

Nerses Khachatryan 1
  • 1 Central Economics and Mathematics Institute, Russian Academy of Sciences , 47, Nakhimovsky Prospect, Moscow, 117418, Russian Federation

Dynamic model of organization of cargo transportation with a limited caracity of the distillation ways

2013. No. 4(26). P. 62–68 [issue contents]

Nerses Khachatryan – Senior Researcher, Central Economics and Mathematics Institute, Russian Academy of Sciences; Senior Lecturer, Department of Business Analytics, Faculty of Business Informatics, National Research University Higher School of Economics.  
Address: 47, Nakhimovskiy Prospect, Moscow, 117418, Russian Federation.
E-mail: nerses@cemi.rssi.ru

This article studies the model of the organizing cargo transportation in a closed chain of stations with a given control system. It is assumed that there is an open-line track between two neighboring stations in which temporarily part of the cargo may be stored. Cargo can be delivered on any station either from the previous station or from the open-line track located between them. Similarly, cargo may be sent either to the next station or to the open-line track between them. Cargo handling occurs at nodes stations. Obviously, the number of nodes involved in the cargo handling under uninterrupted operation of the entire transport chain is limited. The maximum number of such nodes determines the carrying capacity of stations. Capacity of the open-line track is limited. Cargo transportation is fulfilled by means of two technologies. The first technology is based on a set of normative rules of interaction between neighboring stations. It does not take in to account conditions of limited carrying capacity of stations. Furthermore, it does not allow using the full potential of stations. In this regard, along with the first technology, the second technology is used. It allows both to increase the number of involved nodes, and to reduce it. In this case, the cargo is either taken from an open-line track or sent to an open-line track. This model is determined by a system of differential equations describing the intensity of cargo traffic at the stations, which satisfies the additional conditions. These conditions determine the control system and impose restrictions on the capacity of open-line tracks. Particularly interesting is the study of stationary solutions in this system. This system has three types of stationary solutions. The main objective is to study stability of stationary solutions. Analytical study of the set of all solutions is greatly complicated by the fact that the right-hand sides of the differential equations are not continuous functions. Therefore, this model has been studied numerically. Numerical study has shown that only one type of stationary solutions is stable. For these solutions the domain of their stability is described.

Citation: (2013) Dinamicheskaya model' organizatsii gruzoperevozok pri ogranichennosti emkostey peregonnykh putey [Dynamic model of organization of cargo transportation with a limited caracity of the distillation ways] Biznes-informatika, 4(26), pp. 62-68 (in Russian)
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