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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 307652, 11 pages
Research Article

Modelling of Freight Trains Classification Using Queueing System Subject to Breakdowns

Faculty of Mechanical Engineering, VŠB-Technical University of Ostrava, Institute of Transport, 17 listopadu 15, 708 33 Ostrava, Czech Republic

Received 4 July 2013; Accepted 2 September 2013

Academic Editor: Massimo Scalia

Copyright © 2013 Michal Dorda and Dušan Teichmann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper presents a mathematical model and a simulation model of the freight trains classification process. We model the process as a queueing system with a server which is represented by a hump at a marshalling yard. We distinguish two types of shunting over the hump; primary shunting represents the classification of inbound freight trains over the hump (it is the primary function of marshalling yards), and secondary shunting is, for example, represented by the classification of trains of wagons entering the yard via industrial sidings. Inbound freight trains are considered to be customers in the system, and all needs of secondary shunting are failures of the hump because performing secondary shunting occupies the hump, and therefore inbound freight trains cannot be sorted. All random variables of the model are considered to be exponentially distributed with the exception of customer service times which are Erlang distributed. The mathematical model was created using method of stages and can be solved numerically employing a suitable software tool. The simulation model was created using coloured Petri nets. Both models are tested in conditions of a marshalling yard.