Application of queuing theory and Petri nets in the analysis of traction rolling stock maintenance parameters by mathematical modeling

Abstract

Modern traction rolling stock requires an up-to-date system of maintenance and repair, the creation of which requires optimization of its parameters according to the Taguchi diagram. Therefore the importance of the task makes the topic of the article relevant i.e. the development of a simulation mathematical model of operation and maintenance for the purpose of factor analysis and selection of parameters of the trains’ life cycle maintenance system. The maintenance process under the depot conditions involves the use of a limited number of repair positions for both planned mileage repair and unplanned repairs of rolling stock, which corresponds to the topic of the queuing theory. The "Petri net" model is most suitable for this task, when each subsequent state of the model is determined by the previous discrete state and the task for modeling: the size of the polygon, the turnaround time, the number of train pairs per day, the repairs frequency, as well as stochastic processes of failure occurrence and random train delay time after failures and service delay. According to the canons of queuing theory and Petri nets, a program has been developed in the Visual Basic algorithmic language for Applications in the MS Excel environment. The article describes the algorithm of the program. In the program, sequentially for a given number of modeling days for each hour of the day, the need for each of the free trains to be repaired is determined; in the absence of free repair positions the train is queued. Free trains are tied to trains departing at the current hour. During the trip, failures are simulated with a given intensity, which is considered constant. The article provides examples of simulation results in relation to promising high-speed electric trains.