## 1 Introduction
It is known that queuing systems (QS) are well suited to the study of objects in which the same type of activity is regularly repeated [20; 21]. Therefore, it can describe any micro logistic systems, which, firstly, are characterized by repeated execution of standard technological operations, and secondly, the incoming flow and its further processing have a stochastic character. Such logistic systems include railway stations and networks. Therefore, researchers quite often use queuing theory apparatus to describe and analyze them [23; 24]. In [25; 26; 27; 28; 29], this theory is used to model and study the railway network and its particular sections. In [25], an analytical model is proposed for estimating train delays on the Australian rail network. The authors compare the calculation results with the results of simulating. Model validation, which is carried out using a real-life suburban train network consisting of 157 trains, shows the model estimates to be on average within 8% of those obtained from a large-scale simulation. Articles [26; 27] present models of three lines of the Dutch railway network: from Rotterdam to Utrecht, from The Hague to Utrecht, and from Amersfoort to Zwolle. The models are designed to determine train delays, the capacity of rail networks, and a long-term global assessment of their efficiency without regard to train schedules. In these works, the authors use queuing networks with an infinite queue at each node to model the railway network. In [28], a model based on a single-channel queuing system is discussed and used to analyze railway lines' capacity. It is, according to the authors, widely applied in Germany. Mean knock-on delays are used as a quality-dependent indicator of capacity, allowing to determine the admissible number of trains for a level of service prescribed. In [29], the authors deal with a queuing network for modeling the movement of suburban trains, where the network nodes are technical stations. The nodes are arranged sequentially, have a single channel, and a queue of finite length. The effective capacity of the railway and the distribution of train travel time are calculated based on the proposed model. Queuing theory is also used to mathematically describe the operation of railway stations and other elements of railway infrastructure [30; 31]. Therefore, in [30], a railway station model was created, and all its components are written as separate queues. It is also assumed that the arrival time and service time obey an Erlang distribution, and the queues are infinite. Paper [31] presents a mathematical model of the train disbanding by the hump. It has the form of a queuing system with the presence of failures and a final queue. Articles [32; 33; 34] deal with the simulation of the railway hubs operation. In [32], the author uses Markov chains of a special type and calculates the queue length on the tracks adjacent to the railway hubs. In [33], the authors apply a quasi-birth-and-death process approach for the integrated modeling of capacity and reliability. By allowing for phase-type distributed arrival, service, and repair processes, the model permits a wide range of schedule and operational characteristics to be described. At the same time, the solvability of Markovian processes and the information on the queue length distribution are preserved. In article [34], railway nodes are divided up into a set of station tracks and the switching zones constituting a station's \"throats\" (route nodes). The nodes are described in the form of multi-resource queues, and a system of equations to determine exactly the loss probabilities for a route node is suggested. Queuing theory is used in scheduling transportation on railway transport, in particular, to predict the time of clearing the track for the passage of an oncoming train [35]. The proposed approach is based on the use of semi-Markov queuing systems.