## 5 Simulation
### Sukhovskaya Station  
In this section, the freight RS Sukhovskaya is considered. It was selected for the following reasons. First, it is a standard station on the East Siberian Railway. Second, it managed to obtain statistics on arriving train traffic. Sukhovskaya station is designed for the mass loading and unloading of cargo. It includes sorting devices (the hump, humping tracks, draw-out tracks, etc. ), the receiving yard, the sorting bowl, the cargo yard, and the departure yard (see Figure 2). The technological process of the station is standard and shown in Figure 1. Now let us describe its characteristics. The receiving yard has 5 railway tracks with an average capacity of 87 conventional cars (conv. cars); the sorting bowl contains 16 tracks with an average capacity of 73 conv. cars; the departure yard includes 10 tracks with an average capacity of 67 conv. cars. From the receiving yard to the sorting bowl, a single diesel locomotive moves cars using one humping track. Train breaking-up is performed by a low-capacity hump with a processing capacity of up to 1500 cars per day. The processing capacity of the cargo yard is 150 conv. cars per day, at the loading and unloading front, there are 10 servicing devices that can accommodate no more than 30 conv. cars at a time. The total capacity of the front is 300 conv. cars. The supply and retraction of cars from the cargo yard, as well as the complete formation of trains, is carried out by one diesel locomotive in each of the shunting areas. Table 1 shows parameters of the distribution of  
Figure 2: Scheme of Sukhovskaya station. random variables, which describe servicing time and car group size. Here and below, \(N(\mu,\sigma)\) is the normal distribution, \(B(v,p)\) is the binomial distribution. Service time distributions were obtained from regulatory documents [43] and field observations. These data include statistics on 91 trains that arrived at the station in the period from 10 February 2020 to 28 February 2020. Also, by analyzing statistical observations, it was found that the average number of trains arriving at the station during the day and night shifts is 3 and 2, respectively. The number of cars on the train is distributed as \(B(90,\,0.92)\). Trains arrive in the system in day and night shifts with different parameters. Hence, there are two sub-flows, and the control Markov chain \(v_{t}\) has two states \(\{0,\,1\}\). Since the duration of the shifts is the same, the probabilities of the chain transition from one state to another are \(p_{0}=p_{1}=p=0.5\). The maximum number of cars in a train is 90, therefore the _BMAP_ flow includes 91 matrices of size \(2\times 2\), \(D_{k},\,k=\overline{0,90}\). Their elements are calculated by formulas (1), where \(\lambda_{0}=3/12=0.25\), \(\lambda_{1}=2/12=0.16(6)\) and the transition probabilities \(p_{k}v,vt=pf(k)\), \(v,vt=\overline{0,1}\), \(k=\overline{0,90}\), \(f(k)\) is an arrival probability of a group of k cars, the group size obeys binomial distribution \(B(90,\,0.92)\). Thus, in terms of the theory of queuing, the model of the Sukhovskaya station, constructed in accordance with the previously proposed approach, has the following form:  
* Node 0--an external source
* Node 1 (Receiving Yard)--_BMAP_/_GX_/1/435
* Node 2 (Sorting bowl)--*/G^X_/2/730
* Node 3 (Cargo Yard)--*/G^B_/10/300
* Node 4 (Departure Yard)--*/G^X_/2/670  
Here \(X=B(90,\,0.92)\), \(B=30\) is maximum size of the served group. The movement of requests between nodes is carried out by the routing matrix \(P_{1}\). Figure 3 shows the general scheme of Sukhovskaya station model. Table 2 presents the average results for 10 launches of the simulation model. The virtual simulation time for each start is 3 weeks. We have chosen this value because it is the minimum time for which the simulation model allows calculating the stationary character