## 5 Simulation
### Bailey Yard Station  
Consider the largest foreign two-way marshalling yard Bailey Yard, which is located in North Platt, NE, USA (Figure 4). The station has a developed track system (about 114 tracks) with reserves of up to 25%, which ensures high throughput and processing capacity, as well as unhindered receiving of trains even during peak loads. An average of more than 10,000 railroad cars pass through Bailey Yard every day, and the yard sorts approximately 4000 cars daily using the yard's two humps. The eastbound hump is a 10 m tall mound, and the westbound hump is 6.1 m high. The receiving yards (East and West) and departure yards (East and West) have 9 and 10 tracks, respectively. Besides, a coal transit stream passes through the station [45] without processing (up to 32 trains per day). These trains are not re-formed at the station and arrive only for technical and commercial processing, as well as refueling the locomotive. Due to the increase in transport work, Union Pacific has built special transit parks in the \"Western\" system: Coal Spare Yard is designed to form its own coal routes, and the Westbound Mini-Rip Yard is used to receive and send transit non-coal car traffic. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{Arrived groups of requests} & 105.80 & \multicolumn{2}{c}{Probability of failure of a requests group} & 0.022 \\ \multicolumn{1}{c}{Arrived requests} & 8756.80 & \multicolumn{2}{c}{Probability of failure of requests} & 0.022 \\ Accepted groups of requests & 103.20 & \multicolumn{2}{c}{Average sojourn time of a request at the system (h)} & 46.13 \\ Accepted requests & 8540.20 & \multicolumn{2}{c}{Average sojourn time of a request at the system (m)} & 2767.80 \\ \hline
**Node parameters** & **Node 1** & **Node 2** & **Node 3** & **Node 4** \\ \hline Average busy channels & 0.89 & 1.49 & 8.37 & 1.33 \\ Average queue length & 84.74 & 0.00 & 57.96 & 12.84 \\ Average sojourn time of a request at a Node (m) & 400.77 & 288.89 & 1757.86 & 320.28 \\ Total blocking time (m) & 0.00 & 7.40 & 1.60 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation results of the Bailey Yard station. Now let us describe the characteristics of the West part of Bailey Yard station. The receiving yard has 9 railway tracks with an average capacity of 93 conv. cars; the sorting bowl contains 64 tracks with an average capacity of 87 conv. cars; each departure yard includes 8 tracks (for Westbound Mini-Rip Yard--10) with an average capacity of 97 conv. cars. From the receiving yard to the sorting bowl, two diesel locomotives move cars using two tracks. Train breaking-up is performed by the high-capacity hump with a processing capacity of up to 4000 cars per day, and two parallel humping tracks and two diesel locomotives are used. Three diesel locomotives perform the final train formation. This allows the formed trains to be moved to the departure yard reasonably quickly. There are also two transit yards located parallel to the departure park, which are intended for handling coal and non-coal routes. Table 3 shows parameters of the distribution of random variables, which describe servicing time and car group size. This information was obtained from regulatory documents [43], statistical observations, and open data [46; 47]. Arriving car traffic is regulated by the Harriman Dispatching Center (Omaha, Nebraska), the main dispatch center of the Union Pacific Railroad. By analyzing statistical observations and open data [46; 47], it was found that the average sum number of trains arriving at the station for day and night shifts is 36; the average number of cars per train is 85. The number of cars on the train is distributed as \(B(90,\,0.95)\). \(BMAP\) flow is constructed analogically. The model of the West part of Bailey Yard station is as follows. The system has five servicing nodes. Node 1 corresponds to the West Receiving Yard. We assume that the two thrust locomotives and the hump are two channels; the tracks of the yard are the queue with a capacity of 837 cars.