# Modeling of a Coal Transshipment Complex Based on a Queuing Network
## 4 Computational Experiment
### Experiment 2. Estimation of Maximum System Performance  
We modify QN-1 as follows. The service time at Node 4 is reduced to 4 min (\(T_{4}=4\) min), which corresponds to the maximum design capacity of the cargo yard. The average service time at Node 11 is 39.24 h or \(T_{11}=\) N (2354; 500) minutes. The remaining parameters of the model are the same (see Table 3). Table 6 presents the simulation results with an increase in the values of all elements in matrices (2) by 12.5%, 20%, 30%, and 40%, which corresponds to an average overload of 25.7, 27.4, 29.9, and 32.2 million tons of coal per year, respectively.  
Let us interpret the results of Experiment 2. We call \"decline of service\" of the request group a situation when trains are not accepted at Toki station because its tracks are busy. In this case, their schedule is disrupted, and the trains stop at neighboring railway stations to wait for a free space in Toki and a new schedule.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**No** & \(\mathbf{\lambda}\) & \(\mathbf{V}\) & **Input Groups** & **Input Requests** & \(\mathbf{PL}\) & \(\mathbf{TH}\) & \(\mathbf{TS}\) & \(\mathbf{LC}\) & _Max bi_ \\ \hline
1 & 0.75 & 25.7 & 1619.2 & 102,262.5 & 0.0002 & 69.2 & 87.9 & 41.4 & 15.9 \\
2 & 0.80 & 27.4 & 1725.3 & 109,080.0 & 0.0004 & 70.1 & 116.1 & 3217.5 & 17.3 \\
3 & 0.87 & 29.9 & 1881.6 & 118,624.5 & 0.0013 & 72.2 & 168.6 & 10,428.2 & 18.8 \\
4 & 0.94 & 32.2 & 2032.6 & 128,169.0 & 0.0173 & 75.3 & 242.0 & 16,411.0 & 27.4 \\ \hline \end{tabular}  
* In Table 6 and further, \(\mathbf{V}\) is volume (in million tons) of coal that is expected to be transshipped per year at the current intensity \(\lambda\) of train arrivals; \(b_{max}=\max b_{i}\), \(i=6\), \(7\), \(9\)–\(11\), where the nodes listed describe the conveyor system and the berthing cargo yard.  
\end{table}
Table 6: Results of Experiment 2.  
Let us analyze the data in Table 6. With an increase in the intensity of receipt of the request groups by 30% (row 3), you can see that, over 90 days, on average, 1881.6 \(\times\) 0.0013 = 2.5 trains are not accepted. This number of unserviced trains does not significantly affect the operation of the system as a whole. Parameter \(b_{max}\) is less than the same parameter in Experiment 1. Therefore, the system can handle the load. However, the large value \(LC\) = 10,428.2 \(>\) 4286 indicates that the vessels do not manage to export all the incoming coal and the warehouse will be completely full in six months.  
Rows 1 and 2 show that with the transshipment of up to 25-26 million tons of coal per year, all trains will be accepted. The value \(PL\) = 0.0002 (0.33 trains per year) is insignificant since dispatch control can vanish it. At the same time, the resulting estimate (25 million tons of coal per year) corresponds to the recommended loading of Daltransugol JSC, which is 24.98 million tons of coal per year [49]. Moreover, Daltransugol JSC is capable of processing up to 28-29 million tons of coal per year in normal mode.  
Figure 7 shows the values of \(\mathbf{b}_{i}\) for all nodes for each option.  
If \(\lambda\) = 0.94, there is a dramatic increase in blocking duration in Nodes 1-3 due to the insufficient capacity of Node 4 (cargo yard). We also see a significant increase in the blocking duration in Nodes 6-8. The largest increase in \(b_{i}\) occurs in Node 7 (SR) due to a queue overflow in Node 8 (warehouse), and blocking Nodes 9 and 10. Thus, an increase in transshipment volumes over 30 million tons is hard to carry out since warehouse capacity and the capacity of the berthing cargo yard (Node 11) is not enough. Nevertheless, the conveyor system (Nodes 6, 9, and 10), even with an overload of 32.2 million tons per year, has a margin of productivity.