# Modeling of a Coal Transshipment Complex Based on a Queuing Network
## 4 Computational Experiment
### Experiment 3. Evaluation of Complex Performance after the Planned Upgrade of Daltransugol JSC  
Table 7 shows the results of a numerical study of QN-2 with an increase in the values of all elements in matrices (2) firstly by 73%, which corresponds to an average overload of 40 million tons of coal per year, and then consistently by 83%, 93%, and 103%.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**No** & \(\lambda\) & \(V\) & **Input Groups** & **Input Requests** & \(PL\) & **TH** & **TS** & \(LC\) & \(\mathbf{b}_{max}\) \\ \hline
1 & 1.16 & 40.1 & 2505.8 & 158,166.0 & 0.0057 & 62.5 & 71.1 & 0.0 & 7.3 \\
2 & 1.23 & 42.1 & 2658.2 & 167,710.5 & 0.0056 & 63.2 & 75.7 & 0.0 & 8.5 \\
3 & 1.30 & 46.7 & 2804.4 & 177,255.0 & 0.0086 & 64.8 & 77.9 & 0.0 & 10.4 \\
4 & 1.36 & 50.9 & 2939.2 & 185,436.0 & 0.0162 & 67.8 & 82.2 & 0.0 & 11.3 \\ \hline \end{tabular}
\end{table}
Table 7: Results of Experiment 3.  
Figure 7: Experiment 2. Total blocking duration (\(b_{i}\)) of one channel in Node \(i\).  
Based on Table 7, we can conclude the following. With the transshipment of 46.7 million tons of coal per year, an average of 1.9 trains per week will not be accepted at Toki station. This value is approaching the critical one, which is three trains per week for Toki's railway segment, according to expert assessment. Therefore, the maximum capacity of the system can be estimated at 46-47 million tons of coal yearly with timely loading and dispatch of a total of two carriers daily from both berths. In this case, coal will mainly be reloaded immediately from trains to vessels, and the warehouse will be empty (\(LC=0\)). Daltransugol JSC retains a capacity margin of about 10-15%, which is confirmed by lower values of \(TH\), \(LC\), and \(b_{\max}\) compared with similar parameters in Table 6 for all \(\lambda\).  
Figure 8 shows the values of \(\mathbf{b_{i}}\) for all nodes for each option.  
After the modernization of Daltransugol JSC, we can point out two bottlenecks in the system that prevent an increase in transshipment volumes over 47-48 million tons of coal per year. The first is the receiving yard (Node 1), since, at \(\lambda=1.36\), there is a relatively small increase in \(b_{1}\) with a sharp increase in the loss probability (from 0.0086 to 0.0162). The second bottleneck is the cargo yard (Node 4). It causes a significant increase in the blocking duration of Node 3 for \(\lambda=1.36\). The throughput capacity of the conveyor system and two berths is enough to transship 50.9 million tons of coal yearly. In particular, \(\mathbf{b_{i}}\) at Nodes 5, 6, 9, 10, 12, and 13 remain relatively small and stay equal for \(\lambda=1.30\) and \(\lambda=1.36\). Therefore, with an increase in the capacity of the receiving yard and the productivity of the cargo yard, a further increase in transshipment volumes is possible. In particular, the receiving yard at Toki station needs to have four or five additional tracks, along with the capability to unload three cars at a time using the new car dumper. In this case, we estimate it at 52-54 million tons of coal per year, since the conveyor system's capacity reserve is about 10-15%.