## 5 Simulation Test and Data Analysis
### Operation Strategy Analysis  
In this paper, we mainly consider the combination of parallel and serial strategies for the four-way shuttle. Previous papers have mostly used serial operation strategies to represent the whole system, but in order to better reflect the actual system operation, parallel and serial operation strategies should be considered in combination. This subsection focuses on comparing the model built in this paper, incorporating the parallel operation strategy, with a model that uses the serial operation strategy to verify the effect of the operation strategy on the system.  
To eliminate errors, 18 scales of the system were selected for validation and the number of shuttle cars in the system was set to 5 [43]; the selected system scale is shown in Table 9.  
The overall response time of the serial operation strategy is longer than that of the model developed in this paper for large and small size systems with different numbers of layers and columns, increasing from arrival rate \(\lambda_{r}=50\) to arrival rate \(\lambda_{r}=250\) in 50 steps. The theoretical serial-parallel combination model established in this paper tends to increase smoothly in response time, while the single serial operation strategy has a faster growth due to the increasing arrival rate. This is because the system service time of the parallel operation strategy is the maximum value of the shuttle service time and the hoist service  
Figure 12: Error comparison chart.  
Figure 13: Comparison of system response time \(E(T)\), external queue waiting for pair length \(L_{\alpha\alpha}\) error under two solving methods.  
time, while the system service time under the serial operation strategy is the sum of the two equipment service times.  
In the case of a low arrival rate, the two servers, shuttle and hoist produce queues are not too long and the system response time does not result in too much time waiting for the service, so the difference between the two strategies is small. With the increasing arrival rate, the load on the hoist and shuttle increases, and there is an increase in the time that the shuttle needs to wait for the hoist when using the parallel strategy and the serial strategy. However, because the shuttle is independent of the hoist pickup when using the parallel strategy, part of the time waiting for the hoist can be spared, and the service time saved is greater than the time waiting for the hoist, while the serial strategy would cause the overall system response time to become increasingly long because of the accumulation of both the waiting time and service time.  
It can be seen from Figure 14 that, at T = 4 and T = 5, there is an average of one shuttle per layer in the system, representing a fully parallel strategy; thus, the percentage reduction in the system response time is greater than that with the serial operation strategy. At T = 6, the model described in this paper, with the addition of the parallel strategy, reduces the response time by an average of 16.8% compared with the serial model, but the percentage reduction in the response time decreases with the increasing numbers of layers. At T = 9, the percentage of the performance reduction is 8.92% on average. At T = 6, T = 7, T = 8 and T = 9, a combination of 12 serial and parallel systems can reduce the system response time by 12.6% on average.  
For both small-scale and large-scale systems, the model provided in this paper can reduce the response time by percentages as small as \(\lambda_{r}=50\), or 1.8% at T = 9. Thus, the model in this paper can improve the flexibility of the system by reducing the response time and more accurately reflecting the operation of the actual system.