## 5 Experiment
### Results and Discussion  
The results of the experiment will be analyzed in this section. Before simulation, we need to build a better ARMA model as described above. Below, we first analyze the results of the ARMA model. We use the previously established ARMA model to perform curve fitting on the original data. As shown in Figure 6(a), Residual Sum of Squares (RSS) is used to describe the performance of curve fitting, and our model has achieved good results. As an example, we select any period in the experimental data to predict the demand. After prediction and comparison with the original data, we got the results as shown in Figure 6(b). We can see from the prediction results that the overall trends of the forecast curve and the true curve are similar, but the forecast is not accurate sometimes due to the small fluctuation of the bicycle rental, which can be ignored in subsequent dispatching schemes. Next, we will perform an error analysis on the experimental results. In summary, the final results of the experiment will be affected by two factors which are the initial distribution of bicycles and the trip record. The following is a brief introduction. Firstly, the initial distribution of bicycles on the map has a greater impact on experimental results. As shown in Formula (6), we generate two maps with different bicycle distributions, which can be indicated by parameter \(\sigma\). In the traditional public bicycle system, a common dispatching mode is to dispatch excess bicycles at overflow stations directly to an underflow station, where the dispatching distance is taken as the optimization goal. We can call this type of dispatching scheme Commonly Used Manual Dispatching (**CUMD**). In addition, we refer to the manual dispatching strategy and the hybrid dispatching scheme including manual dispatching and user incentive dispatching proposed in this paper respectively as Manual Dispatching Proposed (**MDP**) and Hybrid Dispatching Proposed (**HDP**). Figure 6: The determination of parameters in the ARMA model. Secondly, the HDP proposed in this paper is also influenced by the proportion of riders in the travel record who are willing to accept user incentive dispatching. We set the step to 0.2 to constantly change the proportion of users in the trip record who are willing to accept dispatching tasks from 0 to 1, so as to conduct multiple sets of experiments. Finally, the simulation results are as follows, which are listed to five significant digits. In Table 4, we can see the experimental results of user satisfaction for three dispatching methods. From the experimental results, we can see that **CUMD** is relatively behind **HDP** and **MDP** in terms of user satisfaction for almost 0.02. Since our experiment has more than 40,000 trip records, the improvement of user satisfaction exceeding 0.02 is a considerable improvement for the bicycle dispatching system. Furthermore, the **MDP** and **HDP** proposed in this paper are roughly the same in terms of user satisfaction. However, the value of HDP is going to change a little bit more due to the integration of user incentive dispatching and experimental results also prove it. As shown in Figure 8, the curves of the operator's total revenue \(\mathbf{B}\) over time are shown. Firstly, the **HDP** and **MDP** schemes have almost the same performance in terms of operator revenue. Then, **HDP** is consistent with the other two strategies in the early stage of scheduling, but, after a period of scheduling, its performance in terms of operator revenue is better than the other two strategies. \begin{table}
\begin{tabular}{c c} \hline \hline
**Dispatching Method** & **User’s Satisfaction \(\mathbf{\alpha}\)** \\ \hline \hline Cumb & \(0.767\pm 0.010\) \\ MDP & \(0.787\pm 0.002\) \\ HDP & \(0.788\pm 0.012\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The satisfaction of user. Figure 7: The result of predicting.