# A Hybrid User Mobility Prediction Approach for Handover Management in Mobile Networks
## 5 Experimental Results
### Mobility Model Performance  
To evaluate the error of the mobility model, we considered two metrics: root mean square error (RMSE) and mean absolute error (MAE). Given \(b\) input samples from \(n\) total number of samples, RMSE can be given by  
\[RMSE_{b}(g)=\sqrt{1/n\sum_{i=1}^{b}(y(x)-\bar{y}(x))^{2}} \tag{14}\]  
where \(x\), \(y(x)\), and \(\bar{y}(x)\) are the input sample, actual result, and predicted result. The ideal value for RMSE is zero to show that the predicted and actual values are the same. Additionally, the MAE value can be calculated as  
\[MAE_{b}(\bar{y})=1/n\sum_{i=1}^{b}|y(x)-\bar{y}(x)| \tag{15}\]  
with lower values of MAE and RMSE being better for the predictor.  
Length of the user sequence plays a vital role in evaluating a mobility model performance. Generally, when the length of the sequence is small, it is easier for the model to investigate the correlations. There is a tradeoff between sequence length and mobility behaviour learning. It is hard for the model to extract the user's mobility pattern when it deals with either a too short trajectory or a too long trajectory. Figure 5 shows the impact of different sequence lengths (\(n\)) on the mobility model prediction error. Our model has a same-length input and same-length output structure. As shown, the proposed VAR-GRU mobility model has the lowest prediction error for all values of \(n\).  
One important point for robust and reliable mobility models is the fact that users have different degrees of predictability based on their movement regularities [29]. Some users have more repetitive behaviour and thus are more predictable. Some users tend to have constantly changing mobility behaviour, and therefore, they are more unpredictable. A reliable mobility predictor should be able to model different users' mobility with low error. Figure 6 shows how the proposed mobility model works when dealing with four different users. As shown, the VAR-GRU model outperforms other methods for the four different users.  
Figure 5: Impact of the sequence length on the prediction error.  
Next, we make a comparison between the mobility models based on the MAE value. Table 3 summarizes the results regarding each method. We observe that the proposed VAR-GRU trajectory predictor model outperforms the other approaches in terms of MAE value.  
Next, having predicted the future trajectory of the user, we investigated the impact of this prediction on handover costs in terms of number of messages required and the transmission costs. After obtaining the predicted user future trajectory, we evaluated the accuracy of our predictions based on the actual future trajectory. We evenly distributed the base stations (BS) in the area of the user trajectory within the cell range of 1000 m. Therefore, each location point was within a cell area and we assigned it to the base station of that cell. We performed these steps for both the predicted and the actual user path. Then, we measured the accuracy of our predictions as a classification task and to observe whether the BS associated with the predicted trajectory points matched those of the actual trajectory points.