## 5 Result and Discussion
### The Predictability of Truck Activity Stability  
During the execution of transportation tasks, trucks move sequentially from one destination city to the next over time. The geographical location data of each truck, arranged chronologically, can be represented as a sequence (\(p_{1}\), \(p_{2}\), \(p_{3}\), \(\cdots\), \(p_{n}\)), where \(p_{i}\) denotes the \(i\)-th city visited by the truck during its operation. Consequently, predicting a truck's next  
Figure 1: SSE values for stability pattern clustering with different k.  
Figure 2: The distribution of the stability indicators. (**a**) Distribution of the variation coefficient of travel mileage; (**b**) Distribution of the variation coefficient of travel time; (**c**) Distribution of the variation coefficient of the number of cities visited; (**d**) Distribution of the variation coefficient of interval operating days. location is essentially a sequence prediction problem. Machine learning and deep learning are effective approaches for handling sequence data prediction. Common machine learning algorithms include k-nearest neighbors (KNN) and Support Vector Machines (SVM). Among these, the KNN algorithm is particularly notable for its robustness to outliers, simplicity, efficiency, and strong interpretability. As a foundational machine learning method, KNN has been widely applied in prediction tasks. In the realm of deep learning, frequently used algorithms include Backpropagation Neural Networks (BP Neural Networks), Recurrent Neural Networks (RNN), and Long Short-Term Memory Networks (LSTM). BP Neural Networks, as the simplest form of multi-layer neural networks, exhibit strong nonlinear mapping capabilities and serve as the foundation for many advanced deep learning algorithms. While RNNs improve upon BP Neural Networks, they are prone to vanishing and exploding gradient problems. LSTM, as a more advanced and mature neural network structure, incorporates memory mechanisms that significantly enhance its performance in sequence data prediction tasks. This study focuses on evaluating the predictability of truck spatial locations under different operational scenarios rather than advancing or optimizing prediction models. Therefore, KNN, BP Neural Networks, and LSTM were chosen for comparative analysis. These three algorithms represent instance-based machine learning methods, traditional neural networks, and deep learning time series methods, respectively. Utilizing KNN, BP neural network, and LSTM models, we predicted truck drivers' locations across four datasets. Figure 3 illustrates the cumulative probability distribution. The y-axis is labeled as the cumulative distribution function (CDF), which represents the probability that a random variable takes on a value less than or equal to a given threshold. Comparing the prediction accuracy distributions for the four patterns reveals a significant impact of stability on truck driver location prediction. Higher truck stability correlates with increased prediction accuracy across all three models, with category C1 consistently exhibiting the highest accuracy, followed by C2 and C0. C3 proves to be the most challenging to predict and is negatively correlated with the coefficient of variation of cities passed through. In all three models, LSTM demonstrates the best prediction performance. Specifically, Figure 3c shows over 90% prediction accuracy for C0 truckers, indicative of robust stability and regularity in their transportation routes. Moreover, approximately 20% of trucks in C1 and C2 achieve a prediction accuracy of over 80%, contrasting with only about 4% in the more unstable C4 category. This underscores the feasibility of predicting truck drivers' next locations based on geographic sequences, with superior results in deep learning models. Activity range stability emerges as a critical factor affecting predictability, while continuous operation stability has no significant impact.