With rapid economic development and a continuous increase in motor vehicle numbers, traffic congestion on highways has become increasingly severe, significantly impacting traffic efficiency and public safety. This paper proposes and investigates a traffic congestion prediction and emergency lane development strategy based on object detection algorithms. Firstly, the YOLOv11 object detection algorithm combined with the ByteTrack multi-object tracking algorithm is employed to extract traffic flow parameters—including traffic volume, speed, and density—from videos at four monitoring points on the Changshen Expressway in Nanjing City, Jiangsu Province, China. Subsequently, using an AdaBoost regression model, the traffic density of downstream road sections is predicted based on the density features of upstream sections. The model achieves a coefficient of determination $R^2$ of 0.968, a mean absolute error of 11.2 vehicles/km, and a root mean square error of 19.9 vehicles/km, indicating high prediction accuracy. Building on the interval occupancy rate model, this paper further analyzes the causes of traffic congestion and designs decision-making processes for the activation and deactivation of emergency lanes. By real-time monitoring and calculating the vehicle occupancy rate of the CD interval, threshold conditions for activating emergency lanes are determined. When the interval occupancy rate $K_{CD}(t)$ exceeds 80%, the emergency lane is proactively opened. This method effectively alleviates traffic congestion and reduces congestion duration. Quantitative analysis shows that after activating the emergency lane, the congestion duration in the CD section decreases from 58 min to 30 min, the peak occupancy rate drops from 1 to 0.917, and the congestion duration is shortened by 48.3%. Additionally, for the Changshen Expressway, this paper proposes two optimization points for monitoring point layout, including setting up monitoring points in downstream sections and in the middle of the CD section, to further enhance the scientific and rational management of emergency lanes. The proposed strategy not only improves the real-time extraction and prediction accuracy of traffic flow parameters but also achieves dynamic management of emergency lanes through the interval occupancy rate model, thereby alleviating highway traffic congestion. This has significant practical application value.

This study is motivated by solving the inverse boundary problem of the static Klein-Gordon equation (SKGE), which usually occurs in data assimilation problems. For the purpose of obtaining boundary conditions, the pro forma solution of the problem is provided by using Green’s function. The representation in double series of Green’s function for the SKGE on a rectangular region is obtained by means of the method of images. Convergence analysis shows that the representation is uniformly convergent, which is computer friendly, and can be applied to approximate computations.

The meteorology data assimilation applications often encounter variational problems with unknown weights, where the corresponding Euler equation is an elliptic partial differential equation. This research focused on retrieving the weights in remote sensing data assimilation by means of the computer-friendly form of the Green’s function obtained by eigenfunction expansion for the boundary value problem of the static Klein–Gordon equation on a rectangular region. With the help of the proposed retrieving method, the assimilation problem of estimating regional precipitation with weather radar and rain-gauge is solved in the Green’s function method. Results show that high accuracy of the proposed method makes it a good candidate for data assimilation problems in operational use.