For Connected Automated Vehicles (CAVs), the traffic trajectory recommendation model (Wang et al., 2019; Jaurker and Pradhan, 2023) tries to optimize CAV trajectories, while reducing the total travel time and CAV fuel consumption. Secondly, the model is iteratively optimized in order to use real-time data. The model takes traffic sensor data and CAV trajectory information as input based on a large number of traffic data flows. It aims to minimize the total travel time of the trajectory to obtain the expected velocity profile of CAV. Then, with the goal of reducing fuel consumption, the quadratic optimization is carried out to generate the optimal CAV trajectory conforming to the velocity profile.

Meanwhile, Yang et al. (2021) take advantage of advances in CAV technology to design an ecological driving and queuing system that could improve fuel efficiency and operational efficiency of cars on highways. Yao et al. (2024) present a full-sample trajectory reconstruction method for the mixed traffic flow of common cars and connected cars. Cheng et al. (2023) provide a deep reinforcement learning model for hybrid traffic flow control based on Adam optimization to guide the longitudinal trajectory of CAV on a typical urban road with signal-controlled intersections. Zhang et al. (2023) introduce CAVSim, which is a micro-traffic simulator that emphasizes feedforward decision-making, planning components and collaborative decision in the CAV environment. Zhao et al. (2023) propose a strategy that allows CAV to remain safe with respect to the car in front and behind. Jiang et al. (2024) design an optimal control strategy to coordinate the forced lane change of autonomous cars from the common lane to the special lane. Deng et al. (2025) constructs a trajectory reconstruction method that makes full use of CAV debris observation data.

Traffic trajectory recommendation model based on multi-objective optimization could generally be divided into two modules. The first module is the function optimization module, which uses a multi-objective optimization function to optimize multiple objectives such as minimizing travel time, improving traffic safety and minimizing fuel consumption. It recommends driver trajectory through the ideal value of each target represented in the optimization function. The second module is the traffic track prediction module. This module realizes the prediction of future traffic state by analysing the recent traffic track condition, and timely feedback to the function optimization module to evaluate the future traffic track driving cost.

Ning et al. (2024) present a multi-objective optimization model for autonomous car traffic light intersections based on the near-end strategy optimization algorithm. Xiao et al. (2024) propose a sustainable and stable trajectory planning scheme for smart city public transportation based on multi-objective optimization. Nishida et al. (2024) design an improved version of Pareto Deep Q-Network (PDQN), which is a multi-objective deep reinforcement learning method for optimizing crowd trajectory guidance strategies, etc. Li et al. (2024) provide an improved non-dominated sorting genetic algorithm based on considering the travel intentions of drivers and passengers, which is a multi-objective optimization model with the goal of minimizing the loss of time for drivers and passengers. Peng et al. (2024) develop an improved constrained multi-objective evolutionary algorithm based on designing an improved genetic operator and repairing constraint processing technique to enhance the overall performance of the algorithm in seeking the Pareto optimal solution. Zhao et al. (2025) construct a multi-objective model for system optimization of dynamic traffic guidance.

The core content of the traffic trajectory recommendation model based on trajectory similarity is how to sketch the driven trajectory, so as to recommend the high satisfaction trajectory to the driver. The model can collect massive traffic trajectory data mainly based on the online filtering sampling method and offline filtering sampling method. The online filtering sampling method is primarily aimed at the traffic trajectory data that can be collected in real-time, and these data often require rapid analysis. The online filtering sampling method mainly adopts intermittent sampling, which requires the acquisition device to record the data once every fixed period of time and record the data in the cache area. When the data in the cache area reaches a certain amount, the data would be calculated to get the average value of the trajectory data in the window.

The difficulty of this model lies in how to measure the driver’s satisfaction with a certain trajectory and how to measure the similarity between different trajectories. Measurement of satisfaction with a certain trajectory includes the measurement of a variety of driver concerns, including time cost, economic cost, convenience of driving and road conditions. It is necessary to find a reasonable measurement method to measure it and take them into comprehensive consideration. Similarity measurement between trajectories is also a difficulty in this model. Trajectory states are different in different time and space, and real-time changes in trajectory states may bring difficulties in algorithm complexity and trajectory complexity.

Qu et al. (2019) propose an adaptive shortest-range cruising trajectory method ASER for personalized traffic trajectory recommendation. In ASER, a probabilistic network model is established, which uses Kalman filter method to predict the picking probability and picking capacity of each position. It also considers the load balance between passengers and cars, and introduces the shortest expected cruising distance to calculate the potential cruising distance of cars. In addition, it utilizes MapReduce and KDS-Tree to improve recommendation efficiency. Lim et al. (2021) provide a hybrid trajectory planning method that combines the advantages of sampling and optimization. The sampling method of transverse motion is used to deal with different trajectories of various maneuvers. This helps generating response trajectories in dynamically changing environments. Yu et al. (2023) design a diverse sensory trajectory publication/subscription framework that performs query trajectory matching between continuous location set queries on the trajectory data stream. Liu et al. (2023) develop a spatiotemporal dependency and similarity perception method called dependency and similarity perception temporal graph convolutional network. Lai et al. (2024) solve the problem of insufficient labels by effectively using the knowledge from several existing measurement methods as the source measurement method.

All kinds of personalized recommendation models mentioned above do solve some problems encountered in real life. However, as ignoring driver-car-road preferences, the above models are difficult to carry out personalized recommendations flexibly and timely for drivers with different driver-car-road needs. Meanwhile, the lack of edge-cloud computing results in insufficient computing efficiency of these models when used in our framework.

Figure 2 shows a running example of traffic trajectory. The definitions and formulas in this paper could be more easily understood by referring to this example.

Corresponding to Fig. 2, the set of sectioned trajectories is shown in Fig. 3. For example, t 1 = { s 1 , s 2 , s 7 } and t 2 = { s 1 , s 3 , s 8 } denote two different trajectories, respectively.

Larger | T s i | causes larger MSG s i , indicating that road section s i is more important.

If there are fewer trajectories containing section s i (i.e. smaller | T s i |), then the IDF s i is larger, indicating that section s i has a better trajectory fluency. In other words, trajectories containing this section may provide smooth traffic.

The smaller C s i brings smaller SFQ s i , which indicates that the usage frequency of section s i is lower. That is, the road section may be more smooth for a more possible recommendation.

Larger | d s i j | indicates driver d j prefers road section s i .

Drivers certainly want less driving time. Therefore, the road section with less driving time is more likely to be recommended.

The real-time and unexpected driver-car-road requirements are performed on the edge as follows.

For example, if driver d has already entered fatigued driving, they may need to stay and rest at a hotel on road section s i . In this case, g d s i may be a larger value. Larger g d s i indicates the more urgent need of driver d for road section s i .

For example, driver d’s car needs to be charged or refueled at the gas station on road section s i . In this case, g c d s i may be a larger value. Larger g c d s i indicates the more urgent need of d’s car for road section s i .

For example, if an accident occurs on road section s i , causing certain traffic congestion, g s i is a relatively large value.

Larger RUF s i indicates a more possible recommendation for road section s i .

Larger f ( s i ) indicates that more drivers may prefer road section s i . However, as more and more cars enter s i , f ( s i ) would become smaller, resulting in fewer drivers choosing s i . This is a game process that continuously updates recommendations through our framework.

After getting the section preference and trajectory preference list according to equation (7) and equation (8) respectively, TREDP could recommend personalized traffic trajectories to drivers.

Algorithm 1 takes driver-car-road requirements ( r d , g c d , g S ), a set of historical trajectories T and a set of drivers D as input. Meanwhile, it takes a recommended trajectory T d for driver d as output.

First, Algorithm 1 calculates the importance of road section s i as equation (1) (Steps 2–7). Second, it generates the section preference of s i as equation (7) (Steps 8–19). Third, it computes driver d’s driver-car-road preferences for traffic trajectory t j (i.e. δ ( t j )) (Steps 22–25). Fourth, if road section s i satisfies the following three conditions, t j is the best trajectory for driver d (Steps 28–31). (1) s i is closest to beginning point b d (Step 28). (2) The section preference of s i is the maximum value among all road sections that are closest to b d (Step 28). (3) The trajectory preference of t j containing s i is the maximum value among all trajectories (Step 29). Otherwise, we could only recommend to driver d one section (i.e. s i ) step by step by iteratively calling Algorithm 1 with new r d , g c d , g S , T and D (Steps 32–37).

Actually, Algorithm 1 can serve a group of drivers with the same beginning/ending point at the same time. And it could be naturally extended for serving various drivers with random beginning/ending points. The scheme proposed in this paper has a high requirement for data updates, and only the preferred trajectories calculated according to the latest data could provide drivers with timely recommendation services. Therefore, our framework and scheme are integrated to provide drivers with intelligent transportation services. The continuous iteration of the framework could bring timely data updates to the scheme and real-time personalized services to the driver.

We first establish our experiments from the following three aspects.

Dataset. The experimental dataset used in our experiments is the actual trajectory data of taxis in Shanghai, China during a certain period of time. This dataset uses GPS to record the longitude, dimension, direction, and passenger information of taxis at regular intervals. This dataset contains 4316 taxi drivers, each recording approximately 1800 records, totaling approximately 7.8 million records.

Experimental environment. Table 2 shows the experimental environment.

Compared method. ASER (Qu et al., 2019) is a traffic trajectory recommendation model based on trajectory similarity. As ASER is most relevant to our scheme, we compare our scheme TREDP with ASER in recommended accuracy and computational efficiency.

The dataset is divided into two parts in chronological order, with 70% of the older data used for data analysis and the remaining newer data used for verifying recommended accuracy. When the recommended trajectory is consistent with the actual trajectory, the recommendation is accurate. The calculation method is shown in equation (9), where T denotes a set of trajectories with the same beginning and ending point, T ˜ denotes all trajectories with different beginning and ending points in the system, t d i A denotes the number of actual trajectories (based on the newer data) of driver d i in T, t d i R denotes the number of the recommended trajectories (based on the older data) that are the same as the actual trajectories for driver d i in T, | D T | denotes the set of drivers in T, and Average ( ∑ i = 1 | D T | t d i R t d i A ) represents the average recommended accuracy of trajectory T. (9) Accuracy = Average ( ∑ T ∈ T ˜ Average ( ∑ i = 1 | D T | t d i R t d i A ) ) .

Experimental comparison results are shown in Fig. 4, where | S | denotes the number of road sections that need to be considered in personalized traffic trajectory recommendation.

As shown in Fig. 4, as more road sections | S | are considered by the personalized trajectory recommendation algorithm, the accuracy rate of trajectory recommendation is slightly decreasing. In addition, the preferred trajectories recommended by TREDP are mainly concentrated in the Top-30 part of the trajectory preference list. At the same time, when the number of | S | exceeds 25, TREDP has a 95% recommended accuracy. This proves the effectiveness of TREDP in intelligent traffic trajectory recommendation.

The number of road sections included in the trajectories gradually increases with the total number of trajectories | T | increases. This brings some challenges to TREDP and ASER, but they still maintain a good recommendation effect in Fig. 4. Moreover, TREDP has higher recommended accuracy than ASER method because it takes into account the driver-car-road preferences for numerous practical application requirements and scenarios.

Figure 5 shows the comparison of the recommended accuracy with the change of driver number | D |. When the number of drivers increases, the recommended accuracy of both TREDP and ASER decreases. This is because as | D | increases, a large number of drivers may result in game playing and interference among them. For example, a traffic-free road section may become less traffic-free after being recommended to many drivers, and the probability of this road section being recommended may decrease. The interference makes it more difficult for TREDP and ASER to determine the driver’s preferred trajectory. Meanwhile, TREDP considers the real-time relationship among driver-car-road, thus TREDP has better recommended accuracy than ASER.

Our computational overhead includes all computing and communication time for ASER and TREDP. The experimental results are shown in Fig. 6, where the X-axes denote | T |, | S | and | D | respectively, and Y-axes denote running time whose unit is millisecond (ms).

All calculations of ASER are on the edge. TREDP combines the computing resources of both edge and cloud. Even TREDP consumes the communication cost of edge-cloud, it still significantly reduces the computational overhead based on edge-cloud computing. Therefore, our scheme TREDP consumes less time than ASER in Fig. 6. This shows that our scheme is more suitable for large-scale traffic data. Meanwhile, rapid analysis can provide drivers with trajectory recommendation services in a more timely manner.