## 4 Conclusions  
To address signal optimization and evaluate the control performance of traffic light in a mixed traffic scenario, an algorithm of mobile service computing for traffic state sensing based on connected vehicles and traffic camera is proposed in this paper. The results reveal that the connected vehicles can provide a queue length sensing service by shockwave-based model, but the penetration rate, the position of the last connected vehicle in the queue, and types of vehicles affect the queue length estimation accuracy. The camera-based model can remedy these drawbacks. However, this method requires that the DNN working on the edge server consumes computing and network resources to transfer the information, which delays the sensing result. To take advantage of shockwave-based model and camera-based model, a combined model by a weight shows a better performance in the evaluation. The weight is designed according to the queue length and the last connected vehicle. The error analysis showed that the average relative error is about 10%. This method can resolve the queue length estimation problem in a mixed traffic scenario, especially that there are variable types of vehicles. It can provide almost real time information for traffic lights control and will provide more chance to improve the traffic efficiency.  
What is more, the queue length estimation method designed in this paper could be studied further in the following points in the future work:  
1. The delay of information transmission and the loss of data between the on-board unit and the roadside unit are not considered in this paper. When this situation exists, errors in the prediction results are possible, which could do some further research.
2. Additional research is needed on the effect factors of weight \(\alpha\), connected vehicles penetration rate, and vehicle type difference rate.
3. The proposed methodology framework will be attempted to apply in computing delay at unsignalized intersections and even roundabouts with necessary modifications.
4. The proposed algorithm may be validated by probe vehicles or float car data.  
[PERSON] and [PERSON] conceived the idea; [PERSON] and [PERSON] designed the experiments and analyzed the data; [PERSON] implemented the experiments and wrote the manuscript; [PERSON] and [PERSON] helped with the simulation; [PERSON] and [PERSON] revised the manuscript. All authors have read and agree to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 61973047 and also by the Scientific research project of Double First-Class International Cooperation and Development Project of Changsha University of Science and Technology (2019 IC28). The project was supported by the Open Fund of Human Key Laboratory of Smart Roadway and Cooperative Vehicle-Infrastructure Systems (kfj190701) (Changsha University of Science & Technology).  
In this section you can acknowledge any support given which is not covered by the author contribution or funding sections. This may include administrative and technical support, or donations in kind (e.g., materials used for experiments).  
The authors declare no conflict of interest.