## 1 Introduction  
Intelligent transportation systems (ITS) show the ability to address the issues of traffic efficiency and safety. ITS is an indispensable part of the smart city [1]. To deploy ITS, more and more traffic infrastructures and cars need to be connected, which is a typical application of IoT [2]. Automated cars are equipped with many sensors for environment sensing. Benefiting from the development of -vehicular network, information from sensors and fused sensors' information can be utilized to ITS application. For example, traffic signal optimization at intersections is a promising application for ITS based on vehicular communication networks (vehicle-to-everything, V2X) communication [3, 4] and intelligent camera, which can significantly reduce traffic congestion and emission [5]. The key to traffic signal optimization is traffic states sensing. Inductive loops and traffic cameras are used to evaluate the traffic states, such as queue length at intersections and traffic flow, while these equipments have disadvantages of high installation and maintenance cost and low service life [6]. With the development of V2X, the intelligent vehicle travelling on the road can act as a powerful mobile detector [7, 8]. The intelligent vehicle with GPS can obtain the real time position and speed of the vehicle. This information can be collected to the TSMs and utilized to evaluate the traffic states such as delay time, queue length, etc. [9]. The traffic states can be exchanged among intelligent vehicles, transport infrastructure, and road users, which is a typical application of IoT-based transportation system [10]. Utilizing connected vehicles to sense the traffic states depends on service computing. Service computing has been utilized in many applications with the development of the network. It defines a unified structure of service combined with the computer network [11]. Benefiting from the IoT, the infrastructures in ITS are connected and intelligent. It seems that the connected vehicles can provide some service for traffic states sensing when travelling on the road [11]. The connected vehicle can act as a mobile traffic information sensor [12, 13]. In a mixed traffic scenario, the information from connected vehicle is used in delicate traffic models to estimate the traffic volume at the intersection [14]. The vehicles' queue length and delay are the most important indicators for traffic signal control in signalized intersection. There are some traditional approaches to queue estimation and delay at signalized intersections, such as the Webster theory and highway capacity manual (HCM) method. They are still the fundamentals and used in the handbook for the traffic signal design and optimization [15]. It reveals that Webster theory cannot be used when the degree of saturation approaches one, while HCM method can be used under near saturation and over saturation conditions [16]. Both Webster theory and HCM method are based on statistical data and empirical models. With the development of artificial intelligence (AI), some researchers compared the performance of Webster theory, HCM method, and AI-based model [17] and the AI-based model showed more robustness and adaptiveness than the traditional approaches. A probability distribution method based on mathematical statistics was developed to estimate the queue length by utilizing the last connected vehicle's position in the queue, waiting time, and number of connected vehicles [18, 19]. What is more, the arrival rate of vehicles at the intersection is defined and valuated, as well as the penetration rate of connected vehicles. Most existing queue length estimation models can only be applied for an unsaturated scenario at isolated intersections and need to determine the connected vehicles penetration rate in advance [20]. In order to improve the communication efficiency of V2X, a mechanism that can reduce transmission times without affecting accuracy of length estimation is proposed [21].