# A Two-Level Rolling Optimization Model for Real-time Adaptive Signal Control
## 1 Introduction  
With the development of the social economy, traffic congestion has become one of the most significant problems in many cities. Traffic signal control is a critical form of traffic control and management to reduce urban traffic congestion. Traffic signal control theory has been established for over 60 years, starting from the pioneering work of Webster [1]. Since then, research and development in traffic signal control has largely fallen into three types of control strategies: fixed-time control, actuated control, and responsive control.  
Fixed-time control is based on historic traffic data and assumes traffic demand is constant. Actuated control uses preset rules to adapt traffic flow based on detected traffic data (mainly vehicles passing/existing). Responsive control optimizes the signal timing plans based on real-time detected traffic data and improves the usage of intersection capacity [2; 3; 4]. There are a few widely used responsive traffic control systems in the world [5; 6; 7]: SCATS [8] was developed in Australia, SCOOT [9] was developed in Britain, RODYN [10] and CRONOS [11] were developed in France, UTOPIA [12] was developed in Italy, OPAC [13] and RHODES [14; 15] were developed in the USA.  
The optimization algorithm, which can generate the optimal signal timing plans based on a given objective, is regarded as an indispensable part of adaptive control systems. At present, the optimization algorithm in adaptive control systems can be divided into the following categories [16]: dynamic programming [14; 17; 18], genetic algorithms [19; 20], neural networks [21; 22], and fuzzy logic control [23; 24]. Because of the fast calculation speed, the dynamic programming algorithm is widely used in adaptive control systems such as PRODYN [10], UTOPIA [12], OPAC [13] and RHODES [14; 15]. In the RHODES system, the optimization algorithm is the dynamic programming algorithm named, Controlled Optimization of Phases (COP) [14]. In 2015, Feng et al. [17] proposed a dynamic programming signal timing optimization algorithm based on connected vehicle data. However, these algorithms do not consider the time-varying characteristics of the traffic flow during the optimization horizon. The longer the optimization horizon is, the worse the prediction effect is. Therefore, signal timing plans based on these methods are often unsatisfactory.  
With the development of connected vehicle technology, the time granularity of prediction data is becoming smaller and smaller [25]. Therefore, the use of small granularity predicted data to optimize the signal timing plans has been a popular research topic in the last couple of years. To address this issue, a two-level rolling optimization model for real-time adaptive signal control based on a dynamic traffic flow model was developed. The proposed method consists of two levels, i.e., barrier group and phase. The upper layer optimizes the length of the barrier group based on dynamic programming. The lower level optimizes the signal phase lengths with the objective of minimizing vehicle delay. Then, to capture the dynamic traffic flow, a rolling strategy was developed based on a real-time traffic flow prediction model. Finally, the proposed method was compared with the Controlled Optimization of Phases (COP) algorithm in a simulation experiment.  
The remainder of this paper is structured as follows. The traffic signal timing optimization model and algorithm are described in Section 2. In Section 3, a case study and discussion about the proposed method are presented. Conclusions and future work are discussed in Section 4.