## 1 Introduction  
As the traffic volume in urban areas has increased significantly over the last decades, there has been many demands and efforts to develop and deploy technologies for intelligent transportation systems in order to address issues of traffic congestion, safety, efficiency, and also environmental improvements [1]. Undoubtedly, one of the most complex, dangerous, and important traffic environments on the road is the intersection, where traffic flows from different directions overlap in a common space, and it also has substantial impacts on the overall urban traffic efficiency and safety [2]. At intersections, traffic flows from different directions are typically coordinated through traffic light systems to prevent conflicting traffic flows passing the intersection simultaneously. Therefore, if a traffic participant violates the traffic rules imposed by the traffic light, the other participants in the intersection inevitably face the risk of an accident. The most representative example of such a traffic participant that violates the traffic signal is the Red Light Runner (RLR) [3].  
An RLR is a vehicle passing through an intersection, ignoring the traffic signal when the traffic light is red. According to the AAA Foundation for Traffic Safety, the number of deaths from RLRs increased by 31% from 2009 to 2017. In addition, the Insurance Institute for Highway Safety (IIHS) reported in 2017 that approximately 132,000 casualties were caused by the RLR. Also, the Manual on Uniform Traffic Control Devices (MUTCD), a standard for maintaining and installing traffic control devices, provides the control of intersection signals to reduce RLR accidents [4]. In general, intersection traffic lights consist of green, yellow, red and all-red signals. All-red signals exist when the intersection traffic light changes from yellow to red and red to green, and is used to prevent accidents caused by vehicles entering the intersection with the yellow signal [5]. MUTCD proposes the construction of a system that extends the all-red signal of intersection traffic lights when an RLR is detected. The length of the all-red signal needs to be determined so that collision by RLR does not occur in the intersection. One of the methods of determining the signal extension time is to use a statistical method to extend a constant time regardless of the current state of the vehicle. Another method extends the all-red signal by dividing the distance to the collision prediction point by the speed of the current vehicle.  
The current all-red signal extension system depends only on the vehicle speed at the moment when an RLR is detected. However, if the RLR does not move at a fixed speed as expected, the safety in the intersection cannot be ensured. Therefore, in this paper, we propose a framework for a dynamic all-red signal control system that determines the signal extension time according to the driving pattern of the detected RLR. In this proposed system, driving patterns of RLR vehicles are distinguished through the Multi-Channel Deep Convolutional Neural Network (MC-DCNN) [6]. Also, a multi-level regression strategy, consisting of the Hougen-Watson nonlinear regression model [7] and a quadratic polynomial regression model, is used to estimate the necessary all-red signal extension time with improved accuracy.  
The structure of the paper is organized as follows. Section 2 introduces conventional RLR prediction and signal extension methodologies. An overview of the proposed system is presented in Section 3. Clustering and classification based on the characteristics of RLRs are covered in Section 4. The proposed dynamic signal control model is described in Section 5. We validate the performance of the proposed system in Sections 6 and 7. Finally, conclusions are discussed in Section 8.