# Optimization of Cellular Automata Model for Moving Bottlenecks in Urban Roads
## 1 Introduction  
The \"Moving Bottleneck\" was first introduced by [PERSON] and [PERSON] [1] in 1992. It referred to a phenomenon on multi-lane expressways where a slower-moving vehicle traveling in one lane causes vehicles behind it to queue up or change lanes due to the speed differential with other vehicles. This can result in several or even a large number of vehicles slowing down and following with the slow-moving vehicles forming \"clusters\" of slow-moving traffic, leading to a traffic bottleneck on the expressway. It has often been observed that there is still a gap between the actual traffic volume and the designed capacity. The mixing of slow-moving and fast-moving vehicles is one of the important reasons why the actual traffic volume often fails to reach the design capacity. The moving bottleneck is characterized by its instantaneous and mobile nature, with its formation and dissipation exhibiting strong randomness. It is difficult to completely eliminate traffic congestion causedby moving bottlenecks. Therefore, it is necessary to conduct a comprehensive exploration of traffic phenomena and conduct in-depth research into their evolutionary mechanisms. Researchers at home and abroad have conducted in-depth studies on moving bottlenecks in terms of theoretical modeling, practical observations, mathematical solutions, and other aspects. The current research and application areas of moving bottlenecks and cellular automaton models are primarily concentrated on highways and urban expressways: [PERSON] and [PERSON] [2,3] proposed the KW-MB model based on the LWR model, conducting research and analysis on the traffic flow upstream and downstream of bottlenecks, and initially presenting a mathematical method for solving it. [PERSON] and [PERSON] [4] summarized the progress of research on moving bottlenecks, both domestically and internationally, and analyzed the principles, advantages, and development trends of moving bottleneck theory. [PERSON] et al. [5] studied the possibility of appropriately controlling moving bottlenecks to improve traffic flow by using the Model Predictive Control (MPC) method, with the speed of moving bottlenecks as the control variable. [PERSON] et al. [6] established a model for the effect of moving bottlenecks by analyzing the influence of heavy, slow-moving vehicles on traffic flow on highways. [PERSON] et al. [7] developed a traffic model to simulate network traffic evolution under the impact of controlled autonomous vehicles acting as moving bottlenecks. [PERSON] [8] analyzed the impact of a \"moving bottleneck\" on traffic flow by establishing and simulating a multi-lane cellular automaton model. [PERSON] et al. [9] established a bilateral six-lane motorway model with tidal lane model to study the positive influence of a tidal lane on relieving upstream congestion induced by a moving bottleneck and the negative effect of a moving bottleneck on the tidal lane. [PERSON] et al. [10] present a general multi-scale approach for modeling the interaction of controlled autonomous vehicles (AVs) with the surrounding traffic flow, aiming at improving the overall traffic flow by reducing congestion phenomena and the associated externalities. [PERSON] et al. [11] examined a two-lane traffic cellular automaton model to understand the effects of static (e.g., lane reductions) and dynamic (e.g., slow-moving vehicles) bottlenecks on traffic flow and road safety. [PERSON] and [PERSON] [12] investigated the traffic flow of connected and automated vehicles (CAVs) by inducing a moving bottleneck on a two-lane highway. A heuristic rules-based algorithm (HRA) has been used to control the traffic flow upstream of the moving bottleneck. [PERSON] et al. [13] simulated the mechanical restriction differences between cars and heavy trucks in a two-lane cellular automata traffic flow model, addressing the heterogeneous traffic flow that includes both cars and trucks in real traffic.