# Optimization of Cellular Automata Model for Moving Bottlenecks in Urban Roads
## 3 Simulation Setup and Result Analysis
### Analysis of the Impact of Heavy-Duty Vehicles on Traffic Flow  
#### 3.2.1 Analysis of Spatial-Temporal Operation Diagrams  
As shown in Figure 4, a spatial-temporal operation chart is a graphical representation method that cleverly exhibits the movement trajectories of vehicles across two dimensions: time as the vertical axis and space as the horizontal axis. This study aims to visually present the vehicle movement in model simulations through spatial-temporal charts. Specifically, it precisely records the position information of all vehicles on a certain lane at each time step and plots this information as scatter points on the spatial-temporal operation chart. In the chart, the vertical axis clearly represents the progression of time, with each vertical line perpendicular to it corresponding to a specific time step, showcasing the spatial distribution of all vehicles on the lane at that time step. The horizontal axis, on the other hand, represents the spatial positions along the lane, with each vertical line perpendicular to it corresponding to a specific cell on the lane, indicating the occupancy of that cell by vehicles at different time steps. The concept of cell space is crucial in spatial-temporal operation charts, representing the small spatial units into which the lane is divided. Each point in the chart corresponds to the state where a certain cell is occupied by a vehicle at a specific time step. Notably, the blank areas in the chart explicitly indicate that a particular cell is not occupied by any vehicle at a given time step. By observing the density of scatter points in the spatial-temporal operation chart, we can intuitively capture key information about the traffic flow. For example, densely populated areas often represent traffic congestion points, while the transition from dense to sparse scatter points vividly illustrates the formation and dissipation of traffic bottlenecks. To facilitate observation and reading, this study carefully selects the cell space near intersections along the road segment for plotting. This approach not only focuses the spatial-temporal operation chart on critical areas of the traffic flow but also provides a powerful visual aid for an in-depth understanding and analysis of traffic phenomena.  
By comparing the spatial-temporal operation diagrams when the proportion of heavy-duty vehicles is 0 and 1, it can be observed that when the road network is entirely composed of heavy-duty vehicles, the average speed of the road network is much slower than that of a road network composed entirely of small vehicles from Figures 4 and 5. A commonality between these two scenarios is that the vehicle trajectories are relatively smooth, and there is no crossing or overlapping between the curves, indicating that when only one type of vehicle exists on a road segment, vehicles can achieve coordinated car-following based on the distance to the preceding vehicle, and there is no occurrence of rear-end collisions during the car-following process.  
By setting the proportion of heavy-duty vehicles in the road network traffic flow to 0.3, the formation process of moving bottlenecks becomes clearly visible from Figure 6. Small vehicles, influenced by heavy-duty vehicles, decelerate after accelerating and can only follow at low speeds behind the heavy-duty vehicles, unable to further accelerate. Meanwhile, the lane-changing behaviors of vehicles can be clearly observed in the spatial-temporal diagram, where the vehicle trajectories are no longer complete and continuous  
Figure 4: **(a,b) Spatial-temporal operation diagram when the proportion of heavy-duty vehicles is 0.**  
Figure 5: **(a,b) Spatial-temporal operation diagram when the proportion of heavy-duty vehicles is 1.**  
curves. The discontinuity in the trajectory lines in the diagram represents vehicles changing lanes to merge into or exit from the current lane. The above analysis demonstrates that this model can truly reflect car-following and lane-changing behaviors, achieving the expected simulation effects.