## 5 Conclusions  
This study highlights that traffic incidents are a major cause of congestion and examines the limitations of the Cell Transmission Model (CTM) in accurately simulating traffic jams. While the CTM is widely used, it exhibits two key inaccuracies, emphasizing the need for proper calibration and validation. To address this, we embedded a calibrated CTM into a MATLAB-based simulation of an 8 \(\times\) 8 grid traffic network to analyze accident-induced congestion. Only cell 9 was divided into three smaller cells to represent different movement directions (left-turn, go-straight, and right-turn), ensuring a more accurate depiction of traffic flow. This refinement maintains the standard nine-cell structure elsewhere, balancing computational efficiency with improved intersection modeling. Through two case studies, we compared the traditional and calibrated CTM methods under different traffic conditions. The results revealed that the traditional CTM method often underestimates or overestimates congestion spread and dissipation, leading to unrealistic traffic flow predictions. In contrast, the calibrated CTM method provided more precise estimations, better capturing the dynamic nature of traffic jams. Specifically, the calibrated CTM showed a more accurate representation of queue formation, shockwave propagation, and clearance time, resulting in improved decision-making for traffic control strategies. Here, we explicitly highlight the originality and significance of our research by emphasizing the following key contributions: (1) Introducing a novel refinement to the traditional CTM by dividing only cell 9 into three smaller cells to accurately capture different movement directions, enhancing intersection modeling without increasing overall computational complexity. (2) Identifying critical inaccuracies in the conventional CTM when modeling accident-induced congestion, addressing limitations in congestion propagation and dissipation. (3) Proposing a calibrated CTM framework that significantly improves the representation of congestion dynamics, offering a more realistic depiction of traffic flow disruptions. (4) Demonstrating the effectiveness of the novel H-strategy, which outperforms the existing control methods in mitigating congestion and improving network performance. Our future research directions include the following:  
Scalability to complex networks: Extending the calibrated CTM framework to three-way or four-way grid networks and non-uniform urban layouts, incorporating dynamic lane configurations. Resilience to extreme disruptions: Integrating real-time adaptive mechanisms to address unexpected events (e.g., earthquakes, accidents) and evaluating the H-strategy's performance under stochastic demand fluctuations. Human behavior integration: Enhancing the model to account for heterogeneous driver decisions (e.g., route diversion, compliance variability) using agent-based modeling or empirical trajectory data. Emerging technologies: Exploring synergies between the calibrated CTM and connected/autonomous vehicle (CAV) systems to optimize traffic control strategies in mixed traffic environments. These advancements will further bridge the gap between theoretical models and practical traffic management applications, enabling cities to adopt proactive, data-driven strategies for congestion mitigation. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Time interval** & 500 & 1500 & 2500 & 3500 & 500 & 1500 & 2500 & 3500 \\ \hline
**Strategy** & \multicolumn{4}{c}{**Traditional CTM (\(t_{d}\) = 0.8)**} & \multicolumn{4}{c}{**Calibrated CTM (\(t_{d}\) = 8)**} \\ \hline No strategy N = 20 & 14 & 480 & 210 & 152 & 8 & 73 & 25 & 11 \\ Q1: \(\mathrm{d_{A}}=1\); \(\mathrm{d_{B}}=0.6\) & 8 & 310 & 128 & 88 & 8 & 48 & 15 & 7 \\ Q2: \(\mathrm{d_{A}}=1\); \(\mathrm{d_{B}}=0.8\) & 9 & 261 & 113 & 72 & 9 & 46 & 14 & 6 \\ H-strategy \(\mathrm{d_{A}}=1\); \(\mathrm{d_{B}}=\mathrm{d_{C}}=0.8\) & 10 & 80 & 27 & 11 & 10 & 30 & 6 & 2 \\ \hline \hline \end{tabular}
\end{table}