## 4 Experimental Results
### Analysis of GCL Computation Time  
This subsection evaluates the computational efficiency of the proposed Scheduling Computation Acceleration Algorithm (detailed in Section 2.5). Its GCL computation time is compared against several other scheduling approaches to demonstrate its scalability and suitability for large-scale in-vehicle networks.  
For this evaluation, TSN traffic flow sets were randomly generated, with the number of data streams varying from 25 to 200. For each set, streams were assigned random parameters; cycle periods were selected from the set {125 us, 250 us, 500 us, 1000 us}, priorities (PCP values) were assigned from 0 to 7, and transmission times were configured to ensure the total network bandwidth utilization exceeded 70%.  
The significant variation in schedule quality and runtime among different algorithms necessitates such empirical comparisons, as demonstrated in recent benchmarking studies [34]. The compared methods in our study include an exact Integer Linear Programming (ILP) formulation solved with Z3, metaheuristics like a Genetic Algorithm and Tabu Search, a Domain-Specific Knowledge (DSK)-based heuristic, a DeepScheduler using deep learning, and a simple Random greedy placement algorithm.  
The average GCL computation times across multiple runs are presented in Table 4.  
The results in Table 4 clearly demonstrate the scalability challenges inherent in TSN scheduling. The exact ILP method, while optimal, exhibits exponential time complexity, becoming computationally prohibitive (requiring over an hour) for 100 or more data streams. In contrast, most heuristic and learning-based approaches show approximately linear time growth.  
Notably, our proposed acceleration algorithm consistently outperforms the other scalable methods. This superior efficiency is attributed to its two-level sorting heuristic, which effectively prunes the search space and minimizes the need for extensive backtracking during the placement process. For a demanding scenario with 200 data flows, our algorithm computes the GCL in an average of approximately 1.06 s, confirming its suitability for large-scale networking applications. This sub-second computation time makes the framework viable for dynamic real-time systems where network schedules may need to be adapted or recalculated rapidly in response to changing conditions.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Algorithm** & **25 Flows** & **50 Flows** & **75 Flows** & **100 Flows** & **125 Flows** & **150 Flows** & **175 Flows** & **200 Flows** \\ \hline Random & 0.5 & 0.9 & 1 & 2 & 3 & 5 & 6 & 8 \\ Genetic & 0.5 & 0.9 & 1 & 1.15 & 8 & 20 & 60 & 70 \\ Tabu & 0.05 & 0.2 & 6 & 30 & 90 & 500 & 800 & 2000 \\ DSK & 9 & 19 & 20 & 30 & 40 & 50 & 60 & 70 \\ ILP (Z3) & 500 & 2000 & 3000 & 4000 & \textgreater{}3600 & \textgreater{}3600 & \textgreater{}3600 & \textgreater{}3600 \\ DeepScheduler & 0.8 & 1.5 & 2 & 3 & 4 & 6 & 7 & 9 \\ Proposed & Acceleration & 0.107 & 0.206 & 0.355 & 0.488 & 0.617 & 0.744 & 0.78 & 1.06 \\ Heuristic & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average GCL computation times (seconds) for different algorithms and varying numbers of data flows.