## 2 System Model
### Optimization: Scheduling Computation Acceleration Algorithm  
While the SMT-based approach detailed in Section 2.4 provides a robust method for finding feasible GCLs, its computational complexity can become a bottleneck for scenarios involving a very large number of data streams or requiring rapid GCL recalculation, which are characteristic of complex autonomous driving systems. Handling large-scale periodic scheduling is a significant challenge in TSN [28], and to this end, a scheduling computation acceleration algorithm is proposed. This algorithm employs a heuristic-based, linear-time local search strategy designed to significantly reduce the time required to compute the GCL, while still aiming to satisfy the critical timing constraints of time-sensitive traffic. The acceleration algorithm operates based on the following core principles and steps:  
1. Time Slot Discretization: The entire hyperperiod \(\mathcal{T}\) (obtained from Algorithm 1) is discretized into a sequence of fine-grained, elementary time slots. A typical slot duration is 1 \(\upmu\)s, chosen based on the assumption that underlying TSN switch hardware can support GCL operations at this level of temporal granularity and that per-stream switch processing overheads are generally within this magnitude. Each stream (or sub-stream) transmission will occupy an integer number of these elementary slots. 2. Initial Search Phase-Prioritized Greedy Placement: This phase aims to quickly place a majority of streams into the discretized timeline with minimal conflicts. * Two-Level Sorting Strategy: The set of schedulable streams \(\mathcal{S}_{\textit{sched}}\) (or their constituent sub-streams if \(N_{i}>1\) from Algorithm 1) are first sorted according to a two-level criterion to prioritize their placement. 1. Primary Sort: Streams are sorted by the earliest start time of their respective cycle instances within the hyperperiod, in ascending order. This prioritizes streams that become available for transmission sooner. 2. Secondary Sort: Streams with the same primary sort key (i.e., same cycle start time) are then sorted by their transmission time (\(t_{i}\) or \(a_{i,x}\)), in ascending order (shortest transmission time first). Placing shorter streams first tends to leave larger contiguous blocks of time slots, potentially improving schedulability for subsequent, longer streams. * Sequential Greedy Placement: Following the sorted order, the algorithm attempts to place each stream (or sub-stream) into the earliest available sequence of un occupied time slots on the timeline. The placement must respect the stream's cycle start time within the current instance of its period being scheduled in the hyperperiod and all applicable constraints from Section 2.3 that can be checked at this stage (e.g., deadline, no-conflict with already placed streams). 3. Final Search Phase-Conflict Resolution via Local Search and Limited Backtracking: It is possible that during the initial greedy placement, some streams cannot be placed without violating constraints. This phase attempts to resolve such conflicts: * Direct Alternative Placement: For an unplaced stream, the algorithm first searches for an alternative valid placement in a later available time slot that still satisfies all its constraints (especially its deadline \(D_{i}\)). * Limited Backtracking and Local Search: If no direct alternative slot is available due to occupation by previously placed streams, a limited backtracking or local search mechanism is triggered. This search prioritizes relocating already-placed, lower-priority streams to resolve conflicts, with the constraint of displacing only one conflicting stream at a time. If the displaced stream can be successfully rescheduled to another valid slot without inducing further conflicts, the relocation is accepted, enabling placement of the current stream. This constrained approach prevents degeneration into exhaustive search, thereby preserving the algorithm's near-linear time complexity. 4.