# LTDA-MAC v2.0: Topology-Aware Unsynchronized Scheduling in Linear Multi-Hop UWA Networks +
## 3 Simulation Results
### Discussion  
Figure 3 compares the LTDA-MAC schedules derived by the greedy algorithm proposed in this paper with those derived by our previously proposed GA + PSO method [8]. The parameters of the GA and PSO algorithms are:  
* GA: population size--500, mutation rate--0.1, 80% scattered crossover, 1000 generations limit;
* PSO: swarm size--500, minimum neighbourhood fraction--0.1, adaptive inertia range--[0.05, 0.8], 1000 iterations limit. These parameters were empirically found to produce the best performance in our previous study in [8], by providing a large enough population/swarm to explore the high-dimensional solution space, and to enable a sufficient number of GA generations and PSO iterations to find good suboptimal solutions. This section also provides a baseline comparison with the Spatial TDMA approach (STDMA) [10; 11], tailored to the linear network scenario studied in this paper. An STDMA frame comprises a sequence of synchronized time slots for collision-free multiple access. To avoid inter-slot interference, the slot duration is:  
\[\tau_{\text{slot}}=\tau_{\text{dp}}+\max_{I[i,j]=1}\left\{T_{\text{p}}[i,j] \right\}+\tau_{\text{g}}, \tag{6}\]  
which ensures that no packets transmitted in a given TDMA slot are received at any node in the subsequent slot. The spatial reuse pattern is achieved by computing a binary \(N_{\text{sn}}\times L\) matrix indicating which node transmits in which time slot, such that \(L\) (the number of slots) is minimized with no collisions. The STDMA frame length is then calculated as: \(\tau_{\text{frame}}=L\tau_{\text{slot}}\). Figure 3 shows that the new heuristic optimization algorithm proposed in this paper derives packet schedules with shorter frame duration than the GA + PSO method and the STDMA protocol (despite the latter benefiting from clock synchronization), thus achieving higher network throughput of the LTDA-MAC protocol in both simulated scenarios. Furthermore, the proposed greedy algorithm is more reliable than GA + PSO, because the former is a deterministic method that does not rely on randomly generating and mutating candidate solutions. Therefore, the statistical spread of the results achieved by the greedy algorithm is significantly smaller, and is caused only by the perturbations in the simulated network topologies, rather than the random number generator seed (like GA, PSO and similar methods). The significant difference in the  
Figure 3: The proposed greedy optimization algorithm provides significantly better LTDA-MAC packet schedules (shorter frame duration—higher throughput), compared with the previously proposed “GA + PSO” method and the conventional Spatial TDMA approach. between the proposed greedy algorithm and the GA + PSO method is due to the inherently discontinuous and high-dimensional nature of the optimization problem, where treating the entire scheduling problem as a \"black box\" makes it very challenging for a heuristic algorithm such as GA or PSO to find good solutions. In contrast, the new greedy algorithm deconstructs the problem into a series of much simpler problems, minimizing every transmit delay in isolation, thus resulting in much better performance. Figure 4 gives examples of the LTDA-MAC schedules derived for the 2 km and 20 km pipeline scenarios, showcasing the topology-aware spatial reuse of resources achieved by the LTDA-MAC protocol employing the proposed schedule optimization algorithm. In addition to the notable improvement in the algorithm performance shown in Figure 3, Table 1 highlights the significant reduction in the computational cost of the greedy optimization algorithm compared with our previously proposed GA + PSO method. The number of schedule evaluations before finding a solution is reduced by 2-3 orders of magnitude, thus reducing the computer runtime from several minutes to approximately 1 s or less.