## 6 Discussion
### Future Work
Integrating these topology-aware, stateful reliability methods into the decision-support system will produce more accurate availability estimates, identify critical nodes via centrality metrics, and guide the placement of redundancy where it most effectively mitigates propagation risk in heterogeneous distributed computing deployments. The integration of evolutionary game theory (EGT) or distributed-control theory into the resource-allocation module can endow the system with dynamic adaptability, provable convergence, and robustness against perturbations. In an EGT framework, computational nodes are modeled as players in a game whose strategies correspond to resource-allocation policies. Payoff functions can be defined in terms of local utility metrics--such as throughput, energy efficiency, or queueing delay--and evolutionary dynamics (e.g., replicator equations)  
\[\dot{x}_{i}=x_{i}\big{(}u_{i}(\mathbf{x})-\bar{u}(\mathbf{x})\big{)},\]  
drive the population state \(\mathbf{x}\) toward an evolutionarily stable strategy (ESS) [112]. Under mild assumptions on payoff continuity and concavity, standard Lyapunov arguments guarantee global asymptotic stability of the ESS, ensuring that resource shares converge without oscillation or deadlock. Alternatively, distributed-control theory offers a complementary approach where each node executes a local control law based on neighbor information, leveraging consensus protocols and passivity-based design. For example, define \(r_{i}(t)\) as the resource allocation at node \(i\). A distributed gradient-descent law  
\[\dot{r}_{i}=-\alpha_{i}\
abla_{r_{i}}J_{i}(r_{i})+\sum_{j\in\mathcal{N}_{i}} \beta_{ij}(r_{j}-r_{i})\,,\]  
combines a local cost gradient \(\
abla_{r_{i}}J_{i}\) with consensus coupling over the communication graph \(\mathcal{G}=(\mathcal{V},\mathcal{E})\). Under standard connectivity and step-size conditions (\(\alpha_{i},\beta_{ij}>0\)), this protocol converges to the global minimizer of the aggregate cost \(J_{\text{tot}}=\sum_{i}J_{i}\) with exponential rate [113]. Robustness to link failures and time-delays can be established via input-to-state stability (ISS) or small-gain theorems, granting formal guarantees in volatile network conditions. By unifying EGT's payoff-driven adaptation with distributed control's consensus and stability theory, the proposed decision-support system can automatically adjust resource allocations in response to workload fluctuations, topology changes, or node failures, while mathematically ensuring convergence to optimal or near-optimal operating points and robustness margins against parameter uncertainty. To improve the applicability of the theoretical models presented, it would be beneficial to validate them through empirical testing using a laboratory system comprising computers with different hardware configurations. A verification section will be introduced using a controlled hardware testbed. This testbed will consist of a small cluster of heterogeneous servers--each equipped with Intel CPUs supporting RAPL power-measurement interfaces and NVIDIA GPUs exposing power metrics via NVML--so that both peak and real-time power draw can be recorded with millisecond precision. Prior to workload execution, each node's peak FLOPS capacity and base power consumption will be profiled through microbenchmarks, and network latency and bandwidth will be calibrated using tools such as iPerf3.