(untitled) (International Journal of Computer Science and Engineering, 2026)
Managing multi-dimensional resource flows within large-scale, high-concurrency service platforms under severe computational capacity constraints presents intricate architectural challenges, where traditional single-dimensional scheduling models fail due to cross-resource coupling. This paper presents a joint multi-dimensional resource flow scheduling framework integrated with control-theoretic stability optimization, specifically addressing the non-linear coupling effects across CPU, memory. Recognizing that unexpected traffic surges derail static optimization paradigms, we introduce an adaptive scheduling algorithm leveraging dynamic Lyapunov optimization alongside a non-linear admission control policy. While simulation experiments across heterogeneous workloads demonstrate substantial improvements in throughput and queue stability, anomalies under extreme scenarios suggest that minor system biases might trigger localized bottlenecks, hinting at latent trade-offs between instantaneous responsiveness and long-term structural equilibrium. Considering these fluctuating factors, our theoretical boundary proofs contribute a rigorous foundation for modern cloud-native architectures, though further research is needed to fully reconcile state-space explosions in ultra-large-scale deployments.