Nonlinear Optimization of Computational Resource Allocation Under Time-Varying Workload Constraints

Abstract

Modern computational systems need to allocate computational resources among many workloads. The demand of each workload. The available computational capacity changes over time. This paper develops a continuous‑time optimization framework that takes into account the instantaneous capacity limits and the total workload service needs. The proposed model is a convex optimization problem. Its constraints depend on time and have a Volterra‑type shape. In the first proof, that the optimal resource allocation exists and is unique. Next,the developed a Karush–Kuhn–Tucker characterization to describe the optimal solution. The main contribution of this study is an explicit sensitivity result. It shows that changes in capacity and workload arrival patterns cause at most square‑root changes in the optimal allocation, provided a uniform Slater‑type feasibility condition holds. The derived Hölder stability constant is directly linked to the workload dimension, the planning horizon, the bound on capacity, how the objective function is conditioned and the feasibility margin. In addition, a temporal stability result is derived for a sequence of environments where system conditions change continuously. Numerical experiments confirm the theoretical sensitivity behaviour. Demonstrate how the feasibility margin influences the robustness of the resource allocation. The results give a foundation for assessing how robust and adaptable optimal computational resource allocation systems are when workload conditions vary over time.