This paper presents a novel approach for allocating resources in systems with multiple accelerators. It has three main contributions. First, a new model based on Birkhoff's representation theory in capturing the ordering properties of resource allocation requests (RArs). Second, an effective technique for resource allocation based on this model, targeting systems with multiple accelerators. Third, the evaluation of the proposed approach for Maxeler MPC-X multi-accelerator systems, demonstrating time-efficiency and 30%-50% failure-rate decrease (FRD) on random input dataset.