Before revision:  To address this issue, we develop a simple greedy policy called Delay-based Server-Side-Greedy (D-SSG) with a lower complexity O(n^2) \lower  , and rigorously prove that D-SSG not only achieves throughput optimality, but also guarantees near-optimal rate-function-based delay performance.
After revision:  To address this issue, we develop a simple greedy policy called Delay-based Server-Side-Greedy (D-SSG) with a lower complexity O(n^2) \lower complexity 2n^2+2n , and rigorously prove that D-SSG not only achieves throughput optimality, but also guarantees near-optimal rate-function-based delay performance.