Before revision:  To address this issue, we first develop a simple greedy policy called Delay-based Queue-Side-Greedy (D-QSG ) with a lower complexity O(n ^3 ), and rigorously prove that D-QSG not only achieves throughput optimality, but also guarantees near-optimal rate-function-based delay performance.
After revision:  To address this issue, we first develop a simple greedy policy called Delay-based Queue-Side-Greedy (D-QSG ) with a lower complexity O(n ^3 ), and rigorously prove that D-SSG not only achieves throughput optimality, but also guarantees near-optimal rate-function-based delay performance.