In order to obtain both high resource utilization efficiency and the low queue delay under different traffic conditions in multiple users downlink wireless networks, we formulate the optimization objective for resource allocation as the maximization of the sum of the utility function in this paper. An algorithm for the efficient solution to the optimization problem is proposed using greedy mechanism that considers multiple users diversity in terms of time-varying dynamics including arrival rate, queue length and channel quality. The trade-off between efficiency and fairness is achieved by the proposed algorithm using a set of utility functions with respective to the average queue waiting time. Simulations are conducted to investigate the queue delay performance under different traffic load.