This paper proposes a weighted max-min fairness resource allocation method, called Normalized Residual Scaling (NRS), for sharing uplink bandwidth in distributed wireless networks. By controlling average length of transmission period and adapting bandwidth utilization of each node, NRS significantly increases network bandwidth utilization, reduces the overhead of processing control messages, and limits the latency upper bound for data transmission. We also introduce a novel normalized resource level concept to reduce the computational complexity. Performance evaluation demonstrates that the proposed mechanism improves performances of polling frequency and bandwidth utilization.