In IEEE 802.11e, a centralized polling based channel access mechanism is provided for the quality-of-service (QoS) provision of real-time applications. In order to improve band-width efficiency of polling for uplink variable bit rate (VBR) sources, it has previously been proposed in, e.g., ARROW, that the amount of backlogged traffic is fed back for exact bandwidth allocation. However, due to that the feedback and the bandwidth allocation are performed separately in two different polls, transmission latency incurred by packets could cause them to violate delay constraint. In this paper, a four-way-polling scheduler is first proposed by directly inquiring buffer occupancy information of an uplink station during a poll. Theoretical analysis is then performed to evaluate the performance of both the proposed scheduler and ARROW. From both analytical and ns-2 simulation results, it is shown that packet loss rates can effectively be reduced and more capacity can thereby be obtained under the proposed scheduler, as compared with ARROW.