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Providing wireless service without spatial restriction has been realized due to rapid growth of IEEE 802.11 based wireless technologies. Recently, available bandwidth ("AB") estimation of the wireless medium has received much attention with the widespread use of real-time multimedia applications which requires certain level of QoS (Quality of Service) guarantees. In this paper, we propose an Accurate Passive Bandwidth Estimation (APBE) considering a factor which has been ignored by the previous works: the RTS (Request to send) and CTS (Clear to send) overheads in estimating the "AB". APBE performs "AB" estimation with correct measurement of i) the proportion of DIFS and back-off, ii) packet collision probability, iii) acknowledgement delay, and iv) channel idle time in the measurement period and additionally considers the overhead caused by the RTS and CTS procedure. The performance of APBE has been compared with the previous works and from the simulation results, it is clear that APBE outperforms the existing research in terms of accuracy. Based on correct estimation of "AB" in wireless networks, efficient network resource management, QoS guarantees of multimedia applications, and effective admission control can be realized.