The paper utilizes a single server, single queue, FIFS system model to estimate the parameters describing the buffering occurring in the access points of an IEEE 802.11b wireless LAN. We use experimentation to obtain our model of the access point and buffer-related parameters. Using our test design, we are able to extract the parameters of an analytic equation giving the average service time of a packet as a function of packet IP payload. We focus on buffer size estimation and adaptation. The major observation is that the buffer adapts its size to the different loads. Adaptation occurs at cut-off points of losses by increasing the buffer allocated size. We designed and implemented an algorithm which checks when losses occur and calculates the number of packets in the buffer just before loss. A key result is that different access points have different initially allocated buffer sizes.