Closed-Loop Modeling of the Frame Collision Probability under the IEEE 802.11b DCF

The frame collision probability is an important parameter of the performance modeling of the IEEE 802.11b DCF. This probability has long been assumed to be independent to the medium access control. The validity of this assumption has not been scrutinized. In this paper, we modeled the 802.11b DCF by a closed-loop model. The transient expressions of the collision probability is first derived from the closed-loop model, and its time-invariant expression is further derived. The time-invariant expression is dependent only on the number of contending devices. The validity of our modeling is demonstrated by comparing the analytical results with the measurement results obtained from simulations. The analytical results closely approximate the measurement results.