On the Time-Invariant Feature of the Frame Collision Probability Under IEEE 802.1lb DCF

The frame collision probability is an important parameter in modeling the performance of the IEEE 802.11b DCF. This probability has long been assumed as a value that is determined by the channel characteristics and is 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. In order to make this modeling versatile, the closed-loop model is developed virtually assumption-free. The transient expressions of the collision probability is first derived from the closed- loop model, and then its time-invariant expression is further derived. The time-invariant expression is dependent only on the number of contending stations. 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.