Closed-form expression for the collision probability in the IEEE EPON registration scheme

We derive a closed-form expression for the message collision probability in the IEEE 802.3ah Ethernet passive optical network (EPON) registration scheme. The expression obtained, although based on an approximation, shows a good match with simulation results. We use the results of our analysis to compute the size of the most efficient contention window and the most efficient number of nodes serviced by a given window size.