Upper bound of loss probability in an OFDMA system with randomly located users

For OFDMA systems, we find a rough but easily computed upper bound for the probability of loosing communications by insufficient number of sub-channels on downlink. We consider as random the positions of receiving users in the system as well as the number of sub-channels dedicated to each one. We use recent results of the theory of point processes which reduce our calculations to the first and second moments of the total required number of sub-carriers.