According to one aspect, a method that includes some of the teachings of the present subject technology reduces congestion in a communications network. The method includes, inter alia, letting a persistence value be a function of N, even when ASC=0, and also a function of a constant the emergency services access parameter W, such that the persistence value P0(N) ranges between P1(N) and 1 when the emergency services access parameter W ranges from a first value (e.g. 0) to a second value (e.g. 1), where P(N)=2−(N−1) and where N is transmitted in a system information message. A comparator allows a user to access the communications network only if a random/pseudorandom number is less than the persistence value. Other aspects, such as a computer program product, also reduce congestion in a communications network.