On the cutoff point for pairwise enabling for infinite users in a multiaccess system

Consider a multiaccess channel shared by an infinite set of users, each of which, independently, has a message to transmit with probability p. Pairwise enabling is the scheduling algorithm which enables the users to transmit by pairs, and, if a collision occurs, it lets the two users transmit separately in the next two time slots. M.L. Molle (see ibid., vol.36, no.5, p.1127-33, 1990) showed that pairwise enabling is optimal for 0.5⩽p⩽1/√2 and is not optimal for p⩽0.430. Let p⁰ denote the cutoff point for pairwise enabling, i.e. pairwise enabling is optimal for p ⁰⩽p⩽1/√2 but not optimal for p⩽p⁰. In the present work, Molle´s results are improved by showing that 0.4300<p⁰<0.4745. In addition, it is shown that 0.4400<p⁰ holds when it is assumed that the 1-feedback also reveals the identity of the transmitter