  Slotted Aloha has been widely adopted in various communication networks. Yet
if the transmission probabilities and traffic input rates of transmitters are
not properly regulated, their data queues may easily become unstable. For
stability analysis of Aloha networks with multiple receivers, the focus of
previous studies has been placed on the maximum input rate of each transmitter,
below which the network is guaranteed to be stabilized under any given
topology. By assuming a fixed and identical transmission probability across the
network, however, network stability is found to be unachievable when the input
rate exceeds zero.
  As we will demonstrate in this paper, the key to stabilizing the network lies
in proper selection of transmission probabilities according to the traffic
input rates and locations of all transmitters and receivers. Specifically, for
an Aloha network with multiple capture receivers, by establishing and solving
the fixed-point equations of the steady-state probabilities of successful
transmissions of Head-of-Line (HOL) packets, the exact service rates of all
transmitters' queues are obtained, based on which the operating region of
transmission probabilities for achieving stability and the stability region of
input rates are further characterized. The results are illustrated in various
scenarios of multi-cell and ad-hoc networks. Simulation results validate the
analysis and corroborate that the network can be stabilized as long as the
traffic input rates are within the stability region, and the transmission
probabilities are properly adjusted according to the traffic input rates and
network topology.
