Transmission Control for Stability of Aloha Networks with Multiple Transmitter-Receiver Pairs

Slotted Aloha has been widely adopted in various communication systems, while its stability performance has long been observed as being sensitive to the setting of transmission probabilities. For stability analysis of Aloha networks with multiple transmitter-receiver (T-R) pairs, the focus of previous studies has been placed on characterization of the maximum input rate of T-R pairs, below which the network can be stabilized under any given topology. With a fixed and identical transmission probability for all T-R pairs, nevertheless, network stability is often found to be unachievable, as part of transmitters would become unstable regardless of how small the traffic input rate is. As we will demonstrate in this paper, to stabilize the whole network, transmission probabilities of T-R pairs should be properly adjusted according to their traffic input rates and locations. Specifically, by establishing the fixed-point equations of the steady-state probabilities of successful transmissions of Head-of-Line (HOL) packets, the service rates of transmitters' queues can be obtained, based on which the operating region of transmission probabilities for achieving stability can further be characterized. Simulation results corroborate that all the T-R pairs can be stabilized by choosing transmission probabilities from the region, which highlights the importance of proper transmission control based on the traffic input rates and network topology for Aloha networks.