Throughput of Unslotted ALOHA Channels with Arbitray Packet Interarrival Time Distributions

An unslotted ALOHA channel with dissimilar users and each user having an arbitrary distribution of packet interarrival time, is analyzed for its throughput. It is shown that the throughput behavior of an unslotted channel with a very large number of users is the same as that of Abramson's Poisson channel. When each user transmits many packets almost in succession and then remains silent for a long period, the throughput of the unslotted channel is shown to approach that of the slotted channel. For unslotted channels in which the dead time between successive packet transmissions due to each user exceeds twice the packet duration, the throughput is shown to be independent of the nature of the packet interarrival time distribution of any user, depending only on the average rate at which users transmit packets.