Ultimate instability of exponential back-off protocol for acknowledgment-based transmission control of random access communication channels

When several users simultaneously transmit over a shared communication channel, the messages are lost and must be retransmitted later. Various protocols specifying when to retransmit have been proposed and studied in recent years. One protocol is "binary exponential back-off," used in the local area network Ethernet. A mathematical model with several idealizations (discrete time slots, infinite users, no deletions) is shown to be unstable in that the asymptotic rate of successful transmissions is zero, however small the arrival rate.