Time and Energy Efficient Contention Resolution in Asynchronous Shared Channels (2209.14140v1)

Abstract: A number of stations, independently activated over time, is able to communicate by transmitting and listening to a shared channel in discrete time slots, and a message is successfully delivered to all stations if and only if its source station is the only transmitter at a time. Despite a vast amount of work in the last decades, many fundamental questions remain open in the realistic situation where stations do not start synchronously but are awaken in arbitrary times. In this work we present a broad picture of results for the fundamental problem of Contention resolution, in which each of the contending stations needs to broadcast successfully its message. We show that adaptive algorithms or algorithms with the knowledge of the contention size $k$ achieve a linear $O(k)$ message latency even if the channel feedback is restricted to simple acknowledgements in case of successful transmissions and in the absence of synchronization. This asymptotically optimal performance cannot be extended to other settings: we prove that there is no non-adaptive algorithm without the knowledge of contention size $k$ admitting latency $o(k\log k/(\log\log k)^2)$. This means, in particular, that coding (even random) with acknowledgements is not very efficient on a shared channel without synchronization or an estimate of the contention size. We also present a non-adaptive algorithm with no knowledge of contention size that almost matches the lower bound on latency. Finally, despite the absence of a collision detection mechanism, we show that our algorithms are also efficient in terms of energy, understood as the total number of transmissions performed by the stations during the execution.