Deterministic contention resolution on a shared channel

A shared communication channel (also known as a multiple access channel) is among the most popular and widely studied models of communication and distributed computing. In this model, stations are able to communicate by transmitting and listening to a shared channel. A fundamental problem, called contention resolution, is to allow any station to successfully deliver its message by resolving the conflicts that arise when several stations transmit simultaneously on the channel. Despite a long history, many fundamental questions remain open in the realistic scenario when up to k stations out of n join the channel at different times. In this work we explore the impact of asynchrony, knowledge (or linear estimate) of contenders, and acknowledgments, on latency and channel utilization of non-adaptive deterministic algorithms. We show that if the number of contenders k (or a linear upper bound on it) is known and the stations switch-off after acknowledgment of their successful transmissions, the channel admits efficient solutions. In the same settings, we show that the ignorance of contention k makes the channel nearly quadratically less efficient, even if the stations could switch-off after acknowledgments. We present an algorithm which nearly matches this complexity (for unknown k) which is achieved even if acknowledgments are not provided. We show how the above algorithm could be further improved if stations could switch off upon acknowledgment. Surprisingly, our results imply an exponential impact of knowledge of contention on deterministic utilization of asynchronous channel by deterministic algorithms - it is known that for synchronized channel this feature does not influence asymptotically the channel utilization. The second implication concerns the impact of acknowledgments - they exponentially improve deterministic channel utilization if (some estimate of) k is known, unlike in the case of randomized algorithms where the improvement is only polynomial, while they are not particularly helpful in case of unknown contention. Finally, note that non-adaptive algorithms use fixed transmission schedules, which could be naturally translate into codes in the radio or beeping model - in this context our results indicate under which conditions such codes could be efficient.