Contention resolution on a restrained channel

We examine deterministic contention resolution on a multiple-access channel when packets are injected continuously by an adversary to the buffers of $n$ available stations in the system, arbitrarily at rate at most $\rho$ packets per round. The aim is to successfully transmit packets and maintain system stability, that is, bounded queues, even in infinite executions. The largest injection rate for which a given contention resolution algorithm guaranties stability is called (algorithm's) throughput. In contrast to the previous work, we consider a channel in which there is a strict limit $k$ on the total number of stations allowed to transmit or listen to the channel at a given time, that can never be exceeded; we call such channel a $k$-restrained channel. We construct adaptive and full sensing protocols with optimal throughput 1 and almost optimal throughput $1-1/n$, respectively, in a constant-restrained channel. By contrast, we show that restricted protocols based on schedules known in advance obtain throughput at most $\min\{\frac{k}{n}, \frac{1}{3\log n}\}$. We also support our theoretical analysis by simulation results of our algorithms in systems of moderate, realistic sizes and scenarios, and compare them with popular backoff protocols.