Adversarial Multiple Access Channel with Individual Injection Rates

Abstract

We study deterministic distributed broadcasting on a synchronous multiple-access channel. Packets are injected into stations by a window-type adversary that is constrained by an individual injection rate of each station and a window w. We investigate what queue sizes and packet latency can be achieved with the maximum throughput of one packet per round. A protocol knows the number n of all the stations but does not know the window nor the individual rates of stations. We study the power of full sensing and acknowledgment based protocols as compared to general adaptive ones. We show that individual injection rates make it possible to achieve bounded packet latency by full sensing protocols, what is in contrast with the model of global injection rates for which stability and finite waiting times are not achievable together by general protocols. We show that packet latency is $\Omega\bigl(w\,\frac{\log n}{\log w}\bigr)$ when w ≤ n and it is Ω(w) when w > n. We give a full sensing protocol for channels with collision detection and an adaptive one for channels without collision detection that achieve ${\mathcal O}({\rm min}(n+w,w\log n))$ packet latency. We develop a full sensing protocol for a channel without collision detection that achieves ${\mathcal O}(n+w)$ queues and ${\mathcal O}(nw)$ packet latency.