Scalable wake-up of multi-channel single-hop radio networks

Abstract

We consider single-hop radio networks with multiple channels as a model of wireless networks. There are n stations connected to b radio channels that do not provide collision detection. A station uses all the channels concurrently and independently. Some k stations may become active spontaneously at arbitrary times. The goal is to wake up the network, which occurs when all the stations hear a successful transmission on some channel. Duration of a waking-up execution is measured starting from the first spontaneous activation. We present a deterministic algorithm for the general problem that wakes up the network in O(k log 1/b k log n) time, where k is unknown. We give a deterministic scalable algorithm for the special case when b > d log log n, for some constant d > 1, which wakes up the network in O( k b log n log(b log n)) time, with k unknown. This algorithm misses time optimality by at most a factor of O(log n(log b+log log n)), because any deterministic algorithm requires Ω( k b log n k ) time. We give a randomized algorithm that wakes up the network within O(k 1/b ln 1 ǫ ) rounds with a probability that is at least 1 − ǫ, for any 0 < ǫ < 1, where k is known. We also consider a model of jamming, in which each channel in any round may be jammed to prevent a successful transmission, which happens with some known parameter probability p, independently across all channels and rounds. For this model, we give two deterministic algorithms for unknown k: one wakes up the network in time O(log −1 ( 1 p ) k log n log 1/b k), and the other in time O(log −1 ( 1 p ) k b log n log(b log n)) but assuming the inequality b > log(128b log n), both with a probability that is at least 1 − 1/poly(n).