### 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 that wakes up a network in O(klog1/b klog n) time, where k is unknown. We give a deterministic scalable algorithm for the special case when b> dlog log n, for some constant d>. 1, which wakes up a network in O(kblog nlog (blog 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 a network within O(k^{1/b} ln 1/ε) rounds with a probability that is at least 1 - ε, for any 0 < ε < 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 a 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 (blog n)) when the inequality b> log (128 blog n) holds, both with probabilities that are at least 1 - 1/poly( n).

Original language | English (US) |
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Pages (from-to) | 186-201 |

Number of pages | 22 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 615 |

DOIs | |

State | Published - Feb 15 2016 |

Externally published | Yes |

Event | 18th International Conference on Principles of Distributed Systems, OPODIS 2014 - Cortina d’Ampezzo, Italy Duration: Dec 16 2014 → Dec 19 2014 |

### Keywords

- Deterministic algorithm
- Distributed algorithm
- Multi-channel
- Multiple access channel
- Radio network
- Randomized algorithm
- Synchronization
- Wake-up

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*615*, 186-201. https://doi.org/10.1016/j.tcs.2015.11.046