1. ETH Zurich – Distributed Computing Group Jasmin Smula 1ETH Zurich – Distributed Computing – www.disco.ethz.ch Stephan Holzer Yvonne Anne Pignolet Jasmin Smula Roger Wattenhofer TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA A A A Monitoring Churn in Wireless Networks

2. ETH Zurich – Distributed Computing Group Jasmin Smula 2 Motivation / Intro Network of sensor nodes: Nodes might fail / nodes may be added All nodes should be aware of all present nodes with small delay with little energy consumption using few channels for communication wireless, communicating on several channels battery powered measuring certain properties of their environment

3. ETH Zurich – Distributed Computing Group Jasmin Smula 3 Model n nodes with IDs single-hop synchronized time slots transmit / receive / sleep k channels no collision detection energy 1 / 1 / 0 1011000101 3 1 5 12 2 t sstt s srsr time t t s t s t t s s node 1 node 2 node 3 channel 1 channel 2 channel 1 channel 2 channel 1 channel 2 O(1) IDs r r s rr s r r s r s r s t s t s s bounded message size local computations free

4. ETH Zurich – Distributed Computing Group Jasmin Smula 4 7 Model cont’d Nodes may join or crash at any time Adversary: May let nodes crash or join in order to make an algorithm fail 3 1 5 12 2 3 1 5 2 churn = joins and crashes burst = large number of joins and crashes in short time

5. ETH Zurich – Distributed Computing Group Jasmin Smula 5 Goal Every node must know the IDs of all nodes currently in the network 1235712

6. ETH Zurich – Distributed Computing Group Jasmin Smula 6 Simple Lower Bounds What time / energy is at least necessary in this model? every node can only receive one message per time slot containing at most a constant number of IDs  Ω(b) time slots necessary to learn about b joins / crashes  every node needs Ω(b) energy units to learn about b joins / crashes  on average only constant rate of churn tolerable per time slot

7. ETH Zurich – Distributed Computing Group Jasmin Smula 7 Results tolerates churn bursts in any order of magnitude Our Monitoring Algorithm: handles asymptotically maximum average rate of churn tolerable in this model needs Θ(n/log n) channels after each burst of size b it takes O(b + log n) time slots and O(b + log n) energy per node until all nodes have updated their ID table (optimal up to additive logarithmic term) is deterministic except for detection of joining nodes

8. ETH Zurich – Distributed Computing Group Jasmin Smula 8 Results cont‘d Our Monitoring Algorithm: can get by with less than Θ(n/log n) channels: k channels available  time.

9. ETH Zurich – Distributed Computing Group Jasmin Smula 9 Monitoring Algorithm burst size is assumed to be b'=log n nodes partitioned into n/(2b'+2)-1 sets each set detects crashed and joined nodes on its own channel disseminate information to all nodes all nodes update ID table double b' if algo did not work 2b'+2 nodes in each set Θ(n/b') sets 1 2... 7 12... 3 13 34

10. ETH Zurich – Distributed Computing Group Jasmin Smula 10 Crash Detection nodes send „I am here“ messages I am still here! min(2b'+2,n) time slots necessary

11. ETH Zurich – Distributed Computing Group Jasmin Smula 11 Join Detection Set S 1 joiners send join requests to with S 1 with probability 1/b' I want to join! b' in Ω(b)  in constant number of rounds at least 1 joiner

12. ETH Zurich – Distributed Computing Group Jasmin Smula 12 Information Dissemination every set becomes vertex of balanced binary tree every set forwards information on node v with smallest ID first information on v disseminated after O(log n) time slots depth log n all information disseminated after O(log n + b') time slots

13. ETH Zurich – Distributed Computing Group Jasmin Smula 13 Monitoring Algorithm b' = log n partitioning crash detection dissemination update ID table double b' log(b/log n) times runtime O(b + log n) Time O(1) O(min(b', n)) O(b' + log n) Step 1 2... 7 12... 3 13 34... join detection O(b' + log n)

14. ETH Zurich – Distributed Computing Group Jasmin Smula 14 What if critical nodes crash? in each set node which is responsible for communication with other sets = representative all other nodes replacements replacements take over if representative does not send delay of at most b' still runtime of O(b' + log n) per round

15. ETH Zurich – Distributed Computing Group Jasmin Smula 15 Conclusions & Future Work Model t sstt s srsr Lower Bounds Monitoring Algorithm Future Work: Multi-hop

16. ETH Zurich – Distributed Computing Group Jasmin Smula 16ETH Zurich – Distributed Computing – www.disco.ethz.ch Stephan Holzer Yvonne Anne Pignolet Jasmin Smula Roger Wattenhofer Thank You! Questions & Comments? TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA A A A