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ETH Zurich – Distributed Computing Group Jasmin Smula 1ETH Zurich – Distributed Computing – www.disco.ethz.ch

Stephan HolzerYvonne Anne Pignolet

Jasmin SmulaRoger Wattenhofer

Monitoring Churn in Wireless Networks

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

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

10 1 100 0 101

3

15

122

tssttss r s r time

tt

st

s tt

ssnode 1

node 2

node 3

channel 1

channel 2

channel 1

channel 2

channel 1

channel 2

O(1) IDs

rr s

r rs r

rs

r s r st

st

s s• bounded message

size

• local computations free

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

15

122

3

15

2churn = joins and crashes

burst = large number of joins and crashes in short time

ETH Zurich – Distributed Computing Group Jasmin Smula 5

Goal

Every node must know the IDs of all nodes currently in the network

1 2 3 5 7 12

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

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

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 .

nb

knbO

loglog

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

ETH Zurich – Distributed Computing Group Jasmin Smula 10

Crash Detection

• nodes send „I am here“ messagesI am still

here!I am still here!

I am still here!

• min(2b'+2,n) time slots necessary

ETH Zurich – Distributed Computing Group Jasmin Smula 11

Join Detection

Set S1

• joiners send join requests to with S1 with probability 1/b'

I want to join!

I want to join!

• b' in Ω(b) in constant number of rounds at least 1 joiner

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

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

runtimeO(b + log n)

Time

O(1)

O(1)

O(1)

O(1)

O(min(b', n))

O(b' + log n)

Step

1 2 ......

7 12 ...3 13 34...

• join detection O(b' + log n)

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

ETH Zurich – Distributed Computing Group Jasmin Smula 15

Conclusions & Future Work

• Model tssttss r s r

• Lower Bounds

• Monitoring Algorithm

• Future Work: Multi-hop

ETH Zurich – Distributed Computing Group Jasmin Smula 16ETH Zurich – Distributed Computing – www.disco.ethz.ch

Stephan HolzerYvonne Anne Pignolet

Jasmin SmulaRoger Wattenhofer

Thank You!Questions & Comments?