1. Monitoring Churn in Wireless Networks
TexPoint fonts used in EMF.
Read the TexPoint manual before you delete this box.: AAAAAAA

2. Motivation / Intro Network of sensor nodes:
Mobile Computing
Summer 2002
Motivation / Intro
Network of sensor nodes:
measuring certain properties of their environment
wireless, communicating on several channels
battery powered
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
Distributed Computing Group, Roger Wattenhofer

3. Model n nodes with IDs single-hop synchronized time slots t s r
Mobile Computing
Summer 2002
Model 3 1 5 12 2
n nodes with IDs
single-hop
synchronized time slots t s r
time
transmit / receive / sleep 1
energy 1 / 1 / 0
channel 1 t s
node 1
local computations free
channel 2
k channels
channel 1 r s
node 2
channel 2
no collision detection
channel 1 r s t
bounded message size
node 3
channel 2
O(1) IDs
Distributed Computing Group, Roger Wattenhofer

4. Model cont’d Nodes may join or crash at any time
Mobile Computing
Summer 2002
Model cont’d 3 1 5 2 3 1 5 12 2
Nodes may join or crash at any time
churn = joins and crashes 7
burst = large number of joins and crashes in short time
Adversary:
May let nodes crash or join in order to make an algorithm fail
Distributed Computing Group, Roger Wattenhofer

5. Every node must know the IDs of all nodes currently in the network
Mobile Computing
Summer 2002
Goal
Every node must know the IDs of all nodes currently in the network 1 2 3 5 7 12
Distributed Computing Group, Roger Wattenhofer

6. Mobile Computing
Summer 2002
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
 on average only constant rate of churn tolerable per time slot
 Ω(b) time slots necessary to learn about b joins / crashes
 every node needs Ω(b) energy units to learn about b joins / crashes
Distributed Computing Group, Roger Wattenhofer

7. Results Our Monitoring Algorithm:
Mobile Computing
Summer 2002
Results
Our Monitoring Algorithm:
tolerates churn bursts in any order of magnitude
is deterministic except for detection of joining nodes
handles asymptotically maximum average rate of churn tolerable in this model
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)
needs Θ(n/log n) channels
Distributed Computing Group, Roger Wattenhofer

8. Results cont‘d Our Monitoring Algorithm:
Mobile Computing
Summer 2002
Results cont‘d
Our Monitoring Algorithm:
can get by with less than Θ(n/log n) channels:
k channels available  time
Distributed Computing Group, Roger Wattenhofer

9. Monitoring Algorithm burst size is assumed to be b'=log n
Mobile Computing
Summer 2002
Monitoring Algorithm
burst size is assumed to be b'=log n
2b'+2 nodes in each set
Θ(n/b') sets
nodes partitioned into n/(2b'+2)-1 sets
each set detects crashed and joined nodes on its own channel
disseminate information to all nodes 1 2
... 7 12 3 13 34
all nodes update ID table
double b' if algo did not work
Distributed Computing Group, Roger Wattenhofer

10. Crash Detection I am still here! I am still here! I am still here!
Mobile Computing
Summer 2002
Crash Detection
nodes send „I am here“ messages
I am still here!
I am still here!
I am still here!
min(2b'+2,n) time slots necessary
Distributed Computing Group, Roger Wattenhofer

11. Mobile Computing
Summer 2002
Join Detection
joiners send join requests to with S1 with probability 1/b'
I want to join!
Set S1
I want to join!
b' in Ω(b)  in constant number of rounds at least 1 joiner
Distributed Computing Group, Roger Wattenhofer

12. Information Dissemination
Mobile Computing
Summer 2002
Information Dissemination
every set becomes vertex of balanced binary tree
depth log n
every set forwards information on node v with smallest ID first
information on v disseminated after O(log n) time slots
all information disseminated after O(log n + b') time slots
Distributed Computing Group, Roger Wattenhofer

13. Monitoring Algorithm Step Time b' = log n O(1) partitioning O(1)
Mobile Computing
Summer 2002
Monitoring Algorithm
Step
Time
b' = log n
O(1)
partitioning
O(1)
crash detection
O(min(b', n))
log(b/log n) times
runtime
O(b + log n)
join detection
O(b' + log n)
dissemination
O(b' + log n)
update ID table
O(1) 1 2
... 7 12 3 13 34
double b'
O(1)
Distributed Computing Group, Roger Wattenhofer

14. What if critical nodes crash?
Mobile Computing
Summer 2002
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
Distributed Computing Group, Roger Wattenhofer

15. Conclusions & Future Work
Mobile Computing
Summer 2002
Conclusions & Future Work
Model t s r
Lower Bounds
Monitoring Algorithm
Future Work: Multi-hop
Distributed Computing Group, Roger Wattenhofer

16. Thank You! Questions & Comments?
TexPoint fonts used in EMF.
Read the TexPoint manual before you delete this box.: AAAAAAA