Consensus and Collision Detectors in Wireless Ad Hoc Networks

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Consensus and Collision Detectors in Wireless
Ad Hoc Networks
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Consensus and Collision Detectors in Wireless
Ad Hoc Networks
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Consensus and Collision Detectors in Wireless
Ad Hoc Networks
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Wireless Ad Hoc Networks
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Wireless Ad Hoc Networks

• Challenges
• Unknown number
• No unique ids
• Fault-prone
• Collision-prone communication

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Wireless Ad Hoc Networks

• Challenges
• Unknown number
• No unique ids
• Fault-prone
• Collision-prone communication

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• How to solve problems
• in wireless ad hoc networks with
• unreliable communication?

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• How to solve consensus
• in wireless ad hoc networks with
• unreliable communication?

• Consensus
• Fundamental agreement problem
• in fault-tolerant computation

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Outline

• Introduction
• Collision-prone Networks
• Collision Detectors
• Algorithms and Lower Bounds
• Conclusions

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• Single-hop network
• Synchronous rounds
• Unknown number of nodes
• No unique identifiers

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Single Broadcast
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Single Broadcast
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Ethernet Collisions
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Ethernet Collisions
?
?
?
?
?
?
?
?
?
?
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More Realistic Collisions
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More Realistic Collisions
?
?
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Unfortunately

• Consensus is impossible with
• non-uniform collisions.

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Collision Detection
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Collision Detection
!
!
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!
!
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Collision Detection
!
!
!
!
!

• Receiver-centric
• How many messages lost?
• Who sent lost message?

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Agreement with Collision Detectors

• Collision detectors provide hints about possibly
  incomplete information
• Know when it is not safe to decide
• When is it safe to decide?
• Acks Hear the same value from everybody
• Nacks Veto the decision if might lead to safety
  violation
• Question Acks or Nacks?

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Acks vs. Nacks

• Acks
• Everyone communicates
• Too much contention
• Nacks
• Only communicate if problem detected
• Less contention
• Nacks allow for adaptive algorithms

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Collision Detector Classes
If ?½ messages are lost, then report collision.
If all messages are lost, then report a collision.
Consensus is impossible with ?C
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Consensus with CD
V is the value domain
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Consensus with CD
(Always) Accurate
V is the value domain
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Consensus with CD
Eventually Accurate
V is the value domain
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Eventual Collision Freedom

• Eventually, if only 1 node broadcasts

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Eventual Collision Freedom

• Eventually, if only 1 node broadcasts, then no
  collision occurs.
• Use a contention manager.
• Outputs active/passive at each node.
• Implementation randomized backoff, e.g.

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Eventual Collision Freedom

• Eventually, if only 1 node broadcasts, then no
  collision occurs.
• Use a contention manager.
• Outputs active/passive at each node.
• Implementation exponential backoff, e.g.

• If b nodes broadcast, then no collisions.
• b is an unknown MAC layer constant
• b could be as low as 1

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Consensus with CD
V is the value domain
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Consensus with CD
V is the value domain
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Consensus with CD
V is the value domain
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Consensus with ?AC

• Algorithm executes in super-rounds
• Round 1
• Active nodes vote on a value.
• Round 2
• Veto round.
• Anybody can veto.

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Consensus with ?AC
v2
v1
v2
Round 1
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Consensus with ?AC
v2
v1
v2
Round 1
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Consensus with ?AC
v2
v1
v1
v2
Round 1
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Consensus with ?AC
v1
v1
v2
Round 1
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Consensus with ?AC
v1
v1
v2
v2
Round 1
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Consensus with ?AC
v1
v1
v2
Round 1
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Consensus with ?AC
v1
v1
v2
v2, ?
Round 1
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Consensus with ?AC
v1
v1
v1
v1
v2
v2
Round 1
Round 2
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Consensus with ?AC
v1
v1
veto
v1
v1
veto
v2
v2

• Continue

Round 1
Round 2
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Consensus with ?AC
v1
v1
v2
Round 1
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Consensus with ?AC
v1
v1
v2
Round 1
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Consensus with ?AC
v1
v1
v1
v2
Round 1
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Consensus with ?AC
v1
v1
v2
Round 1
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Consensus with ?AC
v1
v1
v2
v1, ?
(false positive)
Round 1
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Consensus with ?AC
v1
v1
v1
v1
v2
v2
Round 1
Round 2
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Consensus with ?AC
v1
v1
veto
v1
v1
veto
v2
v2

• Continue

Round 1
Round 2
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Consensus with ?AC
v1
v1
v2
Round 1
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Consensus with ?AC
v1
v1
v2
Round 1
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Consensus with ?AC
v1
v1
v1
v2
Round 1
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Consensus with ?AC
v1
v1
v2
Round 1
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Consensus with ?AC
v1
v1
v2
v1
Round 1
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Consensus with ?AC
v1
v1
v1
Round 1
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Consensus with ?AC
v1
v1
v1
v1
v1
v1
Round 1
Round 2
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Consensus with ?AC
v1
v1
Decides at most 3 rounds after stabilization S
tabilization accuracy and collision-freedom
v1
v1
v1
v1
Decide v1
Round 1
Round 2
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Consensus with CD
V is the value domain
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Consensus with CD
V is the value domain
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Consensus with ½-AC
If gt½ messages are lost, then report collision

• ½-complete, accurate collision detector

2r broadcast schedules for the first r rounds V
possible values For k lt log(V), at most V/2
broadcast schedules to follow ? Exists two values
resulting in the same broadcast schedule of
length k
v1
v2
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Maj-?AC Consensus Simulations
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Global Agreement

• Local consensus as a building block

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Global Agreement

• Local consensus as a building block
• Solve locally

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Global Agreement

• Local consensus as a building block
• Solve locally

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Global Agreement

• Local consensus as a building block
• Solve locally
• Propagate outcome

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Global Agreement

• Local consensus as a building block
• Solve locally
• Propagate outcome
• Decide when heard from all cells

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Simulations of Global Agreement
Fixed Diameter 5 hops
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Simulations of Global Agreement
4 hops
10 hops
Fixed Density 0.02667 nodes/m2
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Conclusions

• Realistic framework for wireless networks
• Non-uniform collision patterns
• Eventual collision freedom
• Contention manager
• Collision detection

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Conclusions
(Always) Accurate is hard to implement
??
0-complete is easy to implement
V is the value domain
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Questions?
V is the value domain