Title: Randomized Algorithms for Robust Routing and Adaptive Duty Cycling
1Randomized Algorithms for Robust Routing and
Adaptive Duty Cycling
- Alvise Bonivento
- Dragan Petrovic
- Rahul Shah
2Overview
- Motivation for Randomized Algorithms
- Random Duty Cycling
- Randomized Routing
- System Level Perspective
- Results
- Conclusion
3Randomness Love it or Leave it
- Inherent Randomness
- Channels are unreliable
- Changing multipath environment
- Short time constants
- Nodes are unreliable
- May move
- New nodes
- May run out of energy
- Added Randomness
- Nodes are duty cycled to preserve energy
Randomized Sleep Discipline Randomized Routing
4Randomized Sleep Discipline
- SLEEP IF YOU CAN
- Maintain connectivity
- If the node is not necessary, goes to sleep and
saves power
For how long should the node be allowed to sleep
?
- Given
- Loss rate
- Delay constraint
- Data generation requirement
- Our Solution
- Adaptive
- Traffic node density
- Random
- Exponentially distributed sleeping times.
- Avoid phase synchronization.
5Exploiting density EQUIVALENCE
Geographical routing Forward packet to the first
available node in an adjacent block closer to the
destination
- Nodes know
- Their own location
- The destinations location
6Exponential Sleeping Times
- Memoryless analytically malleable
- Many nodes doing little work each equivalent to
few nodes doing a lot of work each - At infinite density, sum of renewal processes
converges to Poisson
7Region-based opportunistic routing
- Different forwarding regions
- Sector
- Annulus
- Lens optimal
- Opportunistic routing
- Network specifies forwarding region
- MAC chooses next-hop based on connectivity
source
controller
Rin
Lens Minimum distance of progress (Rin)
8System Level Design
- Merging Randomized Algorithms in a Randomized
Stack - Mathematical Model of the Protocol
- Cross Optimization
- Protocol Synthesis
9System Level Perspective
constraints
performances
- Constraints End-to-End delay
- Cost Energy consumption
- Optimization space
- Number of hops
- Hopping distance
- Sleeping parameters
10Refine Abstract
Refine Constraints
Given as a specification
Easier to manage and verify
End to End delay
Per-hop constraints
CONSTRAINT EQUATION
Probabilistic delay more general
Abstract Performances
- Energy spent for each transmission
- Energy spent for each wake up
- Traffic rate
- Wake up rate
- Roll-off factor
Total Energy Consumption as a function of the
number of hops
COST FUNCTION
Constrained Optimization Problem
11Optimization
- Optimum number of hops and hopping distance can
be determined - In some special cases a closed solution is
possible - Otherwise a simple iterative algorithm
- Optimum sleeping discipline parameters as a side
result
We have extended it to
- Arbitrary node layouts
- Arbitrary traffic patterns
12Example
Constraint on average delay
Power v. of hops for avg. delay constraints
Power Consumption
PicoRadio
Number of Hops
Optimum number of hops
13Verification
- Use theoretical model for Protocol Synthesis
- Generate Sleep parameters
- Generate Routing parameters
- Cross Optimization
- How close are we to reality? Verification
- Implement Randomized Stack
- Determine optimal parameters via simulations
- Compare with model prediction
14Theory vs. Simulations
Optimum number of hops for different network
size (average delay)
15Theory vs. Simulations
Optimum number of hops for different delay
constraints (average delay)
Results match
Protocol Synthesis
16Conclusions
- WSN is inherently random
- Randomized Protocols for ensuring Robustness
- Randomized Sleep
- Randomized Routing
- System Level Design Protocol Model
- Cross Optimization
- Parameters tuning
- Sleep parameters
- Transmission range
- Protocol Synthesis
Next Step MAC issues