Bio-inspired network protocols€¦ · Stimergy (deposition of pheromone). Bio-inspired network protocols. Objectives Ants Slime mold Physarum polycephalum Summary A heuristic for

Objectives Ants Slime mold Physarum polycephalum Summary

Bio-inspired network protocols

Department of Mathematical SciencesUniversity of Delaware

Supported byArmy SBIR A072-074-1669, NSF CCF-0726556 and CCF-0829748

November 5, 2013



Graduate students

Wei Chen

Rui Fang

Zequn Huang

Jeremy Keffer

Ke Li

Claudio Torres



What is swarm intelligence?



Modeling and analysis objectives

Construct a complete mathematical model of a basicant-based routing protocol (BARP) and slime mold basedsensor network protocols.

Analyze the model to extract design principles.

Compare with QualNet simulations.

Refine/improve the model.



Individual ant properties

Lifespan: 1-2 years.

Individually inept.

Nearly blind.Fast movers and carriers.Can lay chemical trails of pheromones and detecttrails.Can consume food and regurgitate food throughantennation.

Very simple programming.earching for food (foraging), carrying food,recruiting others, alarm, attack.





Individually inept.







Individually inept.







Individually inept.


Very simple programming.Searching for food (foraging), carrying food,recruiting others, alarm, attack.



Ant colony properties

Lifespan: 10’s of years.

No central control!

Robust. Resilient to environmental changes.

Capable to solving sophisticated problems such as finding theminimum path between the hive and food sources withmultiple barriers and obstacles.

Inspiration for “swarm” algorithms.

Ants account for 15% - 20% of the terrestrial animal biomasson Earth. In tropical climates, estimates are closer to 25%.By this assessment, they are the most successful animals onEarth!





No central control!









No central control!









No central control!









No central control!









No central control!









No central control!







A heuristic for swarm optimization

Food

Nest

Random noisy exploration




Food

Nest

HmmmHmmm

Stimergy (deposition of pheromone).




Food

Nest

???

Evaporation.




Food

Nest

Nonlinear reinforcement.




Food

Nest




Food

Nest



Forward ant propagation

pij =(τij)

α (ηij)β (ψij)

γ∑h∈Ni

(τih)α (ηih)β (ψih)β,




pij =(τij)

β∑h∈Ni

(τih)β,




pij =(τij)

β∑h∈Ni

(τih)β,

Ideal communication: ~y (n+1) = P(n)(β)~y (n), P(n) = [pij ].



Timescales

There are three critical timescales.

h1: time interval over which pheromone evaporates.

h2: time interval at which ants are released into the network.

h3: typical time required to make a single hop.

We assume h3 � h1 ≤ h2 and m = h2/h1.

τ(n+1)ij = (1− h1κ1)mτ

(n)ij + h2κ2

∞∑k=1

1

kp̃sdij (k)



Nonlinear dynamics

~y (n+1) =P(β)~y (n),

~τ (n+1) =(1− h1κ1)m2τ(n)ij + h2κ2

∞∑k=1

1

kp̃sdij (k),

Goal: Identify stationary states of this system, and dynamicresponse to perturbations.



Nonlinear dynamics

Λτij =∞∑k=1

1

kp̃sdij (k), Λ = κ1/κ2.

Goal: Identify stationary states of this system, and dynamicresponse to perturbations.



Model prediction versus Qualnet Simulations

n1

n2

(2.5688,2.5884,2.6098)

n3

(0.2275,0.2199,0.2142)

n4

(0.1456,0.1344,0.1334) n5

(0.0819,0.0854,0.0809)

(0.2275,0.2199,0.2142)

(0.0000,0.0000,0.0000)

(0.0819,0.0854,0.0809)



Experiments on a simple 5 node network

The structure of stable solutions varies based on the routingexponent β:

Example

S1: β = 0.5, Λ = 0.3,

multi-route solution

S5: β = 2, Λ = 0.3,

single-route solution



Trials with varying β

The multi-route solution is dynamically connected to the single-route solution



Varying β

After ramping up β from 0.5 to 2 by time step h3, multiple routesolutions will gradually shift to the stable single route solution:



Design principles for larger networks

Time of Simulation 199.99N 200β 0.5→ 2Λ 0.3h1 1h2 1h3 0.01



Large 50-node networks

Following are some parameters we used Matlab and Qualnetparameters:

Simulation time 200N 200β 0.5→ 2Λ 0.3h1 1h2 1h3 0.01

Random initial conditions.



Exploiting the dynamics

T = 0 (β = 0.5)




T = 30 (β = 0.5)




T = 50 (β = 0.5→ 2)




T = 65 (β = 0.5→ 2)




T = 80 (β = 0.5→ 2)




T = 100 (β = 2)



Hop count versus time



Statistical comparison



Problem: Sensor networks

Given an ad-hoc network of data sources, relay nodes (data sourceswithout data) and a data sink, how do we move the data from thesources to the sink?

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

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What is Physarum polycephalum?















Mold solves hard problems

Steiner problems...

Slime mold solves the problems without central control.T. Nakagaki, A Tero. et al. Nature 407 (2000), Proc. Roy. Soc. 271 (2004), J. Theo. Bio. 244 (2007)



Mold solves hard problems

Steiner problems...

Slime mold solves the problems without central control.T. Nakagaki, A Tero. et al. Nature 407 (2000), Proc. Roy. Soc. 271 (2004), J. Theo. Bio. 244 (2007)



Mold and singular potentials

Attack the problem with an electrostatic model.Application: Sensor/Actor networks.



The Tero model for slime mold

Model the sensor network as a system of pipes.

qij =Dij

Lij(pi − pj),∑

j∈Ni

qij =mi ,

dDij

dt=f (|qij |)− rDij ,

where

f (x) = rDmaxa|x |µ

1 + a|x |µ.

p

p

p

1

3

2

i

p

qi1

qi2

qi3

mi

Note that we need to globally solve the pressure equation.m→ p → q.



The pressure equation

p

p

p

1

3

2

i

p

qi1

qi2

qi3

mi

∑j∈Ni

Dij

Lij(pi − pj) = mi



Synchronized wireless Jacobi iterations

∆ tsync

∆ tsync

∆ tsync

∆ tsync

∆ tsync

∆ tsync

∆ tsync

∆ tsync

∆ tsync

t=0

t=0

Solve ODE

Solve for p2

Solve ODE

Solve for p1

Node 1 time

Node 2 time

Real time

Sen

d p

, D

2

12

Sen

d p

, D1

12

Sen

d p

, D

212

Sen

d p

, D1

12

pi ←mi +

∑j∈Ni

Dij

Lijpj∑

j∈Ni

Dij

Lij



A very small network

µ = 1/2




µ = 2




Linear stability of stationary states in the network.

µ = 1/2



Sample problems

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0.15

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0.25

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0.45

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µ = 1/2 µ = 2



Sample problems

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µ = 1/2 µ = 2



Robustness - degree distribution

10% sources

1 2 3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

0.5

Node Degree (d)

P(d

)

µ = 0.5µ = 2




30% sources

1 2 3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

Node Degree (d)

P(d

)

µ = 0.5µ = 2




50% sources

1 2 3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

Node Degree (d)

P(d

)

µ = 0.5µ = 2



Fault tolerance

10% 30% 50%

µ 0.5 2 0.5 2 0.5 2

1-fault 1 .9851 .9856 .9761 .9799 .9530

2-fault .9998 .9700 .9709 .9616 .9595 .9070



Impact on performance

0 5 10 15 20µ=0.5

0

5

10

15

20µ=

2

10% sources20% sources30% sources40% sources50% sources

Expected hop count



Extension to sensor actor networks



Sensor actor networks with µ = 0.5

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0.33

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Matlab Qualnet



Sensor actor networks with µ = 2

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Matlab Qualnet



Summary

Our model for ant-based and slime-based protocols capturesactual protocol behavior well.

Using pressure rather than pheromone poses special problemson ad-hoc networks that can be addressed with theasynchronous Jacobi algorithm.

Nonlinear dynamics helps us understand phase transitionswhen we vary the routing or flux exponent.

Design principles from small networks transfer to largenetworks.



Summary







Summary







Summary






Documents

Bio-inspired network protocols€¦ · Stimergy (deposition of pheromone). Bio-inspired network protocols. Objectives Ants Slime mold Physarum polycephalum Summary A heuristic for