Evaluation of an Algorithm used in Routing and Service Discovery Protocols of Wireless Sensor Networks The Trickle Algorithm

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Evaluation of an Algorithm used in

Routing and Service Discovery Protocols

of Wireless Sensor Networks

−

The Trickle Algorithm

Markus Becker

[email protected]

ComNets, TZI, University Bremen, Germany

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Outline

IETF Protocol Stack for Wireless Sensor Networks Routing Protocol for Low power and Lossy Networks Trickle Algorithm

Simulation Analytical Model Evaluation

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The Internet Engineering Task Force protocol stack for

Wireless Sensor Networks

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The Internet Engineering Task Force protocol stack for

Wireless Sensor Networks

USB

802.15.

4

80

2.3

WSN node Border Router Node Border Router Host Internet Host

6LoWPAN: IPv6 over Low power Wireless Personal Area Network AM: Active Messaging

CoAP: Constrained Application Protocol IP: Internet Protocol

PPP: Point-to-Point Protocol

RPL: Routing Protocol for Low power and Lossy Networks TCP: Transmission Control Protocol

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The Internet Engineering Task Force protocol stack for

Wireless Sensor Networks

PPP Interface USB 802.15. 4 80 2.3

WSN node Border Router Node Border Router Host Internet Host

MAC: Medium Access Control PHY: Physical Layer

UDP: User Datagram Protocol WSN: Wireless Sensor Network

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The Internet Engineering Task Force protocol stack for

Wireless Sensor Networks

PPP Interface USB 802.15. 4 80 2.3

WSN node Border Router Node Proxy Internet Host

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Routing Protocol for Low power and Lossy Networks

I IETF RFC 6206 and 6550...6554

I _{RFC 6206: The Trickle Algorithm}

I _{RFC 6550: Routing Protocol RPL}

I _{RFC 6551: Routing Metrics}

I _{RFC 6552: Objective Function}

I RFC 6553: IPv6 Option for RPL

I RFC 6554: IPv6 Routing Header for RPL

I Low power and Lossy Networks (LLN) consist Border

Router (BR), Router (R) and Host (H) nodes

I _{H choose only the default router}

I RPL operates only within an LLN and terminates at BR

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RPL: Upward Routes

I DIO: Destination-Oriented Directed Acyclic Graph

Information Object

I DIO announces upward routes (Routes to the BR)

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Trickle Algorithm: Variables and Constants

I Variables

τ Communication interval length

T Timer value in range [τ /2,τ]

C Communication counter

I Constants

K Redundancy constant

τL Lowestτ

τH Highestτ

Note: Notation according to the original Trickle paper: P. Levis, N. Patel, D. Culler, S. Shenker: ’Trickle: A Self-Regulating Algorithm for Code Propagation and Maintenance in Wireless Sensor Networks’ in NSDI’04 Proceedings.

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Trickle Algorithm: Rules

I τ expires

→Doubleτ, up toτH, pick a new T from range [τ /2,τ]

I T expires

→If C < K, transmit

I Received consistent data

→Increment C

I Received inconsistent data

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Simulation Scenarios

I Line scenario with Closest

Pattern Matching Propagation Model (’Line-CPM’)

I Grid scenario (’Grid’)

I Varying number of nodes

I Varying inter-node

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Simulation Execution

I TinyOS application with 6LoWPAN implementationblip

I Simulation toolTOSSIM

I blipextended for simulations

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Analytical Models

I Number of Messages

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Analytical Models

I Number of Messages

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Trickle Algorithm

Trickle algorithm in Line-Direct scenario: τL 0 0. Hop 1. Hop 2. Hop 3. Hop

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Analytical Model: Consistency Time

Modelling consistency time for the Line scenario

τL 2τL 3τL (1) τL 2τL 3τL 1 τL 2τL 3τL 1 τL 2τL 3τL 1 0. Hop: No Delay 1. Hop: Uniformly

distributed delay 2. Hop: Addition of 2 uniformly distributed delays -> Triangle 3. Hop: Addition of 1 uniformly distributed delay and triangle

Central limit theorem: mean of summation of i.i.d. random variables, each with finite mean and variance, will be approximately normally distributed

τL 2τL 3τL

(1/4)

1/4 1/4 1/4

τL 2τL 3τL

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Analytical Model: Consistency Time

Modelling consistency time for the Line scenario

τL 2τL 3τL (1) τL 2τL 3τL 1 τL 2τL 3τL 1 τL 2τL 3τL 1 0. Hop: No Delay 1. Hop: Uniformly

distributed delay 2. Hop: Addition of 2 uniformly distributed delays -> Triangle 3. Hop: Addition of 1 uniformly distributed delay and triangle

Central limit theorem: mean of summation of i.i.d. random variables, each with finite mean and variance, will be approximately normally distributed

τL 2τL 3τL

(1/4)

1/4 1/4 1/4

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Analytical Model: Consistency Time

The probability density function (pdf) of the time to consistency scenario can be modeled in detail by

p(t)= _N1 N−1 P h=0 C−1 P c=0 N−1 P a=1 fh,c,a(t)·ph,c,a(t), where h: hops c: Trickle cycle

a: number of 1-hop ancestors closer to source N: total number of nodes

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Analytical Model: Consistency Time

p(t)= _N1 N−1 P h=0 C−1 P c=0 N−1 P a=1 fh,c,a(t)·ph,c,a(t), where fh,c,a=1(t)=                      δ(t) ,h=0, L−1_{L{_Θ₍_t₋τL 2)−Θ(t−τL)}h} ,h≥1,c=0 Θ(t−τL·(2c+1−1)−τ₂L ·2c) −Θ(t−τL·(2c+1−1)) ,h=1,c≥0 L−1_{L{_Θ₍_t₋τL 2)−Θ(t−τL)}h−c· L{Θ(t−2τL)−Θ(t−3τL)}c} ,h>1,0<c<h.

Θ(·)denotes the Heaviside step function. Ldenotes the

Laplace transform andL−1denotes the inverse Laplace

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Analytical Model: Consistency Time

f

h,c,a

(

t

)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 t [s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p ( t ) Distributions ph,c,a(t) h=1, a=0 c= 0 1 2 3 4 0 2 4 6 8 10 12 14_Time_t_[s]16 18 20 22 24 26 28 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p ( t ) Distributions ph,c,a(t) c=0, a=0 h= 0 1 2 3 4 5 6 7 8

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Analytical Model: Consistency Time

f

h,c,a

(

t

)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 Time t [s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p ( t ) Distributions ph,c,a(t) c=0 h=0, a=0 h=0, a=1 h=0, a=2 h=1, a=0 h=1, a=1 h=1, a=2 h=2, a=0 h=2, a=1 h=2, a=2 h=3, a=0 h=3, a=1 h=3, a=2 h=4, a=0 h=4, a=1 h=4, a=2 h=5, a=0 h=5, a=1 h=5, a=2 h=6, a=0 h=6, a=1 h=6, a=2 h=7, a=0 h=7, a=1 h=7, a=2 h=8, a=0 h=8, a=1 h=8, a=2

The distribution fora6=1

can be calculated from the cdf given by

1−(1−P(X ≤x))aof

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Analytical Model: Consistency Time

f

h,c,a

(

t

)

0 2 4 6 8 10 12 _Time14 _t_[s]16 18 20 22 24 26 28 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p ( t ) Distributions ph,c,a(t) h=2, a=0 c= 0 1 2 3 4 5

Figure:Probability Density Function

forh=2,a=0,cvaried 0 2 4 6 8 10 12 14_Time_t_[s]16 18 20 22 24 26 28 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p ( t ) Distributions ph,c,a(t) h=3, a=0 c= 0 1 2 3 4 5

Figure:Probability Density Function

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Analytical Model: Consistency Time

p

h,c,a

(t

)

PRR1 PRR1 PRR1 PRR2 PRR2 PRR3 0 20 40 60 _{Distance [m]}80 100 120 140 160 180 0.00 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.951.00 PRR

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Algorithm for Analytical Model

I calc_base_dists()

I calc_prr() I calc_neigh(prr)

I calc_tx_outcomes(neighbors, prr)

I calc_hopcounts(prr, inject_node, trickle_k, neighbors, scenario)

I calc_hopcounts_next_cycles(hopcounts)

I calc_neighbors_hop_closer(hopcounts, prr, trickle_k) I calc_prob_mix_from_hopcount(hopcounts)

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Simulation & Analytical Model: Parameters

The Trickle settings for the following results are:

I τL=2 s

I τH =32 s

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Simulation & Analytical Model: Line 9, K = 1

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P ( T ≤ t )

Model Time to Consistency (cdf)

(#Nodes: 9, K: 1)

Distance [m]

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145 analytical

simulated

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Simulation & Analytical Model: Line 9, K = 3

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

Model Time

t

[s]

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Model Time to Consistency (cdf)

(#Nodes: 9, K: 3)

Distance [m]

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Simulation & Analytical Model: Line 9, K = 9

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Model Time to Consistency (cdf)

(#Nodes: 9, K: 9)

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Simulation & Analytical Model: Line 16, K = 3

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

Model Time

t

[s]

0.0

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Model Time to Consistency (cdf)

(#Nodes: 16, K: 3)

Distance [m]

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Simulation & Analytical Model: Line 25, K = 3

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Model Time to Consistency (cdf)

(#Nodes: 25, K: 3)

Distance [m]

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Simulation & Analytical Model: Grid 9, K = 3

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

Model Time

t

[s]

0.0

0.1

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Model Time to Consistency (cdf)

(#Nodes: 9, K: 3)

Distance [m]

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Simulation results and 95% confidence intervals

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 No de s c on sis te nt P ( T ≤ t ) 95 % Confidence Interval

Model Time to Consistency (cdf) (#Nodes: 9, K: 3) Distance [m] 10 20 30 40 50 60 70 80 90 100 110 115 120 125 130 135 140 145

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Trickle/Push Comparison

Trickle Push

tpush= 3 s tpush= 5 s tpush= 39 s

t95% 29.4 s 27.9 s 36.4 s 169.1 s

tmax 34.9 s 33.0 s 47.0 s 240.5 s

Packets until consistent 176 714 196 415 Packets in steady state ≈2.61_s 33.31_s 201_s 2.61_s

I Trickle Settings: τL= 2s,τH = 32s,K=3

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Conclusions & Outlook

I Conclusions

I _{Implemented and studied the Trickle algorithm}

I Important algorithm for RPL and distribution of other information

I Distributes faster and more-efficient than fixed-interval pushing

I _{First analytical model of Trickle algorithm}

I Model for delay distribution was shown here

I Model for number of sent packets exists as well

I Analytical delay model fits simulation results

I Outlook