On Modeling Low-Power Wireless Protocols Based On Synchronous Packet Transmissions

On Modeling Low-Power Wireless Protocols Based On Synchronous Packet Transmissions Marco Zimmerling, Federico Ferrari, Luca Mottola*, Lothar Thiele

ETH Zurich*Politecnico di Milano and SICS Swedish ICT

Accurate mathematical models of low-power wireless protocols are important

» Understanding (e.g., trade-offs, parameters) » Verification» System design (e.g., node placement, power

sources)» Prediction and adaptation at runtime

But traditional link-based multi-hop protocols are intricate and difficult to model (e.g., ZigBee)

Motivation

Highly dynamic network topology due to:» Volatile low-power wireless links» Node mobility, failures

Traditional protocols maintain substantial network state that governs their operation (e.g., link qualities)

» Distributed across nodes» Concurrent, uncontrolled updates

Motivation

Highly dynamic network topology due to:» Volatile low-power wireless links» Node mobility, failures

Traditional protocols maintain substantial network state that governs their operation (e.g., link qualities)

» Distributed across nodes» Concurrent, uncontrolled updates

Motivation

Modeling often stops at the link layer, where interactions are single-hop

insufficient!

Example: End-to-End Delivery

Devise a model of the packet deliveryrate (PDR) observed at the sink

PDR = f()


A

B

A:B:

= network state

Media Access

Radio Driver

wake-uptimes

timePDR = f( , …)wake-up

times

one-hop


A

B

= network state

Tree Routing

Media Access

Radio Driver

linkqualitieswake-up

times0.9

0.7

PDR = f( , , …)wake-uptimes

linkqualities

one-hop

one-hop/end-to-end


A

B

= network state

Tree Routing

Media Access

Radio Driver

linkqualitieswake-up

times

PDR = f( , , …)wake-uptimes

linkqualities

one-hop

one-hop/end-to-end


A

B

= network state

Application

Reliable Transport

Tree Routing

Media Access

Radio Driver

queuesizeslink

qualitieswake-up

times

PDR = f( , , , …)wake-uptimes

linkqualities

queuesizes

one-hop

end-to-end

one-hop/end-to-end


A

B

= network state

Application

Reliable Transport

Tree Routing

Media Access

Radio Driver

queuesizeslink

qualitieswake-up

times


linkqualities

queuesizes

one-hop

end-to-end

one-hop/end-to-end

Continuouslychanging


A

B

= network state

Application

Reliable Transport

Tree Routing

Media Access

Radio Driver

queuesizeslink

qualitieswake-up

times0.8

0.95


linkqualities

queuesizes

one-hop

end-to-end

one-hop/end-to-end



A

B

= network state

one-hop

end-to-end

one-hop/end-to-end

Application

Reliable Transport

Tree Routing

Media Access

Radio Driver

queuesizeslink

qualitieswake-up

times0.8

0.95

Protocols abstract the unreliable wireless channel as point-to-point links major

reason for complexity


Multiple nodes send simultaneously to the same receiver, as opposed to pairwise link-based transmissions (LT)

Synchronous Transmissions (ST)

RR

Enabled by IEEE 802.15.4 physical-layer phenomena:

» Power (and delay) capture different/identical packets

» Constructive baseband interference identical packets

Several recent protocols exploit ST for various purposes:

» A-MAC [SenSys 10]: contention resolution» Glossy [IPSN 11]: network flooding » Splash [NSDI 13]: code updates» CAOS [SenSys 13]: all-to-all communication


Enabled by IEEE 802.15.4 physical-layer phenomena:

» Power (and delay) capture different/identical packets

» Constructive baseband interference identical packets

Several recent protocols exploit ST for various purposes:

» A-MAC [SenSys 10]: contention resolution» Glossy [IPSN 11]: network flooding » Splash [NSDI 13]: code updates» CAOS [SenSys 13]: all-to-all communication


ST enable efficient and reliable multi-hop protocols with very little network

state

Open Question

Do ST also enable simple yet accurate modeling?

Modeling Trade-Off Space

Accuracyof Models

Modeling Scope

Tree Routing

Radio Driver

High

Low

Low High


Park et al.[IPSN 10]

Buettner et al.[SenSys 06]

Zimmerling et al.[IPSN 12]

Langendoen & Meier[TOSN 10]

Polastre et al.[SenSys 04]

Challen et al.[MobiSys 10]

Tree Routing

Radio Driver

2-7 % error

Accuracyof Models

Modeling Scope

High

Low

Low High

Linklayer







Challen et al.[MobiSys 10] Bruneo et al.

[PE 12] Gelenbe et al.[TOSN 07]Guenther et al.[UKPEW 12]

Tree Routing

Radio Driver

2-7 % error

Accuracyof Models

Modeling Scope

High

Low

Low High

Linklayer

Fullstack








Our work

Tree Routing

Radio Driver

2-7 % error 0.25 % error

Bruneo et al.[PE 12] Gelenbe et al.

[TOSN 07]Guenther et al.[UKPEW 12]

Accuracyof Models

Modeling Scope

High

Low

Low High

Linklayer

Fullstack

Validity of the Bernoulli assumption to ST vs LTModeling an ST-based multi-hop protocolModel validation through real-world experiments

Outline


Outline

Intended receiver of a sequence of packets observes a sequence of i.i.d. Bernoulli trials

» Success (packet received) with probability p» Failure (packet lost) with probability 1 – p

Empirical studies showed that this assumption is not always valid to LT (esp. when packets are close in time)

Bernoulli Assumption

S R

S

SReceptions/losses areindependent over time

Intended receiver of a sequence of packets observes a sequence of i.i.d. Bernoulli trials

» Success (packet received) with probability p» Failure (packet lost) with probability 1 – p

Empirical studies have shown that this assumption is not always valid to LT

Bernoulli Assumption

S R

S

S

What about ST?

Receptions/losses areindependent over time

Glossy [IPSN 11] leverages ST for efficient and reliable network flooding

Methodology


Methodology


Methodology


Methodology


Methodology

Methodology139-node testbed at NUS

20-byte packets at 20 ms IPI



ST-Type: how protocols perceive Glossy» 70 equally distributed nodes» 50,000 Glossy floods each» Remaining 138 nodes log




LT-Type: how protocols perceive LT» All 139 nodes» 50,000 broadcasts each» Nodes within radio range log





Tx power: 0 dBm (max) and -15 dBm (lowest possible)





Tx power: 0 dBm (max) and -15 dBm (lowest possible)Collected >1,200,000,000 packet reception events

1) Represent every trace as a discrete-time binary time series {xi}n of length n = 50,000:

010011100111110011101010…

2) Keep only weakly stationary time series, using two empirical tests for non-constant mean/variance

3) Check the validity of the Bernoulli assumption, using a statistical test based on the sample autocorrelation

Trace Analysis

Bernoulli Results

20 200 10000

10

20

30

40

Inter-packet interval (milliseconds)

Trac

es fo

r w

hich

the

Bern

oulli

ass

umpt

ion

does

no

t ho

ld (%

)

1010111110111101100110111111101111101110110001111111001111011101011111000111110100111101011001100110

200 1000

Bernoulli Results

20 200 10000

10

20

30

40ST-Type 0 dBmST-Type -15 dBmLT-Type 0 dBmLT-Type -15 dBm


Trac

es fo

r w

hich

the

Bern

oulli

ass

umpt

ion

does

no

t ho

ld (%

)

0.5 0.1 0.03

200 1000

Bernoulli Results

20 200 10000

10

20

30



Trac

es fo

r w

hich

the

Bern

oulli

ass

umpt

ion

does

no

t ho

ld (%

)40.0

14.5

2.60.5 0.1 0.03

200 1000

Bernoulli Results

20 200 10000

10

20

30



Trac

es fo

r w

hich

the

Bern

oulli

ass

umpt

ion

does

no

t ho

ld (%

)

8.7

34.6

4.0

14.1

0.3 2.50.5

40.0

0.1

14.5

0.032.6

200 1000

Bernoulli Results

20 200 10000

10

20

30



Trac

es fo

r w

hich

the

Bern

oulli

ass

umpt

ion

does

no

t ho

ld (%

)

8.7

34.6

4.0

14.1

0.3 2.50.5

40.0

0.1

14.5

0.032.6

The Bernoulli assumption is highly valid to ST and significantly more valid

to ST than to LT


Outline

Low-Power Wireless Bus (LWB)LWB [SenSys 12] uses only ST for communication

» Turns a multi-hop network into a “virtual” single-hop network, similar to a shared bus

Centralized scheduling» A controller node orchestrates all

communication

LWB

controllermulti-hop network Glossy floods shared bus

Low-Power Wireless Bus (LWB)LWB [SenSys 12] uses only ST for communication

» Turns a multi-hop network into a “virtual” single-hop network, similar to a shared bus

Centralized scheduling» A controller node orchestrates all

communication

LWB

controllermulti-hop network Glossy floods shared bus

Does the validity of the Bernoulli assumption to ST help devise a simple yet accurate

energy model of LWB?

A single event − the reception of schedules from the controller − drives the operation of all LWB nodes

Schedule-Driven Operation

Communication rounds

schedule data data …data

Finite-State Machine

= schedule received= schedule missed

Finite-State Machine

= schedule received= schedule missed

The Bernoulli assumption allows us to characterize schedule receptions through

a single parameter p

Discrete-Time Markov Chain

p

1-p

pp

p

p

p p

p

p

1-p

1-p

1-p1-p

1-p

1-p1-p

1-p1-p1-p

p

p

= schedule received, with probability p= schedule missed, with probability 1-p

p

0 0.2 0.4 0.6 0.8 10

0.5

1

Probability of receiving a schedule p

Stat

iona

rydi

stri

buti

on

Stationary distribution of the DTMC gives the frequency of visits to each state in the long run for a given p

Combined with the well-defined cost of each state, we get the long-term expected energy cost of a LWB node

Energy Model


Outline

30-node testbed at ETH Zurich

15-byte payload at 6 sec IPI

Tx power: o dBm (max)

Estimate several model parameters at runtime, such as:

Measure energy consumption using established software-based methods

Model Validation

p = number of received schedulesnumber of expected schedules

Energy Validation Results

0 5 10 15 200

50100150200250300350400450

Discarded schedule and data packets (%)

Radi

o on

-tim

e pe

r ro

und

(mse

c)

reality


0 5 10 15 200

50100150200250300350400450 Mea-

sured


Radi

o on

-tim

e pe

r ro

und

(mse

c)

reality


0 5 10 15 200

50100150200250300350400450 Mea-

sured


Radi

o on

-tim

e pe

r ro

und

(mse

c)average model error: 0.25%

reality artificial


Tree Routing

Radio Driver

Application

LWB

Glossy

Radio DriverPark et al.[IPSN 10]






Our work

2-7 % error 0.25 % error

Bruneo et al.[PE 12] Gelenbe et al.

[TOSN 07]Guenther et al.[UKPEW 12]

Accuracyof Models

Modeling Scope

High

Low

Low High

Linklayer

Fullstack

The Bernoulli assumption is highly valid to ST but often illegitimate to LT

ST enable simple yet accurate modeling of a complete state-of-the-art low-power wireless networking stack

Conclusions

0 200 400 600 800 1000Time (seconds)

0.2

0

.4

0.

6

0.8

1Pa

cket

rec

epti

on r

ate

Weakly stationaryNon-stationaryLinear fit

Formal tests (e.g., KPSS, ADF) often fail in practice

Empirically declare a trace as non-stationary if» PRR changes by 0.015 or more over the entire

trace, or» PRR drops/rises by >0.05 within 40 seconds

(2,000 packets)

Test for Weak Stationarity

Type Tx power Total Non-stationary

Weakly stationary

ST-Type 0 dBm 9660 47 9613ST-Type -15 dBm 9660 256 9404LT-Type 0 dBm 4189 1418 2771LT-Type -15 dBm 1777 588 1189

Trace Statistics

0 5 10 15 20Lag

-0.0

5

0

0.0

5

0.

1Sa

mpl

e au

toco

rrel

atio

n

Trace 1Trace 2Bounds

Let {xi}n a realization of an i.i.d. sequence {Xi}∞ of random variables with finite variance

» For large n, about 95% of the sample autocorrelation values should lie within the confidence bounds ±1.96/n1/2

» We consider the Bernoulli assumption valid for a given trace if the above holds already at lag 1

Validating Bernoulli

On Modeling Low-Power Wireless Protocols Based On Synchronous Packet Transmissions

Documents

network stateonehopend

t endtoend deliveryab

lowpower mac protocols

substantial network

endtoend deliveryaba

endtoend deliverydevise

failures traditional

power sourcesprediction