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()

= network state

Media Access

Radio Driver

wake-uptimes

timePDR = f( , …)wake-up

one-hop

= network state

Tree Routing

Media Access

Radio Driver

linkqualitieswake-up

times0.9

PDR = f( , , …)wake-uptimes

linkqualities

one-hop

one-hop/end-to-end

= network state

Tree Routing

Media Access

Radio Driver

linkqualitieswake-up

PDR = f( , , …)wake-uptimes

linkqualities

one-hop

one-hop/end-to-end

= network state

Application

Reliable Transport

Tree Routing

Media Access

Radio Driver

queuesizeslink

qualitieswake-up

PDR = f( , , , …)wake-uptimes

linkqualities

queuesizes

one-hop

end-to-end

one-hop/end-to-end

= network state

Application

Reliable Transport

Tree Routing

Media Access

Radio Driver

queuesizeslink

qualitieswake-up

linkqualities

queuesizes

one-hop

end-to-end

one-hop/end-to-end

Continuouslychanging

= network state

Application

Reliable Transport

Tree Routing

Media Access

Radio Driver

queuesizeslink

qualitieswake-up

times0.8

linkqualities

queuesizes

one-hop

end-to-end

one-hop/end-to-end

= 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

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)

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

Open Question

Do ST also enable simple yet accurate modeling?

Modeling Trade-Off Space

Accuracyof Models

Modeling Scope

Tree Routing

Radio Driver

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

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

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

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

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

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

What about ST?

Receptions/losses areindependent over time

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

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

Inter-packet interval (milliseconds)

1010111110111101100110111111101111101110110001111111001111011101011111000111110100111101011001100110

200 1000

Bernoulli Results

20 200 10000

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

0.5 0.1 0.03

200 1000

Bernoulli Results

20 200 10000

2.60.5 0.1 0.03

200 1000

Bernoulli Results

20 200 10000

0.3 2.50.5

0.032.6

200 1000

Bernoulli Results

20 200 10000

0.3 2.50.5

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

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

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

1-p1-p

1-p1-p1-p

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

0 0.2 0.4 0.6 0.8 10

Probability of receiving a schedule p

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 (%)

reality

0 5 10 15 200

50100150200250300350400450 Mea-

reality

0 5 10 15 200

50100150200250300350400450 Mea-

c)average model error: 0.25%

reality artificial

Tree Routing

Radio Driver

Application

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

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)

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

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

network stateonehopend

t endtoend deliveryab

lowpower mac protocols

substantial network

endtoend deliveryaba

endtoend deliverydevise

failures traditional

power sourcesprediction

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