Upload
barbara-ford
View
225
Download
1
Embed Size (px)
Citation preview
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()
Example: End-to-End Delivery
A
B
A:
B:
= network state
Media Access
Radio Driver
wake-uptimes
time
PDR = f( , …)wake-up
times
one-hop
Example: End-to-End Delivery
A
B
= network state
Tree Routing
Media Access
Radio Driver
linkqualities
wake-uptimes
0.9
0.7
PDR = f( , , …)wake-up
timeslink
qualities
one-hop
one-hop/end-to-end
Example: End-to-End Delivery
A
B
= network state
Tree Routing
Media Access
Radio Driver
linkqualities
wake-uptimes
PDR = f( , , …)wake-up
timeslink
qualities
one-hop
one-hop/end-to-end
Example: End-to-End Delivery
A
B
= network state
Application
Reliable Transport
Tree Routing
Media Access
Radio Driver
queuesizes
linkqualities
wake-uptimes
PDR = f( , , , …)wake-up
timeslink
qualitiesqueuesizes
one-hop
end-to-end
one-hop/end-to-end
Example: End-to-End Delivery
A
B
= network state
Application
Reliable Transport
Tree Routing
Media Access
Radio Driver
queuesizes
linkqualities
wake-uptimes
PDR = f( , , , …)wake-up
timeslink
qualitiesqueuesizes
one-hop
end-to-end
one-hop/end-to-end
Continuouslychanging
Example: End-to-End Delivery
A
B
= network state
Application
Reliable Transport
Tree Routing
Media Access
Radio Driver
queuesizes
linkqualities
wake-uptimes
0.8
0.95
PDR = f( , , , …)wake-up
timeslink
qualitiesqueuesizes
one-hop
end-to-end
one-hop/end-to-end
Continuouslychanging
Example: End-to-End Delivery
A
B
= network state
one-hop
end-to-end
one-hop/end-to-end
Application
Reliable Transport
Tree Routing
Media Access
Radio Driver
queuesizes
linkqualities
wake-uptimes
0.8
0.95
Protocols abstract the unreliable wireless channel as point-to-point links major
reason for complexity
Continuouslychanging
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
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
Synchronous Transmissions (ST)
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
Modeling Trade-Off Space
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
Modeling Trade-Off Space
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] 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
Modeling Trade-Off Space
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]
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 LT
Modeling an ST-based multi-hop protocol
Model validation through real-world experiments
Outline
Validity of the Bernoulli assumption to ST vs LT
Modeling an ST-based multi-hop protocol
Model 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
S R
S
S
Receptions/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
Glossy [IPSN 11] leverages ST for efficient and reliable network flooding
Methodology
Glossy [IPSN 11] leverages ST for efficient and reliable network flooding
Methodology
Glossy [IPSN 11] leverages ST for efficient and reliable network flooding
Methodology
Glossy [IPSN 11] leverages ST for efficient and reliable network flooding
Methodology
Methodology139-node testbed at NUS
20-byte packets at 20 ms IPI
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
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
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)
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)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)
Tra
ces f
or
wh
ich
th
e
Bern
ou
lli assu
mp
tion
does
not
hold
(%
)
1010111110111101100110111111101111101110110001111111001111011101011111000111110100111101011001100110
200 1000
Bernoulli Results
20 200 10000
10
20
30
40ST-Type 0 dBmST-Type -15 dBmLT-Type 0 dBmLT-Type -15 dBm
Inter-packet interval (milliseconds)
Tra
ces f
or
wh
ich
th
e
Bern
ou
lli assu
mp
tion
does
not
hold
(%
)
0.5 0.1 0.03
200 1000
Bernoulli Results
20 200 10000
10
20
30
40ST-Type 0 dBmST-Type -15 dBmLT-Type 0 dBmLT-Type -15 dBm
Inter-packet interval (milliseconds)
Tra
ces f
or
wh
ich
th
e
Bern
ou
lli assu
mp
tion
does
not
hold
(%
)40.0
14.5
2.60.5 0.1 0.03
200 1000
Bernoulli Results
20 200 10000
10
20
30
40ST-Type 0 dBmST-Type -15 dBmLT-Type 0 dBmLT-Type -15 dBm
Inter-packet interval (milliseconds)
Tra
ces f
or
wh
ich
th
e
Bern
ou
lli assu
mp
tion
does
not
hold
(%
)
8.7
34.6
4.0
14.1
0.32.5
0.5
40.0
0.1
14.5
0.032.6
200 1000
Bernoulli Results
20 200 10000
10
20
30
40ST-Type 0 dBmST-Type -15 dBmLT-Type 0 dBmLT-Type -15 dBm
Inter-packet interval (milliseconds)
Tra
ces f
or
wh
ich
th
e
Bern
ou
lli assu
mp
tion
does
not
hold
(%
)
8.7
34.6
4.0
14.1
0.32.5
0.5
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
Validity of the Bernoulli assumption to ST vs LT
Modeling an ST-based multi-hop protocol
Model validation through real-world experiments
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
controller
multi-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
controller
multi-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 1
0
0.5
1
Probability of receiving a schedule p
Sta
tion
ary
dis
trib
uti
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
Validity of the Bernoulli assumption to ST vs LT
Modeling an ST-based multi-hop protocol
Model validation through real-world experiments
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
50
100
150
200
250
300
350
400
450
Discarded schedule and data packets (%)
Rad
io o
n-t
ime p
er
rou
nd
(m
sec)
reality
Energy Validation Results
0 5 10 15 200
50
100
150
200
250
300
350
400
450Mea-sured
Discarded schedule and data packets (%)
Rad
io o
n-t
ime p
er
rou
nd
(m
sec)
reality
Energy Validation Results
0 5 10 15 200
50
100
150
200
250
300
350
400
450Mea-sured
Discarded schedule and data packets (%)
Rad
io o
n-t
ime p
er
rou
nd
(m
sec)average model error: 0.25%
reality artificial
Modeling Trade-Off Space
Tree Routing
Radio Driver
Application
LWB
Glossy
Radio DriverPark 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]
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 1000
Time (seconds)
0.2
0.4
0
.6
0
.8
1
Packet
recep
tion
rate
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 9613
ST-Type -15 dBm 9660 256 9404
LT-Type 0 dBm 4189 1418 2771
LT-Type -15 dBm 1777 588 1189
Trace Statistics
0 5 10 15 20Lag
-0.0
5
0
0.0
5
0.1
Sam
ple
au
tocorr
ela
tion
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