extracting markov chain models from protocol execution ... · extracting markov chain models from...
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Extracting Markov Chain Models fromProtocol Execution Traces for End to End
Delay Evaluation in WSNs
Francois DespauxUniversite de Lorraine
IoT Lab Conference - Grenoble 2014
November 6, 2014
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OUTLINE
Part 1 - Context
Part 2 - Novel Methodology for Modelling WSNs
Part 3 - Results & Contributions
Part 4 - Conclusions & Ongoing Work
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Context & Motivation Existing Models Limitation of Existing Models
Part I
Context
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Context & Motivation Existing Models Limitation of Existing Models
ESTIMATING END TO END (E2E) IN WSNS
� To be able to estimate the e2e delay in WSNs< Measurement
◦ clock synchronization
◦ delay in terms of average delay but not the probabilitydistribution
< Simulation◦ Normally not enough accurate (radio model, capture effect,
etc)
◦ Operating System not taken into account
< Analytic approach◦ Due to stochastic nature of WSNs and underlying MAC
protocols: Markov chains
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Context & Motivation Existing Models Limitation of Existing Models
ESTIMATING END TO END (E2E) IN WSNS
� To be able to estimate the e2e delay in WSNs< Measurement
◦ clock synchronization
◦ delay in terms of average delay but not the probabilitydistribution
< Simulation◦ Normally not enough accurate (radio model, capture effect,
etc)
◦ Operating System not taken into account
< Analytic approach◦ Due to stochastic nature of WSNs and underlying MAC
protocols: Markov chains
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Context & Motivation Existing Models Limitation of Existing Models
ESTIMATING END TO END (E2E) IN WSNS
� To be able to estimate the e2e delay in WSNs< Measurement
◦ clock synchronization
◦ delay in terms of average delay but not the probabilitydistribution
< Simulation◦ Normally not enough accurate (radio model, capture effect,
etc)
◦ Operating System not taken into account
< Analytic approach◦ Due to stochastic nature of WSNs and underlying MAC
protocols: Markov chains
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Context & Motivation Existing Models Limitation of Existing Models
SOME LIMITATIONS OF EXISTING MARKOV CHAIN
� Misic et al., Park et al.
� Existing models limited to one-hop transmission scenarios.
� Poisson distribution assumptions (arrival rate).
� Why we cannot extend existing models to considermulti-hop transmission scenarios ?
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Context & Motivation Existing Models Limitation of Existing Models
SOME LIMITATIONS OF EXISTING MARKOV CHAIN
� Misic et al., Park et al.
� Existing models limited to one-hop transmission scenarios.
� Poisson distribution assumptions (arrival rate).
� Why we cannot extend existing models to considermulti-hop transmission scenarios ?
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Context & Motivation Existing Models Limitation of Existing Models
SOME LIMITATIONS OF EXISTING MARKOV CHAIN
� Misic et al., Park et al.
� Existing models limited to one-hop transmission scenarios.
� Poisson distribution assumptions (arrival rate).
� Why we cannot extend existing models to considermulti-hop transmission scenarios ?
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Context & Motivation Existing Models Limitation of Existing Models
SOME LIMITATIONS OF EXISTING MARKOV CHAIN
� Misic et al., Park et al.
� Existing models limited to one-hop transmission scenarios.
� Poisson distribution assumptions (arrival rate).
� Why we cannot extend existing models to considermulti-hop transmission scenarios ?
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Context & Motivation Existing Models Limitation of Existing Models
SOME LIMITATIONS OF EXISTING MARKOV CHAIN
� Misic et al., Park et al.
� Existing models limited to one-hop transmission scenarios.
� Poisson distribution assumptions (arrival rate).
� Why we cannot extend existing models to considermulti-hop transmission scenarios ?
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Context & Motivation Existing Models Limitation of Existing Models
SOME LIMITATIONS OF EXISTING MARKOV CHAIN
� Misic et al., Park et al.
� Existing models limited to one-hop transmission scenarios.
� Poisson distribution assumptions (arrival rate).
� Why we cannot extend existing models to considermulti-hop transmission scenarios ?
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Context & Motivation Existing Models Limitation of Existing Models
SOME LIMITATIONS OF EXISTING MARKOV CHAIN
� Misic et al., Park et al.
� Existing models limited to one-hop transmission scenarios.
� Poisson distribution assumptions (arrival rate).
� Why we cannot extend existing models to considermulti-hop transmission scenarios ?
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Context & Motivation Existing Models Limitation of Existing Models
SOME LIMITATIONS (CONT)� Underlying Operating System
< In our previous work 1 we shown that the underlying OSintroduces extra delays that affect the whole e2e delay
Conclusions� Proposed models are normally abstraction of the reality
and sometimes not accurate for estimating performanceparameters.
� The extension of the proposed model for a real WSNscenario is not straightforward (multi-hop scenario, forinstance).
1On the Gap Between Mathematical Modelling and MeasurementAnalysis for Performance Evaluation of the 802.15.4 MAC Protocol - RTN2013, Paris, France
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Context & Motivation Existing Models Limitation of Existing Models
SOME LIMITATIONS (CONT)� Underlying Operating System
< In our previous work 1 we shown that the underlying OSintroduces extra delays that affect the whole e2e delay
Conclusions� Proposed models are normally abstraction of the reality
and sometimes not accurate for estimating performanceparameters.
� The extension of the proposed model for a real WSNscenario is not straightforward (multi-hop scenario, forinstance).
1On the Gap Between Mathematical Modelling and MeasurementAnalysis for Performance Evaluation of the 802.15.4 MAC Protocol - RTN2013, Paris, France
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Objectives On the road End to end delay estimation
Part II
Novel Methodology for ModellingWSNs
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Objectives On the road End to end delay estimation
OBJECTIVE
� A novel approach< We combine measurement-based and analytic approaches
based on process mining techniques for discovering aMarkov chain model.
◦ We discover a local Markov chain for each node.
◦ By analysing the MAC protocol execution log file.
◦ From this Markov chain we obtain the one-hop delaydistribution function in one node.
< A mathematical technique for estimating the e2e delaydistribution function.
◦ Based on one-hop delay distributions found previously.
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Objectives On the road End to end delay estimation
OBJECTIVE
� A novel approach< We combine measurement-based and analytic approaches
based on process mining techniques for discovering aMarkov chain model.
◦ We discover a local Markov chain for each node.
◦ By analysing the MAC protocol execution log file.
◦ From this Markov chain we obtain the one-hop delaydistribution function in one node.
< A mathematical technique for estimating the e2e delaydistribution function.
◦ Based on one-hop delay distributions found previously.
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Objectives On the road End to end delay estimation
METHODOLOGY (MODELLING ONE NODE)
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Objectives On the road End to end delay estimation
METHODOLOGY (MODELLING ONE NODE)
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Objectives On the road End to end delay estimation
METHODOLOGY (MODELLING ONE NODE)
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Objectives On the road End to end delay estimation
METHODOLOGY (MODELLING ONE NODE)
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Objectives On the road End to end delay estimation
METHODOLOGY (MODELLING ONE NODE)
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Objectives On the road End to end delay estimation
METHODOLOGY (MODELLING ONE NODE)
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Objectives On the road End to end delay estimation
METHODOLOGY (MODELLING ONE NODE)
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Objectives On the road End to end delay estimation
METHODOLOGY (MODELLING ONE NODE)
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Objectives On the road End to end delay estimation
ONE-HOP DELAY FROM MARKOV CHAIN (1/4)
Figure: Markov chain (one node)
� From the empiricalMC we canobtain:< States and transitions of the
protocol.
< Probability transitions betweenstates.
< Sojourn time on each state Sk,γSk
� Then is it possible to create the Adjacency matrix A
A =
0 ps1s2 es1 0 · · · 00 0 ps2s3 es2 · · · 0...
... 0. . .
...0 0 0 · · · 0
(1)
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Objectives On the road End to end delay estimation
ONE-HOP DELAY FROM MARKOV CHAIN (1/4)
Figure: Markov chain (one node)
� From the empiricalMC we canobtain:< States and transitions of the
protocol.
< Probability transitions betweenstates.
< Sojourn time on each state Sk,γSk
� Then is it possible to create the Adjacency matrix A
A =
0 ps1s2 es1 0 · · · 00 0 ps2s3 es2 · · · 0...
... 0. . .
...0 0 0 · · · 0
(1)
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Objectives On the road End to end delay estimation
ONE-HOP DELAY FROM MARKOV CHAIN (2/4)
Figure: Markov chain (one node)
A =
0 ps1s2 es1 0 · · · 00 0 ps2s3 es2 · · · 0...
... 0. . .
...0 0 0 · · · 0
� Adjacency matrix A< esk is the sojourn time
distribution γsk of state Sk infrequency domain1 (LaplaceTransform). Negativeexponential distribution,
◦esk =
γsk
γsk + s(2)
< psk,sl is the probability transitionbetween states Sk and Sl.
1To avoid calculating convolutions over per-hop delay distribution
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Objectives On the road End to end delay estimation
ONE-HOP DELAY FROM MARKOV CHAIN (3/4)� Being sf the final state (ACK RECEIVED), we compute
~Arsk,sf
= A · ~Ar−1sk,sf
(3)
< where ~A1sk,sf
is the vector containing the delay distributionfrom state sk to sf , path length = 1.
� Begin si the initial state, Arsi,sf
gives the delay distributionfrom source to destination, path length = r, r = {1, 2, ...}.
� Then, the whole delay distribution in frequency domaincan be computed as follows:
Df−dom(s) =∑r=1
Arsi,sf
(4)
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Objectives On the road End to end delay estimation
ONE-HOP DELAY FROM MARKOV CHAIN (3/4)� Being sf the final state (ACK RECEIVED), we compute
~Arsk,sf
= A · ~Ar−1sk,sf
(3)
< where ~A1sk,sf
is the vector containing the delay distributionfrom state sk to sf , path length = 1.
� Begin si the initial state, Arsi,sf
gives the delay distributionfrom source to destination, path length = r, r = {1, 2, ...}.
� Then, the whole delay distribution in frequency domaincan be computed as follows:
Df−dom(s) =∑r=1
Arsi,sf
(4)
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Objectives On the road End to end delay estimation
ONE-HOP DELAY FROM MARKOV CHAIN (4/4)� By derivating Df−dom(s), we can obtain the average delay
in time domain
D =∂Df−dom(s)
∂s
∣∣∣∣s=0
(5)
� By means of the Inverse Laplace Transform (ILT), we obtainthe delay distribution in time domain
Dt−dom(t) = ILT(Df−dom(s)) (6)
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Objectives On the road End to end delay estimation
ESTIMATING END TO END DELAY
N1 N2 Ny Nz
N1 Nj
Nk
Np
Ns
Nt Ny Nz
pjk
pjp
pjs
� The e2e delay distribution infrequency domain (serial)<
De2e(f−dom)(s) =
y∏i=1
D(Ni)f−dom(s)
� The e2e delay distribution in frequency domain (parallel)<
De2e(f−dom)(s) =
j∏i=1
D(Ni)f−dom(s)·
(s∑
i=k
pj,i ·D(Ni)f−dom(s)
)·
y∏i=t
D(Ni)f−dom(s)
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Contributions
Part III
Results & Contributions
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Contributions
CONTRIBUTIONS
� X-MAC & RPL< Dynamic routing.
< Tested in a Large-scale infrastructure (IoT-Senslab)
< Comparition between routing strategies in terms of e2edelay.
� Two more contributions< ContikiMAC
◦ IEEE DCOSS 2014, Marina del Rey, Californie, May 26 - 28.
< Standard IEEE 802.15.4 (slotted version)◦ IEEE ISCC 2014, Madeira, Portugal, June 23-26.
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Contributions
X-MAC & RPL� X-MAC & RPL Scenario
< INRIA Rennes with 256 WSN430 opennodes.
< Seven nodes from the testbed wereselected to carry out the experiments.
< Buffer size = 8.Poisson arrival rate λ = 0.5, 1, 2, 4 p/s.42 bytes (25 bytes of payload + 17bytes of header).
� Two metrics of the RPL were considered< RPL objective function 0 (OF0) (number of hops)
< RPL objective function ETX (Expected number oftransmissions)
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Contributions
X-MAC & RPL� X-MAC & RPL Scenario
< INRIA Rennes with 256 WSN430 opennodes.
< Seven nodes from the testbed wereselected to carry out the experiments.
< Buffer size = 8.Poisson arrival rate λ = 0.5, 1, 2, 4 p/s.42 bytes (25 bytes of payload + 17bytes of header).
� Two metrics of the RPL were considered< RPL objective function 0 (OF0) (number of hops)
< RPL objective function ETX (Expected number oftransmissions)
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Contributions
X-MAC & RPL � Average e2e delay (OF0 & ETX).OF0 Emp. Global Av. Delay Theo. Global Av. Delayλ One-Hop e2e One-Hop e2e
0.5 0,1409 0,2406 0,1408 0,25071 0,1507 0,2439 0,1488 0,25802 0,1556 0,2531 0,1518 0,26444 0,1864 0,3189 0,1846 0,3202
ETX Emp. Global Av. Delay Theo. Global Av. Delayλ One-Hop e2e One-Hop e2e
0.5 0,1503 0,2497 0,1482 0,25161 0,1467 0,2427 0,1472 0,25302 0,1613 0,2605 0,1569 0,27174 0,1685 0,2981 0,1627 0,2870
� Packet reception rate for OF0 &ETX.
OF0 ETXλ PRR (%) PRR (%)
0.5 p/sec 97 981 p/sec 96 952 p/sec 33 354 p/sec 2.8 9.9
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Contributions
X-MAC & RPL
Figure: Markov chain: λ = 4
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Contributions
X-MAC & RPL
� PDF of the e2e delay< From node 166 to the sink (145)
< For both RPL objective functions
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4timeHsecL0.0
0.5
1.0
1.5
2.0
2.5
3.0
E2e delay distribution: OF0 and ETX for node 166 Hlambda = 4p�sL
ETX
oF0
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Contributions
LIMITATIONS OF OUR METHODOLOGY
� Obtained model depends strictly on the input parameters(traffic).< To generate traces for several scenarios with different traffic
patterns to draw more general conclusions.
� It is imperative to have the source code of the protocol tobe able to instrument it.
� Code instrumentation using printf-like instructions affectsthe execution timing and non-intrusive approaches are noteasy to implement.
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Contributions
LIMITATIONS OF OUR METHODOLOGY
� Obtained model depends strictly on the input parameters(traffic).< To generate traces for several scenarios with different traffic
patterns to draw more general conclusions.
� It is imperative to have the source code of the protocol tobe able to instrument it.
� Code instrumentation using printf-like instructions affectsthe execution timing and non-intrusive approaches are noteasy to implement.
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Contributions
LIMITATIONS OF OUR METHODOLOGY
� Obtained model depends strictly on the input parameters(traffic).< To generate traces for several scenarios with different traffic
patterns to draw more general conclusions.
� It is imperative to have the source code of the protocol tobe able to instrument it.
� Code instrumentation using printf-like instructions affectsthe execution timing and non-intrusive approaches are noteasy to implement.
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Conclusions Questions
Part IV
Conclusions & Ongoing Work
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Conclusions Questions
CONCLUSIONS
� Contributions< A novel methodology to obtain a Markov chain model from
any MAC protocol by analysing execution traces.
< A mathematical technique for estimating the e2e delaydistribution in both one-hop and multi-hop transmissionscenarios.
< Our methodology is suitable for modelling WSNs in realtestbed scenarios taking into account, not only theunderlying duty-cycled MAC protocol, but also a dynamicrouting protocol.
![Page 46: Extracting Markov Chain Models from Protocol Execution ... · Extracting Markov Chain Models from Protocol Execution Traces for End to End ... (radio model, capture effect, ... We](https://reader033.vdocuments.us/reader033/viewer/2022042620/5aea05417f8b9a6d4f918546/html5/thumbnails/46.jpg)
Conclusions Questions
CONCLUSIONS
� Contributions< A novel methodology to obtain a Markov chain model from
any MAC protocol by analysing execution traces.
< A mathematical technique for estimating the e2e delaydistribution in both one-hop and multi-hop transmissionscenarios.
< Our methodology is suitable for modelling WSNs in realtestbed scenarios taking into account, not only theunderlying duty-cycled MAC protocol, but also a dynamicrouting protocol.
![Page 47: Extracting Markov Chain Models from Protocol Execution ... · Extracting Markov Chain Models from Protocol Execution Traces for End to End ... (radio model, capture effect, ... We](https://reader033.vdocuments.us/reader033/viewer/2022042620/5aea05417f8b9a6d4f918546/html5/thumbnails/47.jpg)
Conclusions Questions
CONCLUSIONS
� Contributions< A novel methodology to obtain a Markov chain model from
any MAC protocol by analysing execution traces.
< A mathematical technique for estimating the e2e delaydistribution in both one-hop and multi-hop transmissionscenarios.
< Our methodology is suitable for modelling WSNs in realtestbed scenarios taking into account, not only theunderlying duty-cycled MAC protocol, but also a dynamicrouting protocol.
![Page 48: Extracting Markov Chain Models from Protocol Execution ... · Extracting Markov Chain Models from Protocol Execution Traces for End to End ... (radio model, capture effect, ... We](https://reader033.vdocuments.us/reader033/viewer/2022042620/5aea05417f8b9a6d4f918546/html5/thumbnails/48.jpg)
Conclusions Questions
ONGOING WORK
� To study the influence of the arrival rate in the Markovchain (generalization).
� Considering the independence of our methodology withregard to the overlying routing protocol< To compare routing protocol’s performance in terms of end
to end delay (RPL vs OC-Routing).
![Page 49: Extracting Markov Chain Models from Protocol Execution ... · Extracting Markov Chain Models from Protocol Execution Traces for End to End ... (radio model, capture effect, ... We](https://reader033.vdocuments.us/reader033/viewer/2022042620/5aea05417f8b9a6d4f918546/html5/thumbnails/49.jpg)
Conclusions Questions
ONGOING WORK
� To study the influence of the arrival rate in the Markovchain (generalization).
� Considering the independence of our methodology withregard to the overlying routing protocol< To compare routing protocol’s performance in terms of end
to end delay (RPL vs OC-Routing).
![Page 50: Extracting Markov Chain Models from Protocol Execution ... · Extracting Markov Chain Models from Protocol Execution Traces for End to End ... (radio model, capture effect, ... We](https://reader033.vdocuments.us/reader033/viewer/2022042620/5aea05417f8b9a6d4f918546/html5/thumbnails/50.jpg)
Conclusions Questions
QUESTIONS ?