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A Simulation Package for an Energy-Aware Comparison of ARQ Protocols

9th Annual Industrial Simulation Conference, ISC’2011 Gian-Luca Dei Rossi Andrea Marin Matteo Rosati Simonetta Balsamo

Dipartimento di Scienze Ambientali, Informatica e Statistica Universit` a Ca’ Foscari, Venezia

June 6, 2011

Outline

• Context and motivations
• Background
• Theoretical Model
• Simulation Package
• Validation
• A Heuristic for energy efficiency optimisation
• Simulation results and heuristic comparison
• Conclusions

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Context and motivations

• ARQ protocols are widely used
• Used in different networking stack layers to achieve reliability
• data link
• transport
• Throughput vs. Energy efficiency (mobile applications)
• Error prone channels, correlation of errors in wireless networks

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Go-Back-N

• Sliding window protocol
• Automatic Repeat Request (ARQ)
• See Tanenbaum (2002)

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Theoretical Model: assumptions

• Two agents: Sender S and Receiver R
• Noisy channel C with bandwidth b and propagation delay d
• S is always ready to send packets unless window is full
• All packets have size s, time to send a single packet is f = s

b

• Optimal window size N = f+2d

f

• ACKs have a negligible size (modelled as 0) and are never lost
• Optimal time-out t = 2d + f
• Two states of the channel: good (G) or bad (B)
• At each transmission:
• if the channel was in G, it remains in G with probability p or

switches to B with probability 1 − p

• if the channel was in B, it switches to G with probability q or it

remains in B with probability 1 − q

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Theoretical Model: channel

Pe =

• 1 − q

q 1 − p p

• .

π(B) = 1 − p 1 − p + q π(G) = q 1 − p + q .

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Theoretical Model: sender

1 2 3 N E

p[f][1][1] p[f][1][1] p[f][1][1] q∗[f][1][1] (1 − p)[t][N][0] (1 − p)[t][N][0] (1 − p)[t][N][0] (1 − q∗)[t][N][0] p[f][1][1] (1 − p)[f][1][0]

q∗ = P N

e (1, 1) .

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Theoretical Model: lumped sender model

E T q∗[f] (1 − p)[t] p[f] (1 − q∗)[t]

P =

• 1 − q∗

q∗ 1 − p p

• ,

π(E) = 1 − p 1 − p + q∗ π(T) = q∗ 1 − p + q∗ .

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Theoretical Model: performance indices

Energy efficiency: Eeff = PT = f(π(E)q∗ + π(T)p) π(E)[fq∗ + t(1 − q∗)] + π(T)[fp + t(1 − p)] . Throughput: Th = 1 f Eeff.

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Theoretical Model: correlation

Correlation expressed in terms of π(G) and a correlation parameter k. p = (1 − π(G))k + π(G) q = π(G)(p − 1) π(G) − 1 . −1 ≤ k ≤ 1, k = 0 when p = q

91.040 91.040 91.050 91.050 91.060 91.060 91.070 91.070 91.080 91.080 91.090 91.090 91.100 91.100 91.110 91.110 91.120 91.120 91.130 91.130 91.140 91.140 91.150 91.150 91.160 91.160 91.170 91.170 91.180 91.180 91.190 91.190 91.200 91.200 91.210 91.210 B G 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 100 110 110 120 120 130 130 140 140 150 150 160 160 170 170 180 180 B G

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Simulation Package

• Based on OMNeT++ (see Varga (2010))
• Extensible software Components for sender, receiver and channel

with error correlation

• In the next examples used for Go-Back-N, but it can be extended to

model other ARQ protocols

• RNG: Mersenne Twister (see Matsumoto and Nishimura (1998)).

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Simulation Metodology and Validation

• Each measurement is the mean of r = 100 repeated runs without

resetting the RNG.

• Simulation time: 300s per run
• Transient phase elimination (see Welch (1981))
• Measurements are assumed to be IID
• Normal distribution
• Confidence intervals
• Validation: theoretical model prediction vs. simulator outcome
• All theoretical predictions inside confidence intervals for c = 0.95

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Energy Efficiency p = 0.90, q=0.05..1 Simulation Results Theoretical Results

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A Heuristic for energy minimisation

• Strong correlation → error concentration
• Trying to send packets continuously is a bad strategy for energy

saving

• Not transmitting packets continuously is a bad strategy for

throughput.

• If the channel is in a bad state, at the next packet transmission it

will remain in bad state with probability (1-q), or it would move to the good state with probability q.

• Residence time modelled as a geometric random variable, expected

value E[X] = 1

q

• We can skip those 1

q transmission

• Sender notices errors in the channel after t

f transmissions, so it

should skip only the s remaining packet transmission that are estimate to be bad: s = max 1 q

• − t

f , 0

• .

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Simulation results and heuristic comparison

We can use the simulator to compare the performances indices of our heuristic with the one described in Chockalingam and Zorzi (2008) and with the naive Go-Back-N implementation. Simulation parameters: Parameter Value Bandwidth 54Mbps Delay 0.99ms Frame size 1492 B Timeout 2.21ms π(G) 0.9

Table: Parameter values for the simulation.

All simulations were done according to the previously described criteria.

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Simulation results: Energy efficiency

0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Energy efficiency Correlation parameter k Heuristic GBN MS + LBO

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Simulation results: Throughput

3300 3400 3500 3600 3700 3800 3900 4000 4100 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Throughput Correlation parameter k Heuristic GBN MS + LBO

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Conclusions

• A simulation package to analyse energy efficiency and other

performance indices of ARQ protocols

• A theoretical model for Go-Back-N on optimality condition
• A novel heuristic for energy efficiency optimisation in channel with

strongly-correlated errors.

• A comparison with a state-of-the-art heuristic in this field.

Future works:

• Theoretical model extensions
• Simulation package extensions
• Heuristic modifications for weakly correlated errors
• Techniques to efficiently estimate π(G) and k from statistics.

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References

Chockalingam A. and Zorzi M., 2008. Adaptive ARQ with energy efficient backoff on Markov fading links. Wireless Communications, IEEE Transactions on, 7, no. 5, 1445–1449. ISSN 1536-1276. Matsumoto M. and Nishimura T., 1998. Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number

• generator. ACM Transactions on Modeling and Computer Simulation

(TOMACS), 8, no. 1, 3–30. ISSN 1049-3301. Tanenbaum A., 2002. Computer Networks. Prentice Hall Professional Technical Reference, 4th ed. ISBN 0130661023. Varga A., 2010. OMNeT++. In K. Wehrle; M. G¨ unes; and J. Gross (Eds.), Modeling and Tools for Network Simulation, Springer. ISBN 978-3-642-12330-6. Welch P.D., 1981. On the problem of the initial transient in steady-state

• simulations. Tech. rep., IBM Watson Research Center, Yorktown

Heights, NY.

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Any question?

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