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 A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 2 of 19
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 A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 3 of 19
Go-Back-N • Sliding window protocol • Automatic Repeat Request (ARQ) • See Tanenbaum (2002) A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 4 of 19
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 +2 d f • ACKs have a negligible size (modelled as 0 ) and are never lost • Optimal time-out t = 2 d + 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 A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 5 of 19
Theoretical Model: channel � 1 − q � q P e = . 1 − p p 1 − p q π ( B ) = π ( G ) = 1 − p + q . 1 − p + q A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 6 of 19
Theoretical Model: sender p [ f ][1][1] p [ f ][1][1] p [ f ][1][1] p [ f ][1][1] 1 2 3 N q ∗ [ f ][1][1] (1 − p )[ f ][1][0] (1 − p )[ t ][ N ][0] (1 − p )[ t ][ N ][0] (1 − p )[ t ][ N ][0] E (1 − q ∗ )[ t ][ N ][0] q ∗ = P N e (1 , 1) . A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 7 of 19
Theoretical Model: lumped sender model q ∗ [ f ] (1 − q ∗ )[ t ] p [ f ] E T (1 − p )[ t ] � � 1 − q ∗ q ∗ P = , 1 − p p 1 − p q ∗ π ( E ) = π ( T ) = 1 − p + q ∗ . 1 − p + q ∗ A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 8 of 19
Theoretical Model: performance indices Energy efficiency: f ( π ( E ) q ∗ + π ( T ) p ) E eff = P T = π ( E )[ fq ∗ + t (1 − q ∗ )] + π ( T )[ fp + t (1 − p )] . Throughput: Th = 1 f E eff. A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 9 of 19
Theoretical Model: correlation Correlation expressed in terms of π ( G ) and a correlation parameter k . q = π ( G )( p − 1) p = (1 − π ( G )) k + π ( G ) . π ( G ) − 1 − 1 ≤ k ≤ 1 , k = 0 when p = q 91.040 91.050 91.060 91.070 91.080 91.090 91.100 91.110 91.120 91.130 91.140 91.150 91.160 91.170 91.180 91.190 91.200 91.210 G B 91.040 91.050 91.060 91.070 91.080 91.090 91.100 91.110 91.120 91.130 91.140 91.150 91.160 91.170 91.180 91.190 91.200 91.210 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 G B 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 10 of 19
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)). A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 11 of 19
Simulation Metodology and Validation • Each measurement is the mean of r = 100 repeated runs without resetting the RNG. • Simulation time: 300 s 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 0.09 Simulation Results Theoretical Results 0.08 0.07 Energy Efficiency 0.06 0.05 0.04 0.03 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 p = 0.90, q=0.05..1 A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 12 of 19
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 : �� 1 � − t � s = max f , 0 . q A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 13 of 19
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. A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 14 of 19
Simulation results: Energy efficiency 1 0.98 0.96 0.94 Energy efficiency 0.92 0.9 0.88 Heuristic GBN 0.86 MS + LBO 0.84 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Correlation parameter k A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 15 of 19
Simulation results: Throughput 4100 4000 3900 3800 Throughput 3700 3600 3500 Heuristic GBN 3400 MS + LBO 3300 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Correlation parameter k A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 16 of 19
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. A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 17 of 19
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. A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 18 of 19
Any question? A Simulation Package for an Energy-Aware Comparison of ARQ Protocols 19 of 19
Recommend
More recommend
