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Modeling and Throughput Analysis for SMAC Ou Yang

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2 Outline Motivation and Background Methodology - 1-D Markov Model for SMAC without retx - 2-D Markov Model for SMAC with retx Throughput Analysis - 1-D Markov Model for SMAC without retx - 2-D Markov Model for SMAC with retx Model Validation Conclusions

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3 Motivation Good to know the performance of SMAC - sleep at MAC layer or not? - which duty cycle should be chosen? No analytical model for SMAC - quantitative estimation of throughput - throughput under different scenarios

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4 Background – SMAC Protocol Duty-cycled MAC to reduce idle listening - fixed active period in a cycle - variable sleep period in a cycle - duty cycle = active period / cycle length

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5 Background – SMAC Protocol Synchronization - SYNC pkt carries sleep-awake schedule - broadcast SYNC pkt Medium access - RTS/CTS/DATA/ACK - carrier sensing ( virtual + physical ) - fixed contention window size

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6 Background – SMAC Protocol Reasons of packet loss (ideal channel) - SMAC without retx: RTS failed - SMAC with retx: retx over limit - queue overflow

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7 Methodology Assumptions - packet arrive independently - finite FIFO queue at each node - channel is ideal no hidden terminals no capture effects no channel fading

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8 Methodology 1-D Markov Model for SMAC without retx 0 pkts in the queue1 pkts in the queue2 pkts in the queueMaximum Q pkts in the queue

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9 Methodology 1-D Markov Model for SMAC without retx

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10 Methodology Example of the 1-D Markov Model 012 Transition Matrix P known unknown

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11 Methodology 2-D Markov Model for SMAC with retx Retx stage 0 Retx stage 1 Retx stage R 1 pkt in the queueQ pkts in the queue

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12 Methodology Example of the 2-D Markov Model 0,00,10,2 1,11,2 2,12,2 0,00,10,2

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13 Methodology Example of the 2-D Markov Model 0,00,10,2 1,11,2 2,12,2 1,11,2

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14 Methodology Example of the 2-D Markov Model 0,00,10,2 1,11,2 2,12,2 2,12,2

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15 Throughput Analysis Definition of throughput Solve 2 variables!

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16 Throughput Analysis – 1-D Markov Model According to the Markov Model - stationary distribution: - is the only unknown variable in - curve Assume each node behaves independently - prob. of to contend the media in a cycle - randomly select a backoff window in [0,W-1] - curve

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17 Throughput Analysis – 1-D Markov Model

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18 Throughput Analysis – 1-D Markov Model Intersections of and - - is obtained To solve similar to Assume each node behaves independently - prob. of to contend the media in a cycle - randomly select a backoff window in [0,W-1] - -

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19 Throughput Analysis – 2-D Markov Model According to the Markov Model - stationary distribution: - and are unknown variables in - surface Assume each node behaves independently - prob. of to contend the media in a cycle - randomly select a backoff window in [0,W-1] - curve

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20 Throughput Analysis – 2-D Markov Model is obtained!

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21 Model Validation Varying the number of nodes

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22 Model Validation Varying the queue capacity

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23 Model Validation Varying the contention window size

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24 Model Validation Varying the data arrival rate

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25 Discussions Effects of retransmissions - not obvious difference in throughput - extra traffic at the head of the queue Reasons - saturation: no improvement - far from saturation: trivial improvement - close to saturation: some improvement

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26 Conclusion 1-D Markov Model to describe the behavior of SMAC without retx 2-D Markov Model to describe the behavior of SMAC with retx Models well estimate the throughput of SMAC Application - estimate throughput - optimize the parameters of SMAC - trade off throughput and lifetime

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27 Thank you Q & A

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28 Methodology Example of the 1-D Markov Model 012 Transition Matrix P known unknown

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29 Background – Markov Model Markov model of IEEE

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