Multiple MAC Protocols Selection Strategies. Presented by Chen-Hsiang Feng

Transcription

1 Multiple MAC Protocols Selection Strategies Presented by Chen-Hsiang Feng

2 Outline Motivation and Goal Simulation Environment MAC Selection Strategies Conclusions

3 Motivation Today's devices have multiple PHY and MAC Ex. Cell phone: 3G, 4G, WiMax, Wi-Fi, Bluetooth, Infrared, USB... Each of them using independent PHY/MAC Personal computer Multiple Ethernet cards, Multiple Wi-Fi cards, 3G, USB... Each of them using independent PHY/MAC

4 Motivation -- 2 Communication conditions change dynamically, there is no definite good or bad for these PHY/MAC pairs.

5 Goal If we can freely select any of the PHY/MAC pairs to use at run time, what is the best selection strategy? Optimize Packet Success Rate

6 Outline Motivation and Goal Simulation Environment, Assumptions Methods Conclusions

7 System Model Can reach any neighbor using any MAC/PHY Currently only one node can select MAC Optimize packet success rate of that node

8 Traffic Model Poisson traffic is not realistic (no memory) Wide-Area Traffic: The Failure of Poisson Modeling (1995), by Vern Paxson, Sally Floyd If there is no memory, you can learn nothing more than λ

9 Traffic Model - 2 In general, there is relation of consecutive traffics in time. Short-range dependence (SRD) ACF of the form Long-range dependent (LRD) ACF of the form ρ k ~ e βk,β> 0 ρ k ~ k β =e β log k,β> 0 Definition: = E[ X t X t ] 2

10 Poisson vs. LRD Ex. for similar mean traffic

11 Generating LRD Traffic Modeling Video Traffic Using M G Input Processes: A Compromise Between Markovian and LRD Models (1998), by Marwan M. Krunz, Armand M. Makowski Use M/G/ input processes M for exponential inter-arrival time distribution (Poisson) G for general service time distribution distribution (arbitrary) for infinity number of servers The pdf of G can be derived from ACF k

12 Sigma = 214 A(1) =1 A(2) =2 A(3) =1 A(4) = R = t

13 Instantaneous Traffic

14 Average Traffic Load G Average traffic is the average of instantaneous traffic over a window period. (EX, 10 time instances)

15 Packet Success Rate Traffic Load G Throughput S Aloha :S= Ge G Slotted non persistent CSMA :S= age ag 1 e ag a p persistent CSMA :S= 1 e ag [ P s ' 0 P s 1 0 ] 1 e ag [a t 0 a t a] a 0 Packet Success Rate = S/G Packet Switching in Radio Channels: Part I - Carrier Sense Multiple-Access Modes and Their Throughput-Delay Characteristics (1983), by Leonard Kleinrock, Fouad, A. Tobagi

16 Measurement of PSR We assume MAC protocol can measure the previous slots' packet success rate The measurement is exact value + noise P s [s]= P s [ s] [s] ω[s] is Gaussian noise term with fixed variance σ ω2 = 0.09 in the emulation

17 Ref:

18 Measurement of PSR - 2 In practice we can count the number of packets (collision & success) during a window period, thus packet success rate.

19 Outline Motivation and Goal Emulation Environment MAC Selection Strategies Conclusions

20 Two MACs Setting Both Non-persistent CSMA Traffic Both long-range dependent (LRD)

21 Saturating Counter

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23 Optimal Stopping Choosing a optimal stopping time of using a MAC to minimize the expected total cost The problem is to find a threshold V* that If x < V*, switch to next MAC If x >= V*, stay using the current MAC

24 Optimal Stopping - 2 The reward sequence is defined as Y 0 =,Y 1 = X 1 c,...,y n = X n c,...,y = Assumption X 1, X 2,... are observations of PSR iid with known distribution F(x) The real distribution of F(x) is intractable Assume F(x) ~ N(μ,σ 2 )

25 Optimal Stopping - 3 V* can be calculated from the optimality Equ. Where F is the CDF of Gaussian distribution N(μ,σ 2 ) Thus, Where Φ(x) is the standardized Gaussian CDF

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27 Multi-armed Bandit Only one machine is operated at each time Machines that are not operated remain frozen Machines are independent Frozen machines contribute no reward

28 Multi-armed Bandit - 2 We model the state of each MAC with a Markov chain State i has reward K+1-i The smaller state represents higher success rate and thus higher reward

29 Multi-armed Bandit - 3 By calculating the expected reward of each machine from the current states, the optimal solution is the machine (MAC) with the highest expected reward. Extensions of the multiarmed bandit problem: The discounted case (1985), by P. Varaiya, J. Walrand, and C. Buyukkoc

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31 Proactive MAC Selection Until now, we only use the PSR estimation of the chosen MAC What can we do if all MAC can update PSR estimation at every time slot?

32 New Bounds

33 Parallel Saturating Counter Each MAC is model by a separate saturating counter. All counters are updated at every time instance Choose the counter with best previous state as the current selected MAC

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35 Kalman Filter Model the system using an AR(p) process u[n] ~ N(0,σ u2 ) is the state variance, and w[n] ~ N(0,σ w2 ) is the observation noise variance AR:Autoregressive

36 Kalman Filter - 2 We can rewrite the state equation in the form Ref: Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory (v. 1, p.426) by Steven M. Kay

37 The updating rules Kalman Filter - 3 Ref: Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory (v. 1, p.436), by Steven M. Kay

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39 Traffic is Matter So far Kalman filter is the best This is only true for certain testing traffic. Kalman Filter state variance σ u 2 Small σ u2 filter out noise, large σ u2 track channel variation Can not do both things good at the same time if σ u2 is fixed

40 Example of traffic defeat Kalman filter Success Rate Last Best Perfect Knowledge 82 % Last Best 75 % Kalman Filter 73%

41 New State Space Equation The system is still modeled by u[n] ~ N(0,σ u2 [n]) is the state variance, and w[n] ~ N(0,σ w2 ) is the observation noise variance

42 Tracking σ u 2 We model the state variance as h[n]= h[n 1] u[n] y[n]= h[n] w [n] Where h[n] is the estimation of state variance σ u2, and Σ u [n] ~ N(0,η u2 ), where η u2 is the variance of σ u 2, given as 2 u= 2 u [ 1] 2 N Ref: Estimation with Applications to Tracking and Navigation by Yaakov Bar-Shalom, X. Rong Li, Thiagalingam Kirubarajan, chapter The variance of the sample mean and sample varinace, page 106.

43 Estimation The idea is, we use Kalman filter to track the variance σ u2 [n], and then use Particle (Kalman) filter to track the system state. Improved bayesian MIMO channel tracking for wireless communications : Incorporating a dynamical model, by HUBER Kris and HAYKIN Simon

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45 Outline Motivation and Goal Emulation Environment MAC selection Methods Conclusions

46 Conclusion We investigated many MAC selection strategies under the cases that PSR estimations are (1)updated only at the chosen MAC, or (2)always updated for all MAC For (1), Multi-armed Bandit method gave good performance if right model is chosen For (2), Kalman Filter with varying σ u2 [n] gave good performance

47 Conclusion - 2 If computation power is limited, just choose the best MAC in previous slot. It also gives very good result.

48 Future Work Do simulation that multiple nodes can select MAC Currently we only select the best MAC Choose the best N MACs to increase throughput Sending redundant (overlapped ) date via N MACs to increase reliability.