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Markov Chain of DCF

Markov Chain of DCF. Speaker : 林益宏 Date : 10/26/’05 COMM, CCU E-mail : g92430006@comm.ccu.edu.tw. Outline. Stochastic process Markov process Discrete time MC (DTMC) DCF Summary. Stochastic process. Define : A stochastic process is a family of random variables X(t) X() : state space

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Markov Chain of DCF

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  1. Markov Chain of DCF Speaker : 林益宏 Date : 10/26/’05 COMM, CCU E-mail : g92430006@comm.ccu.edu.tw

  2. Outline • Stochastic process • Markov process • Discrete time MC (DTMC) • DCF • Summary

  3. Stochastic process • Define : A stochastic process is a family of random variables X(t) • X() : state space • t : time index X: {X(t), tT} is called a stochastic process

  4. Types of stochastic process • Discrete state, discrete time • e.g : 第t天收到的mail數 • Discrete state, continuous time • e.g : (0,t)時間內瀏覽網頁的次數 • Continuous state, discrete time • e.g : 第t天使用MSN的時間 • Continuous state, continuous time • e.g : (o,t)時間內伺服器忙碌的時間

  5. ? Markov Process • Markov Process • future evolution of stochastic process depends only on current state • Markov Chain • A discrete stateMarkov Process forms a Markov Chain (MC) if the probability of the next state depends only on current state t

  6. Discrete Time MC (DTMC) • discrete state, discrete time random process • possible set of countable states • All past history summarized in current state • Transitions between states take place only at discrete time

  7. Example • 天氣預測 • 假設昨天的天氣只跟今天有關… State=(sunny, cloudy, rainy) 0.9 sunny 0.95 0.01 0.5 0.09 0.01 cloudy rainy 0.1 0.04 0.4

  8. m-step Transition Probability Chapman-Kolmogorov equation m–step transition probability

  9. 0.3 0 1 0.6 0.4 Steady State Probability • 系統穩定性(stationary) • 無論初始值是什麼,最後系統都能趨於穩定 0.7

  10. Example 0.3 0 1 0.7 0.6 0.4

  11. DCF( Distributed Coordination Function) • CSMA/CA - Carrier Sense Multiple Access with Collision Avoidance • Sense before transmission • If idle transmit • Else backoff

  12. Binary Exponential Backoff • Backoff_Counter= INT (CW * Rnd( )) * slot time • INT (x) : maximal int ≤ x • CW : integer between CWmin and CWmax • Rnd( ) : real number between 0 and 1

  13. Binary Exponential Backoff 1023 Contention Window Size CWmax 511 255 127 63 31 31 CWmin t

  14. Backoff Contention Window • Backoff time random chosen from (0,W-1) • After fail transmission w is doubled, up to 2mW • W is CWmin+1 • 2mW is CWmax+1 CW

  15. Markov chain model 1 1 1 0,0 0,1 0,2 0,W0-1 1-p p 1 1 1 1,0 1,1 1,2 1,W1-1 1-p 1 1 1 i,0 i,1 i,2 i,Wi-1 1-p p 1 1 1 m,0 m,1 m,2 m,Wm-1 1-p

  16. Throughput Analysis 某一個station想傳送的機率 至少有一個station傳送的機率 傳送成功的機率 Payload平均長度 Throughput Idle Success collision

  17. F & Q

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