Presented by Hoang Nguyen Performance Analysis of the IEEE 802.11 Distributed Coordination Function Giuseppe Bianchi Presented by Hoang Nguyen CS598JH - Spring 06

Saturation Throughput Problem Formulation Saturation Throughput Asymptotic throughput Assumptions Ideal Channel Condition (No Hidden Terminal, No Channel Capture) Finite Number of Stations Constant & Independent Collision Probability Overload Condition

Outline Analytical Model Saturation Throughput Analysis Maximum Saturation Throughput Performance Evaluation Conclusion

Analytical Model

Analytical Model b(t): stochastic process representing the backoff counter s(t): stochastic process representing the backoff stage (0..m) W = CWmin and CWmax = 2mW Wi = 2i W at stage i 2 (0,m) {s(t), b(t)}: bidimensional process with discrete-time Markov Chain Conditional Collision Probability p Transmission Probability 

Markov Model for Single Station (1-p)/W0 Successful Transmission 1 1 …. 1 1 1 0,0 0,1 0,2 0,W0-2 0,W0-1 …. p/W_1 The backoff time is decremented at the beginning of each slot time i-1,0 p/Wi p/Wi 1 1 1 1 1 i,0 i,1 i,2 …. i,Wi-2 i,Wi-1 Unsuccessful Transmission …. p/Wm p/Wm 1 1 1 1 1 m,0 m,1 m,2 m,Wm-2 m,Wm-1 p/Wm p/Wm i,j Stage I, Backoff Window j

Stationary Distribution Derivation Derivation for bi-1,0.p = bi,0 p/Wi p/Wi 1 1 …. 1 i,0 i,1 i,Wi-1 W_0. (1-p)/W_0 Flow-in Flow-out Wi+1. p/Wi+1 bi-1,0.p/Wi + bi+1,0.1 = bi,0 + bi-1,0.p/Wi + bi+2,0.1 = bi,1 …. bi-1,0.p/Wi = bi,Wi-1 bi-1 p = bi,0

Stationary Distribution Derivation Use similar derivation, we get… Use the fact that We get Plus . Therefore, Then,

Transmission Probability Now, we have… And, p = 1 – (1-)n-1 Thus, p and  can be solve by numerical techniques

Saturation Throughput Analysis

Saturation Throughput Consider a slot time… Probability at least one transmission Ptr = 1 – (1-)n Probability of successful transmission Ps = n(1-)n-1 / Ptr

Saturation Throughput (cont.) S = E[payload information transmitted in a slot time] / E[length of a slot time] where Ts = average time channel sensed busy due to a successful transmission Tc = average time channel sensed busy due to a collision  = duration of empty slot time E[P] = average packet payload size Probability of a collision Probability of a successful transmission Probability of idle slot

Saturation Throughput (cont.) Ts and Tc depend on channel access mechanism For basic access mechanism Similarly, for RTS/CTS mechanism

Model Validation Very accurate

Maximum Saturation Throughput

Maximum Saturation Throughput Re-arrange S To maximize S, maximize this term… Take the derivation and impose to 0…

Approximate Solution More sensitive n is unknown;  depends on m and W, which are fixed in hardware!

Performance Evaluation

Saturation Throughput vs. Initial Window Size Almost independent when W · 64 Saturation throughput highly depends on W and n

Maximum Backoff Stage Greater than 4 is fine

Conclusions

Conclusions Pros Cons: Analytical Model Accurate Simple Performance Evaluation on saturation Throughput Cons: Only Saturation Throughput Only Overload Condition Only Ideal Channel Condition

Thank You!

Backup Slides

Markov Model for Single Station (1-p)/W0 1 1 1 …. 1 1 0,0 0,1 0,2 0,W0-2 0,W0-1 …. p/W_1 i-1,0 p/Wi p/Wi 1 1 1 1 1 i,0 i,1 i,2 …. i,Wi-2 i,Wi-1 …. p/Wm p/Wm 1 1 1 1 1 m,0 m,1 m,2 m,Wm-2 m,Wm-1 p/Wm p/Wm i,j Stage I, Backoff Window j