Analytic Performance Evaluation of the RED Algorithm

Transcription

1 Prof. Dr. P. Tran-Gia Analytic Performance Evaluation of the RED Algorithm Stefan Köhler, Michael Menth, Norbert Vicari TCP Model RED Model TCP over RED Results

2 TCP > Reliable transmission > Closed loop flow control > Elastic traffic without real-time requirements > Major part of Internet traffic > Interactive Applications

3 TCP s slow start and congestion avoidance window size segment loss detected... advertised window... = all outstanding s of the previus burst are acknowledged slow start slow start congestion avoidance transmission number

4 TCP s fast retransmit algorithm window size 3* fast retransmit... advertised window... 3* = three duplicate s are received for the segment sent immediately before the lost segment fast recovery = all outstanding s of the previus burst are acknowledged congestion avoidance transmission number

5 Analytical Approach > Semi-Markov process (SMP) > Renewal points: Time instant when last packet that has seen the last renewal point has left the queue. > TCP rounds Sender Receiver

6 Renewal Points Q t 0 C t 1 t 2 t 3 t n t n+1 t

7 Discrete-Time Model for a Single TCP Connection > Assumptions TCP Reno FTP-source Independent packet losses (later based on RED) State variables: (W n, S n, M n ) := (CWND(t), SSTRESH(t), Loss(t)) Observation: TCP-Round

8 A Single TCP Connection Input: model state (W n, S n, M n ), model factor (L(W n )) if (M n = 0) then S n+1 := S n if (W n = W max ) then {no loss last round} {full window possible} W n+1 := W n else if (W n < S n ) then {slow start} endif else W n+1 := 2*W n else W n+1 := W n + 1 endif {congestion avoidance}

9 A Single TCP Connection else if (M n = 1) then S n+1 := max(w n /2,2) W n+1 := S n+1 else endif endif S n+1 := max(w n /2,2) W n+1 := 1 M n+1 := min(l(w n ),2) {one loss last round} {more than one loss last round} Output: model state(w n+1, S n+1, M n+1 )

10 Simulation Analysis (I) simulation analysis p=0.01 P{ CWND } CWND

11 Simulation Analysis (II) 0.9 P{ CWND } simulation analysis p= CWND

12 Random Early Discard (RED) Queue Drop Probability: P(AQL(t)) 1.0 p max r min r max Queue Length Average p( A = i) = 0 i rmin r r max 1 min p max r 0 i < r min r max min i r max < i

13 RED Queue Mechanism Input: model state (A n ), model factor (B, L(B,A n )) Q := B - L(B, A n ) A n+1 := Q + (1- ) A n Output: model state (A n+1 ) B: batch of packets A: average queue size L: loss Q: actual queue size : weighting factor The probability of k losses within a batch B of j packets follows a binomial distribution: l( A j p k k =, = )[ ] = ( ) (1 ( )) i B j k A = i p A = i j k

14 Compound Analysis > h TCP Connections under RED: Input: model state ((Wi n, Si n, Mi n ),(A n )), model factor Li(A n,wi n ) for i {1,, h} do (Wi n+1, Si n+1, Mi n+1 ) := TCP((Wi n, Si n, Mi n ), Li(A n, Wi n )) end for A n+1 := RED( (A n ), (Σ Wi n, Σ Li(A n,wi)) ) Output: model state ((Wi n+1, Si n+1, Mi n+1 ),(Q n+1,a n+1 ))

15 Prof. Dr. P. Tran-Gia Results

16 Parameters If not stated differently R min =9 R max =18 =0.3 3 TCP sources CWND=6

17 Influence of the Weighting Factor p max = CWND S.T.P CWND, S.T.P C var of CWND, S.T.P CWND S.T.P > Increased throughput, reduced variance

18 Influence of the Loss Function mean CWND = 0.1 = 0.3 simulation succ. transmitted packets = 0.1 = p max p max > High loss probability reduces throughput. > Long Memory provides better results.

19 Influence of the Buffer Size =0.3 succ. transmitted packets = 0.3, R max = 18 = 0.3, R max = 12 = 1.0, R max = 12 mean CWND = 0.3, R max = 18 = 0.3, R max = 12 = 1.0, R max = p max p max > Short (or congested) queues limit the congestion window size. > FIFO RED

20 Distribution of CWND P{ CWND } p max = 0.1 p max = 0.5 p max = 1.0 = 1.0 R max = 12 P{ CWND } p max = 0.1 p max = 0.5 p max = 1.0 = 0.3 R max = CWND CWND > Long Memory and small loss probabilities show larger congestion windows

21 Conclusion and Outlook > Summary Discrete-Time Model of TCP and RED Correlation of TCP sources Analytical Performance Evaluation Distributions for all TCP state variables > Results Sensitivity of TCP to Weighting factor Loss function Congestion or short queues Good Performance: Smoothed FIFO-Queues > Outlook Comparison of different TCP implementations Influence of non-linear loss functions Fairness studies

22 Prof. Dr. P. Tran-Gia THE END