1. 27th, Nov 2001 GLOBECOM2001 1 /16 Analysis of Dynamic Behaviors of Many TCP Connections Sharing Tail-Drop / RED Routers Go Hasegawa Osaka University, Japan hasegawa@cmc.osaka-u.ac.jp

2. GLOBECOM2001 2 /16 27th, Nov 2001 Backgrounds TCP (Transmission Control Algorithm) TCP (Transmission Control Algorithm)  Majority in the current Internet, also in the future Analytic investigation is necessary to understand its characteristics Analytic investigation is necessary to understand its characteristics

3. GLOBECOM2001 3 /16 27th, Nov 2001 Past researches on TCP throughput analysis Long-term average throughput Long-term average throughput  Short-term throughput is important for short file transfer Assume constant packet loss ratio Assume constant packet loss ratio  Packet loss ratio changes dynamically due to bursty packet loss Assume RED works fine at the router Assume RED works fine at the router  Bad parameter setting degrades RED performance, causing bursty packet loss

4. GLOBECOM2001 4 /16 27th, Nov 2001 Objectives Analysis of window size distribution of TCP connections Analysis of window size distribution of TCP connections  Using simple Markov modeling of TCP behavior  Many TCP connections accommodated  TD (Tail-Drop) and RED (Random Early Detection)  Effect of bursty packet loss Evaluation of TD/RED routers in terms of … Evaluation of TD/RED routers in terms of …  Short-term fairness among TCP connections  Effect of poor parameter set of RED  Effect of TD buffer size

5. GLOBECOM2001 5 /16 27th, Nov 2001 Network model N sender hosts transmit packets to receiver host by TCP Reno N sender hosts transmit packets to receiver host by TCP Reno Two packet dropping disciplines at router Two packet dropping disciplines at router  TD (Tail Drop)  RED (Random Early Detection) Focus on changes of window size, and ssthresh value of TCP connection Focus on changes of window size, and ssthresh value of TCP connection Sender Host 1 Sender Host 2 Sender Host N Receiver Host TD/RED Router Buffer Size: B packets

6. GLOBECOM2001 6 /16 27th, Nov 2001 Markov modeling of TCP behavior State is a combination of window size and ssthresh values of a TCP connection State is a combination of window size and ssthresh values of a TCP connection  (w i, t i ) State transition occurs at every RTT State transition occurs at every RTT  cwnd increases when no packet loss occurs  cwnd and ssth decrease when packet loss occurs State transition probabilities are dependent on… State transition probabilities are dependent on…  Packet loss probability at the router buffer  Slow start, congestion avoidance algorithms of TCP

7. GLOBECOM2001 7 /16 27th, Nov 2001 Increasing window size When no packet loss occurs When no packet loss occurs  Probability: (1 – p) w i State transition from (w i, t i ) to … State transition from (w i, t i ) to …  (2w i, t i ) When w i < (1/2)t i (Slow Start Phase) When w i < (1/2)t i (Slow Start Phase)  (t i, t i ) When (1/2)t i < w i < t i (Phase Shift) When (1/2)t i < w i < t i (Phase Shift)  (w i +1, t i ) When t i < w i (Congestion Avoidance Phase) When t i < w i (Congestion Avoidance Phase)

8. GLOBECOM2001 8 /16 27th, Nov 2001 Decreasing window size When packet loss occurs When packet loss occurs  Probability: 1- (1 - p) w i State transition from (w i, t i ) to … State transition from (w i, t i ) to …  (1, w i /2) When timeout occurs When timeout occurs  (w i /2, w i /2) When fast retransmit occurs When fast retransmit occurs Probability of timeout Probability of timeout  Dependent on w i and number of lost packets in a window

9. GLOBECOM2001 9 /16 27th, Nov 2001 Packet loss probability: p Past researches assume p is constant Past researches assume p is constant Actually dependent on… Actually dependent on…  Router buffer size: B  Window size: w i  Packet discarding discipline TD (Tail Drop), RED (Random Early Detection) TD (Tail Drop), RED (Random Early Detection)

10. GLOBECOM2001 10 /16 27th, Nov 2001 Tail-drop router Bursty packet loss occurs when the router buffer overflows Bursty packet loss occurs when the router buffer overflows To calculate p, we have derived … To calculate p, we have derived …  p overflow : frequency of buffer overflow  L overflow : # of lost packets in each buffer overflow  L i : # of lost packets for each TCP connection in each buffer overflow p = min(1, p overflow ・ L i /w i ) p = min(1, p overflow ・ L i /w i )

11. GLOBECOM2001 11 /16 27th, Nov 2001 Tail-drop router (2) p overflow : frequency of buffer overflow p overflow : frequency of buffer overflow  Considering queue dynamics  1/(N(W f – Nw’) L overflow : # of lost packets in each buffer overflow L overflow : # of lost packets in each buffer overflow  Each TCP connection increases its window size by 1 packet at every RTT  N packets are lost in total L i : # of lost packets for each TCP connection in each buffer overflow L i : # of lost packets for each TCP connection in each buffer overflow  Proportional to window size of each TCP connection

12. GLOBECOM2001 12 /16 27th, Nov 2001 RED router Packet discarding probability is determined from average queue length Packet discarding probability is determined from average queue length For applying to our model, we use instantaneous queue length; For applying to our model, we use instantaneous queue length;

13. GLOBECOM2001 13 /16 27th, Nov 2001 RED router (2) q: queue length q: queue length  Assume that other TCP connections are in steady state, and queue length is affected only by w i q = ((N-1)/N)w* + w i – 2  q = ((N-1)/N)w* + w i – 2  p = p red (q) p = p red (q)

14. GLOBECOM2001 14 /16 27th, Nov 2001 Accuracy of Analysis 1e-005 0.0001 0.001 0.01 0.1 1 0102030 Probability Density Function Window Size TD: Simulation TD: Analysis RED: Analysis RED: Simulation 1e-005 0.0001 0.001 0.01 0.1 1 0102030 Window Size TD: Simulation TD: Analysis RED: Analysis RED: Simulation B=8000 [packets]B=3000 [packets] N=1000, BW=1.5 Mbps,  =2 msec N=1000, BW=1.5 Mbps,  =2 msec

15. GLOBECOM2001 15 /16 27th, Nov 2001 Fairness evaluation Fairness of TD is much affected by buffer size Fairness of TD is much affected by buffer size Variation of window size of RED is small, regardless of buffer size Variation of window size of RED is small, regardless of buffer size RED can provide better fairness in short-term TCP throughput RED can provide better fairness in short-term TCP throughput 0 10 20 30 40 50 60 70 80 200300400500600700800900 Window Size [packets] Buffer Size / max th [packets] TD 99.9999% TD 99.99% RED 99.9999% RED 99.99%

16. GLOBECOM2001 16 /16 27th, Nov 2001 Conclusion Analysis of window size distribution of TCP connections Analysis of window size distribution of TCP connections  TD/RED disciplines  Burst packet loss Fairness evaluation of TD/RED router Fairness evaluation of TD/RED router  RED can give short-term fairness among connections

17. GLOBECOM2001 17 /16 27th, Nov 2001

18. GLOBECOM2001 18 /16 27th, Nov 2001 RED router Probability is changed according to average queue length Probability is changed according to average queue length Avoid buffer overflow, keep queue length low Avoid buffer overflow, keep queue length low max th min th １ max p 0 20 40 60 80 100105110115120 Queue Length Average Queue Length max th min th Queue Length [packets] Time [sec] Average Queue Length [packets] Packet Discarding Probability