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					                 Analysis of Dynamic Behaviors
                 Many TCP Connections
                 Sharing Tail-Drop / RED Routers
                                              Go Hasegawa
                                     Osaka University, Japan

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         n   TCP (Transmission Control Algorithm)
                 ¨ Majority in the current Internet, also
                  in the future
         n   Analytic investigation is necessary  
             to understand its characteristics

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 Past researches on TCP throughput
   n   Long-term average throughput
        ¨ Short-term throughput is important for
            short file transfer
   n   Assume constant packet loss ratio
        ¨ Packet loss ratio changes dynamically
            due to bursty packet loss
   n   Assume RED works fine at the router
        ¨ Bad parameter setting degrades RED
            performance, causing bursty packet loss
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 n   Analysis of window size distribution of TCP
      ¨ Using simple  Markov modeling of TCP behavior
      ¨ Many TCP connections accommodated
      ¨ TD (Tail-Drop) and RED (Random Early
      ¨ Effect of bursty packet loss
 n   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
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  Network model
                  TD/RED Router Buffer Size:
                         B packets
Sender Host 1

                                               Receiver Host
Sender Host 2
                      n   N sender hosts transmit packets
                          to receiver host by TCP Reno
                      n   Two packet dropping disciplines
                          at router
Sender Host N
                           ¨   TD (Tail Drop)
                           ¨   RED (Random Early Detection)
                      n   Focus on changes of window
                          size, and ssthresh value of TCP
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 Markov modeling of TCP behavior

 n   State is a combination of window size and
     ssthresh values of a TCP connection
      ¨ (wi , ti )
 n   State transition occurs at every RTT
      ¨ cwnd     increases when no packet loss occurs
      ¨ cwnd     and ssth decrease when packet loss occurs
 n   State transition probabilities are dependent
      ¨ Packet loss probability at the router buffer
      ¨ Slow start, congestion avoidance algorithms of

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 Increasing window size
 n   When no packet loss occurs
      ¨ Probability: (        1 – p ) wi
 n   State transition from (wi , ti ) to …
      ¨ (2w i , ti)
            n    When wi < (1/2)t i (Slow Start Phase )
      ¨ ( t i , t i)
            n    When (1/2)t i < wi < ti (Phase Shift )
      ¨ (wi+1, ti)
            n    When ti < wi (Congestion Avoidance Phase )

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 Decreasing window size
 n   When packet loss occurs
      ¨ Probability:       1- (1 - p)wi
 n   State transition from (wi , ti ) to …
      ¨ (1,      wi /2 )
            n    When timeout occurs
      ¨ (wi /2,      wi /2 )
            n    When fast retransmit occurs
 n   Probability of timeout
      ¨ Dependent on           wi and number of lost packets in
          a window
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 Packet loss probability: p
  n Past researches assume p is constant
  n Actually dependent on…
       ¨ Router buffer size:         B
       ¨ Window size:         wi
       ¨ Packet discarding discipline
             n   TD (Tail Drop), RED (Random Early Detection)

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 Tail-drop router
 n Bursty packet loss occurs when the
   router buffer overflows
 n To calculate p, we have derived …
      ¨ poverflow  : frequency of buffer overflow
      ¨ Loverflow : # of lost packets in each buffer
      ¨ Li : # of lost packets for each TCP
        connection in each buffer overflow
 n   p = min(1, poverflow ・Li /wi )
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 Tail-drop router                     (2)

 n   poverflow : frequency of buffer overflow
      ¨ Considering queue dynamics
      ¨ 1/(N(W f – Nw ’)
 n   Loverflow : # of lost packets in each buffer
      ¨ Each TCP connection increases its window size
          by 1 packet at every RTT
      ¨ N packets are lost in total
 n   Li : # of lost packets for each TCP
     connection in each buffer overflow
      ¨ Proportional to window size         of each TCP
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 RED router
  n   Packet discarding probability is determined
      from average queue length
  n   For applying to our model, we use
      instantaneous queue length ;

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 RED router             (2)

 n   q: queue length
      ¨ Assume that other TCP connections are
          in steady state, and queue length is
          affected only by wi

 n   q = ((N-1)/N)w* + wi – 2 tr

 n   p = pred (q)
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                         Accuracy of Analysis
                                   n     N=1000, BW=1.5 Mbps, t =2 msec
                                    1                                          1
Probability Density Function

                                               B=8000 [packets]                         B=3000 [packets]
                                  0.1               RED: Simulation           0.1
                                                                                             RED: Simulation
                                 0.01                    TD: Simulation     0.01

                                0.001                                      0.001              TD: Analysis

                                                                                               TD: Simulation
                               0.0001                                     0.0001
                                         RED: Analysis    TD: Analysis
                                                                             RED: Analysis
                               1e-005                                    1e-005
                                     0         10         20          30       0       10        20            30
                                             Window Size                              Window Size
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                        Fairness evaluation
                        80                                   n   Fairness of TD is much
                                        TD 99.9999%              affected by buffer size
Window Size [packets]

                        60                                   n   Variation of window
                        50   TD 99.99%                           size of RED is small,
                        40                                       regardless of buffer size
                        30                                   n   RED can provide better
                                          RED 99.9999%           fairness in short-term
                        10                 RED 99.99%            TCP throughput
                        200 300 400 500 600 700 800 900
                             Buffer Size / maxth [packets]

              27th, Nov 2001                           GLOBECOM2001                     15 /16
 n   Analysis of window size distribution
     of TCP connections
      ¨ TD/RED disciplines
      ¨ Burst packet loss

 n   Fairness evaluation of TD/RED router
      ¨ RED can give short-term fairness among

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 RED router
         n       Probability is changed according to average
                 queue length
         n       Avoid buffer overflow, keep queue length low
        Packet Discarding Probability               Queue Length [packets]
             1                            80   max th
                                                                Queue Length

        max p                                                 Average Queue Length
                                               min th
                  min th    max th         100          105       110      115       120
         Average Queue Length [packets]                       Time [sec]

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