Modeling TCP-Vegas under On/Off traffic. Fifth Workshop on MAthematical performance Modeling and Analysis (MAMA) San Diego, June 10-11, 2003. Talk by Jörgen Olsén Joint work with Adam Wierman and Takayuki Osogami. Goal of paper.
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Modeling TCP-Vegas under On/Off traffic
Fifth Workshop on MAthematical performance Modeling and Analysis (MAMA)
San Diego, June 10-11, 2003
Talk by Jörgen Olsén
Joint work with Adam Wierman and Takayuki Osogami
Slow-start
Congestion avoidance
Fast Retransmit / Fast Recovery
Timeout
Aggregated load l
Network
TCP Source
Loss and Delay
Separate the models of the TCP source and the network and allow interaction via feedback
Assume the network model has delivered
Then,
Slow-start – transition rates
Below delay threshold:
Transition to intermediate state from window size w: Pw(0) P(Nb≤) / RTT
From intermediate state to doubling: Pw(0) P(Nb≤) / RTT
Above delay threshold(exit to C.A):
Transition to intermediate state from window size w: Pw(0) P(Nb>) / RTT
From intermediate to congestion avoidance w+1: Pw(0) P(Nb>) / RTT
Congestion Avoidance – transition rates
If no packets are lost:
Increase:P(Nb<) Pw(0) / RTT
Decrease:P(Nb>) Pw(0) / RTT
Stay:P( <Nb< ) Pw(0) / RTT
Fast retransmit – transition rates
To fast retransmit:
Pfr/fr / RTT
From fast retransmit back to congestion avoidance: 1 / RTT
Timeout – transition rates
To timeout:
Pto(w) / RTT
From timeout back to slow-start:
P1(0) / T
Exponential backoff – transition rates
From exponential backoff state k to k+1:
[1-P1(0)] / 2kT
From exponential backoff k back to slow-start:
P1(0) / 2kT
Application web On/Off traffic
Transport TCP mechanisms
Network
Link
Physical
Our TCP-Vegas source model mimics the structure of a network stack:
Aggregated load l
Network
TCP Source
Loss and Delay
Separate the models of the TCP source and the network and allow interaction via feedback
Offered traffic from TCP sources
Server speed is the speed of the bottleneck link
Buffer size of the bottleneck link
Offered traffic from TCP sources
Server speed is the speed of the bottleneck link
Buffer size of the bottleneck link
Aggregated load l
TCP Source
Network
l* - average load
p* - average loss rate
Loss and Delay
Find fixed-point (l*,p*, Dq*)
{
l*
= f(p*,Dq*)
(p*,Dq*)
= g(l*)
Single source model - renewal theory model for TCP
Fixed-point methods - Markov Chain model for TCP
Fixed-point methods – square root of p-law for TCP and multiple bottlenecks
A step forward in the modeling of TCP-Vegas
Showed the extensibility of the framework
The Source Model is extensible
The Network Model is extensible
Questions?
Estimated throughput
Number of back-logged packets
Approximate by
Queuing delay
Every source tries to keep a≤Nb ≤ b packets backlogged in the network
M/M/1/B queuing model: