Peformance models of TCP

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Peformance models of TCP

• can simulate (ns-2)
• faithful to operation of TCP
• - expensive, time consuming
• deterministic approximations
• quick
• - ignore some TCP details, steady state
• fluid models
• transient behavior
• - ignore some TCP details

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TCP behavior
TCP runs at end-hosts

• congestion control
• decrease sending rate when loss detected,
  increase when no loss
• routers
• discard, mark packets when congestion occurs
• interaction between end systems (TCP) and
  routers?
• want to understand (quantify) this interaction

congested router drops packets
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Generic TCP behavior

• window algorithm (window W )
• up to W packets in network
• return of ACK allows sender to send another
  packet
• cumulative ACKS
• increase window by one per RTT
  W lt- W 1/W per ACK
• ? W lt- W 1 per RTT
• seeks available network bandwidth

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Generic TCP behavior

• window algorithm (window W)
• increase window by one per RTT
  W lt- W 1/W per ACK
• loss indication of congestion
• decrease window by half on detection of loss,
  (triple duplicate ACKs), W lt- W/2

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receiver
TD
sender
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Generic TCP Behavior

• window algorithm (window W)
• increase window by one per RTT W lt-
  W 1/W per ACK
• halve window on detection of loss, W lt- W/2
• timeouts due to lack of ACKs -gt window reduced to
  one, W lt- 1

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receiver
sender
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Generic TCP Behavior

• window algorithm (window W)
• increase window by one per RTT (or one over
  window per ACK, W lt- W 1/W)
• halve window on detection of loss, W lt- W/2
• timeouts due to lack of ACKs, W lt- 1
• successive timeout intervals grow exponentially
  long up to six times

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TCP throughput/loss relationship
loss occurs

• Idealized model
• W is maximum supportable window size (then loss
  occurs)
• TCP window starts at W/2 grows to W, then halves,
  then grows to W, then halves
• one window worth of packets each RTT
• find throughput as function of loss, RTT

W
TCP window size
W/2
time (rtt)
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TCP throughput/loss relationship
packets sent per period
W
TCP window size
W/2
period
time (rtt)
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TCP throughput/loss relationship
packets sent per period
W
TCP window size
W/2
period
time (rtt)
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TCP throughput/loss relationship
packets sent per period
W
TCP window size
W/2
period
time (rtt)
B throughput formula can be extended to model
timeouts and slow start (PFTK)
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B
p
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Recall RED queue management

• dropping/marking packets depends on average queue
  length -gt p p(x)
• more generally active queue management (AQM)

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Marking probability p
pmax
0
tmin
tmax
2tmax
Average queue length x
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Bottleneck behavior

• bottleneck router
• capacity fully utilized
• all interfering sessions see same loss prob.
• do all sessions see same thruput?

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Single bottleneck infinite flows

• N infinite TCP sessions
• two way propagation delay Ai, i 1,,N
• throughput Bi(p,RTTi)

• one bottleneck router
• RED queue management
• avg. queue length x dropping probability p(x)
• to obtain
• Bi TCP sessions throughput,
• router behavior, e.g., drop prob. avg. queue len.

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Model and solution

• model
• solve a fixed point problem for x
• unique solution provided B is monotonic and
  continuous on x
• resulting x can be used to obtain RTTi and p

p p(x) (AQM) RTTi Ai
x /C (round trip time) ?i B (p , RTT
i) C, for j 1 ,,N
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Model versus simulation single bottleneck,
infinite flows

• fixed router capacity 4 Mbps and RED parameters
• 10-120 TCP flows
• two-way prop. delay 202i ms, i 1,,N

router loss
throughput
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Aside other applications

• comparing different congestion control algorithms
• is forward error correction useful?

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New and improved TCP
BUMass(p)

• new/improved, BUMass(p)

• TCP, BTCP(p)

thruput
BTCP(p)
BUMass(p) gt BTCP(p)
p
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Sharing bottleneck with TCP
NUM
NTCP
NUM BUM(p) NTCP Bni(p) C
? BUM(p) gt BTCP(p)

• a win!

friendly?
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Replacing TCP with TCP UMass
N BUM(pUM) C
N
vs N BTCP(pTCP) C
? pUM gt pTCP

• a loss!

pTCP
pUM
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Use of FEC

• 10 pkt loss

? poor thruput
use packet level FEC!
p
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Use of FEC

• 10 pkt loss

? poor thruput
use packet level FEC!
p

• pFEC ltlt p

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Use of FEC

• available bandwidth, CFEC lt Cwo

• BFEC( ) Bwo( ) BTCP( )
• N Bwo(pwo) Cwo
• N BFEC(pFEC) CFEC
• ? pFEC gt pwo
• FEC reduces performance!

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Bottleneck behavior

• bottleneck router
• capacity fully utilized
• all interfering sessions see same loss prob.

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Multiple Bottleneck infinite flows

• N TCP flows
• throughputs B ltBi (Ri,pi)gt
• V congested AQM routers
• capacities C ltCv gt
• avg. queue lengths x ltxv gt
• discard prob. p ltpv (xv )gt

bottleneck router model ?i Bi (x ) Cv , v
1,,V V equations, V unknowns
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Results multiple bottleneck, infinite flows

• tandem network core, 5 -10 routers
• 2-way propagation delay 20-120 ms
• bandwidth, 2-6 Mbps
• PFTK model error
• throughput lt 10
• loss rate lt 10
• avg. queue length lt 15
• similar results for cyclic networks

throughput
router loss
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Comments

• what about UDP / non-TCP flows?
• if there are non-responsive flows, just
  decrease bottleneck capacity by non-responsive
  flow rate
• what about short lived flows?
• hard (some work in sigcomm 2001 Massoulie)
• note throughout, assumption that time to send
  packets in window is less that RTT

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Dynamic (transient) analysis of TCP fluids

• model TCP traffic as fluid
• describe behavior of flows and queues using
  Ordinary Differential Equations
• solve resulting ODEs numerically

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Loss Model
AQM Router
B(t)
p(t)
Sender
Receiver
Loss Rate seen by Sender l(t) B(t-t)p(t-t)
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A Single Congested Router

• focus on single bottlenecked router
• capacity C (packets/sec)
• queue length q(t)
• discard prob. p(t)
• N TCP flows thru router
• window sizes Wi(t)
• round trip time
• Ri(t) Aiq(t)/C
• throughputs
• Bi (t) Wi(t)/Ri(t)

TCP flow i
AQM router C, p
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Adding RED to the model
RED Marking/dropping based on average queue
length x(t)
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Marking probability p
pmax
tmin
tmax
2tmax
Average queue length x
x(t) smoothed, time averaged q(t)
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System of Differential Equations
Timeouts and slow start ignored
Window Size
Additive increase
Mult. decrease
Arrival rate
Queue length
Outgoing traffic
Incoming traffic
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System of Differential Equations
if we ignore feedback delay, t ? 0 (not R(t) 0)
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System of Differential Equations (cont.)
Red queue length smoothing
Where a averaging parameter of RED(wth) tk1
tk d sampling interval 1/C
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System of Differential Equations (cont.)
Average smoothed queue length
Where a averaging parameter of RED(wth) d
sampling interval 1/C
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N2 coupled equations
N flows Wi(t) Window size of
flow i Ri(t) RTT of flow i p(t) Drop
probability q(t) queue length
Equations solved numerically using MATLAB
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Steady slate behavior

• let t ? 8
• this yields
• the throughput is

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Steady slate behavior

• let t ? 8
• this yields
• the throughput is

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A queue is not a Network
Network - set of AQM routers, V
sequence Vi for session i
Round trip time - aggregate delay
Ri(t) Ai Sv?Vi qv(t)/Cv

Loss/marking probability - cumulative prob
pi (t) 1-Pv ?Vi (1 - pv(qv(t)))
Link bandwidth constraints Queue equations
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How well does it work?

• OC-12 OC-48 links
• RED with target delay 5msec
• 2600 TCP flows

OC-12
OC-48

• decrease to 1300 at 30 sec.
• increase to 2600 at 90 sec.

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Good queue length match
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Scaling Properties
Wk(t) Wj
k(t) qv(t)
qjv(t)/100
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Summary TCP flows as fluids

• What have we seen?
• model TCP as constant rate fluid flows
• rate sensitive to congestion via
• capacities C ltCv gt
• avg. queue lengths x ltxv gt
• discard prob. p ltpv (xv )gt
• dynamic (transient) behavior of TCP modeled as
  system of differential equations

ability to predict performance of system of TCP
flows using fluid models
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Other uses

• droptail queue
• other congestion control algorithms

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• Standard TCP connection with
• 1500-byte packets
• 100 ms round-trip time
• steady-state throughput of 10 Gbps
• requires average congestion window of 83,333
  segments
• at most one drop (mark) every 5,000,000,000
  packets equivalently, one drop every 1 2/3 hours).

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41,000 packets
60,000 RTTs 100 minutes
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• In practice, users do one of
• open N parallel TCP connections
• use MulTCP (roughly an aggregate of N virtual TCP
  connections).
• Can we do better?

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• At one end of spectrum
• simple, incremental, and easily-deployable
  changes to current protocols
• HighSpeed TCP (TCP with modified parameters)
• QuickStart (IP option to allow high initial
  congestion windows.)
• At other end of spectrum
• new transport protocol, more explicit feedback
  from routers

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Another choice of response function
Scalable TCP - S 0.15/p
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High speed TCP

• additive increase, multiplicative decrease
• increments, decrements depend on window size

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Scalable TCP (STCP)

• multiplicative increase, multiplicative decrease
• W ? W a per ACK
• W ? W b W per window experiencing loss

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STCP in images
From 1st PFLDnet Workshop, Tom Kelly