Hybrid Modeling of TCP Congestion Control João P. Hespanha, Stephan Bohacek, Katia Obraczka, Junsoo...
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Transcript of Hybrid Modeling of TCP Congestion Control João P. Hespanha, Stephan Bohacek, Katia Obraczka, Junsoo...
![Page 1: Hybrid Modeling of TCP Congestion Control João P. Hespanha, Stephan Bohacek, Katia Obraczka, Junsoo Lee University of Southern California.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bf731a28abf838c7f596/html5/thumbnails/1.jpg)
Hybrid Modeling ofTCP Congestion Control
João P. Hespanha, Stephan Bohacek,Katia Obraczka, Junsoo Lee
University ofSouthern California
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Background
• TCP/IP– Transmission Control Protocol/Internet Protocol– WWW, Telnet, FTP – UNIX, Windows 98, Windows 2000 all include
TCP/IP– The evolution of TCP/IP is supported by Internet
Engineering Task Force(IETF)– Window based congestion control– If congestion occurs reduce sending rate to half,
otherwise increase window size by 1 for each round trip time
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Congestion control in data networks
Congestion control problem:How to adjust the sending rates of the data sources to make sure that the bandwidth B of the bottleneck link is not exceeded?
B
sourcesdestinations
B is unknown to the data sources and possibly time-varying
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Congestion control in data networks
q( t ) ´ queue size
r1 bps
r2 bps
r3 bps
rate · B bps
Congestion control problem:How to adjust the sending rates of the data sources to make sure that the bandwidth B of the bottleneck link is not exceeded?
queue (temporary storage for data)
![Page 5: Hybrid Modeling of TCP Congestion Control João P. Hespanha, Stephan Bohacek, Katia Obraczka, Junsoo Lee University of Southern California.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bf731a28abf838c7f596/html5/thumbnails/5.jpg)
Congestion control in data networks
When i ri exceeds B the queue fills and data is lost (drops)
rate · B bps
) drop (discrete event)
Event-based control:The sources adjust their rates based on the detection of drops
r1 bps
r2 bps
r3 bpsq( t ) ´ queue size
queue (temporary storage for data)
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Window-based rate adjustmentwi (window size) ´ number of
packets that can remain unacknowledged for by the destination
1st packet sent
e.g., wi = 3
t
2nd packet sent3rd packet sent 1st packet received & ack. sent
2nd packet received & ack. sent3rd packet received & ack. sent1st ack.
received )4th packet can be sent
t
source i destination i
wi effectively determines the sending rate ri :
round-trip time
t0
t1
t2
t3
0
1
2
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Window-based rate adjustmentwi (window size) ´ number of
packets that can remain unacknowledged for by the destination´ sending rate
totalround-trip
time propagationdelay
per-packettransmission time
time in queueuntil transmission
This mechanism is still not sufficient to prevent a catastrophic collapse of the
network if the sources set the wi too large
queuegets full
longerRTT
ratedecreases
queuegets empty
negative feedback
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TCP Reno congestion control
1. While there are no drops, increase wi by 1 on each RTT2. When a drop occurs, divide wi by 2
disclaimer: this is a simplified version of Reno that ignores some interesting phenomena…
Network/queue dynamics Reno controllers
drop occurs
drop detected(one RTT after occurred)
(congestion controller constantly probe the network for more bandwidth)
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Switched system model for TCPqueue-not-full
queue-full
(drop occurs)
(drop detected)
transition enabling condition
state reset
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Switched system model for TCPqueue-not-full
queue-full
(drop occurs)
(drop detected)
2 {1, 2 }
alternatively…continuous dynamics
discrete dynamics
reset dynamics
= 2
= 1
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Linearization of the TCP model Time normalization ´ define a new “time” variable by
queue-not-full
queue-full
In normalized time, the continuous dynamics become linear
1 unit of ´ 1 round-trip time
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Switching-by-switching analysis
queue-not-full queue full
queue-not-full queue full
queue-not-full queue full
t0 t1 t2 t3 t4 t5 t6
´ kth time the system enters the queue-not-full mode
x1 x2T
state space
x1
x2
impact map
queue-not-full
queue-full
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Switching-by-switching analysis
queue-not-full queue full
queue-not-full queue full
queue-not-full queue full
t0 t1 t2 t3 t4 t5 t6
´ kth time the system enters the queue-not-full mode
x1 x2T
Theorem. The function T is a contraction. In particular, Therefore
• xk ! x1 as k !1 x1 ´ constant• x( t ) ! x1 ( t ) as t ! 1 x1(t) ´ periodic limit cycle
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NS-2 simulation results
0
100
200
300
400
500
0 10 20 30 40 50
Win
dow
an
d Q
ueu
e S
ize (
pack
ets
)
time (seconds)
window size w1window size w2window size w3window size w4window size w5window size w6window size w7window size w8queue size q
Router R1
Router R2
TCP Sources TCP SinksBottleneck link
20Mbps/20ms
Flow 1
Flow 2
Flow 7
Flow 8
N1
N2
N7
N8
S1
S2
S7
S8
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Results
queue-not-full queue full
queue-not-full queue full
queue-not-full queue full
t0 t1 t2 t3 t4 t5 t6
Window synchronization:
convergence is exponential, as fast as .5k
Steady-state formulas:
average drop rate
average RTT
average throughput
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What next?
queue-not-full
queue-full
One drop per flow is very specific to this network:•all flows share the same
queue•similar propagation
delays for all flows•constant bit-rate cross
traffic•“drop-tail” queuing
discipline
r1 bps
r2 bps
r3 bps
B bps
queue
Other models for drops:
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What next?Other models for drops:
How many drops?
t
q( t )
queue-not-full queue full
qmax
# of drops ´ squeue-full (inrate outrate)
Which flows suffer drops?number of
packets that are out for flow i
total number of packets that are
outThis probabilistic hybrid model seems to match well with packet-level simulations, e.g., with drop-head queuing disciplines. Analysis ???
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What next?More general networks:
qA
qC
qD
qB
flow 1
flow 2
flow 3
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What next?More general networks:
portion of the queue due to flow i
outgoing rate of flow i
total queue size
drop occurs
qA
qC
qD
qB
flow 1
flow 2
flow 3
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What next?More general networks:
qC
qDqA
qB
flow 1
flow 2
flow 3
drop occurs
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What next?Even multicast (current work)…
qC
qDqA
qB
flow 1
flow 2
drop occurs
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Conclusions
Hybrid systems are promising to model network traffic in the context of congestion control:• retain the low-dimensionality of continuous
approximations to traffic flow•are sufficiently expressive to represent event-
based control mechanisms
Hybrid models are interesting even as a simulation tool for large networks for which packet-by-packet simulations are not feasible
Complex networks will almost certainly require probabilistic hybrid systems
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END
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Switching-by-switching analysis
state space
xk
xk+1
impact map
queue-not-full
queue-full
Impact maps are difficult to compute because their computation requires:Solving the
differential equations on each
mode(in general only
possible for linear dynamics)
Intersecting the continuous trajectories
with a surface(often transcendental
equations)It is often possible to prove that T is a contraction without an
explicit formula for T…