Simulating Large Networks using Fluid Flow Model

Yong LiuJoint work with

Francesco LoPresti, Vishal Misra

Don Towsley, Yu Gu

Outline

• Fluid Flow Model

• ODE solving Methods

• Account for Topology

• Computation Savings

• Model Adjustments

• Integration with Packet Level Simulators

• Open Issues

network

TCP runs at the “edge”

Routers within network drop/markpackets when buffersfill up

Fluid Model of a Network of AQM Routers Supporting TCP Flows

TCP Congestion Control: window algorithm

Window: can send W packets at a time

• increase window by one per RTT if no loss

• decrease window by half on detection of loss

TCP Congestion Control: window algorithm

Window: can send W packets

• increase window by one per RTT if no loss

• decrease window by half on detection of loss

sender

receiver

W

TCP Congestion Control: window algorithm

Window: can send W packets

• increase window by one per RTT if no loss

• decrease window by half on detection of loss

sender

receiver

W

Active Queue Management:RED

• RED: Random Early Detect proposed in 1993

• Proactively mark/drop packets in a router queue probabilistically to– Prevent onset of congestion by reacting early – Remove synchronization between flows

The RED Mechanism

RED: Marking/dropping based on average queue length x (t) (EWMA algorithm used for averaging)

tmin tmax

pmax

1

2tmax

Mar

king

pro

babi

lity

p

Average queue length x

t ->

- q (t)- x (t)

x (t): smoothed, time averaged q (t)

Modeling RED: A Single Congested Router

TCP flow i, prop. delay Ai

AQM router

C, p

• One bottlenecked AQM router– service capacity {C (packets/sec) }

– queue length q(t)

– drop prob. p(t)

• N TCP flows

– window sizes Wi (t)– round trip time

Ri (t) = Ai+q (t)/C– throughputs

Bi (t) = Wi (t)/Ri (t)

System of Differential Equations

Window Size:

All quantities are average values. Timeouts and slow start ignored

dtdWi

Additiveincrease

))(( tqR1

i

Loss arrivalrate

)())(()(

tptqRtW

i

i

Mult.decrease

2Wi

Queue length: dtdq

Outgoingtraffic

C1 0tq ])([

Incomingtraffic

))(()(

tqRtW

i

i

System of Differential Equations (cont.)

Average queue length:

Where = averaging parameter of RED(wq)= sampling interval ~ 1/C

Loss probability:

Where is obtained from the marking profile

p

x

)()ln(

)()ln(

tq1

tx1

dtdx

dtdx

dxdp

dtdp

dxdp

Stepping back: Where are we?

N+2 coupled equations solved numerically

W=Window size, R = RTT, q = queue length, p = marking probability

N1iRpfdtdW

i1i ),(

)( i2 Wfdtdq

)(qfdtdp

3

Fluid Flow Model for a Network with Multiple Bottle-necks

Scalable with link bandwidth and flow population within each class

Network of M RED queues, K TCP classes, flows in class kkn

ODE Solving Methods• Matlab ODE Solver Suit

• Error control, automatically adjusted step-size• Cannot handle delayed differential equations• Lack of flexibility of programming• Computational Inefficiency

• Fixed Stepsize Runge-Kutta Method

• FFM: Time stepped numerical fluid model solver in C

Computation Cost: Matlab vs. FFM

80 TCP Classes x 20 RED Queues, Random Routing Matrix

Matlab: 1572 seconds FFM: 5 seconds

0

2

4

6

8

10

12

window1 window2 window3

0

2

4

6

8

10

12

window1 window2 window3

Accuracy: FFM vs. NS

Single Bottle Neck Network, 2 TCP Classes, Flows Per Class: 60 40 20

Account for Topology

Fact: TCP sending rate will be reshaped in each queue it traverses

C C

0

0.01

0.02

0.03

0.04

0.05

FFMNS

Q1 Q2

Packet Loss Probability (I)

0

0.01

0.02

0.03

0.04

0.05

FFMNS

Packet Loss Probability (II)

Account for Topology

Keep track of each TCP class’s arrival rate and departure rate at each queue:

Account for Topology

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

FFFMFFMNS

0

0.005

0.01

0.015

0.02

0.025

FFFMFFMNS

FFFM: Finer Fluid Flow Model

Packet Loss Probability (I) Packet Loss Probability (II)

Refined Fluid Model Solver

Initialiazation

End ofSimulation?

Update Windowsof All TCP Classes

Update QueueLength & Loss

Probability at allCongested Link

Update Each TCP’sState Variables at AllQueues on its Route

Dumping Data

YES

NO

Start

END

Model Adjustment 1In ns, actual packet drop/mark prob. is not equal to loss probability calculated from RED formula.Given a RED calculation value p, RED tries to make the interval between two drops/marks uniformly distributed in [1/p, 2/p] when“wait” option is on and [1, 1/p] when “wait” is off. Actual loss prob. is 2p/3 if “wait” on; 2p if “wait” off

Model Adjustment 1With wait:

Without wait:

Model Adjustment 2

NS won’t drop packet if the queue is empty

Adjustment:

Other Adjustments • TCP Newreno and SACK only backoff once for multiple losses within one window.

• Adjustment 1:

•Adjustment 2:

• At a given time, only TCP flows without packet loss will increase their congestion window.

{1,2} {1}{1,2,3}

NS vs. FFFM

NS vs. FFFM (cont.)

3 TCP Classes, 8 RED Queues

Scale bandwidth and flow population with k=1, 10, 50.Link Bandwidth: (black) 100M*k, (red) 10M*kFlows within each class: 40*k

Class1

Class2

Class3

TCP Average Sending Rate, K=1

Class NS Mean

NS Std.

FFFM

Abs. Err.

1 42.0 1.72 41.6 1.41

2 41.8 1.84 41.2 1.54

3 17.2 1.47 18.2 1.42

Class1 Class2

Class3

Queue Length, K=1

Queue NS Mean NS Std. FFFM Abs. Err.

1 100.4 18.7 99.1 14.5

2 79.6 26.1 74.6 20.2

Bottle-neck1 Bottle-neck2

TCP Average Sending Rate, K=10

Class NS Mean

NS Std.

FFFM

Abs. Err.

1 41.6 0.59 41.6 0.47

2 41.4 0.60 41.2 0.50

3 17.6 0.47 18.2 0.64

Class1 Class2

Class3

Queue Length, K=10

Queue NS Mean NS Std. FFFM Abs. Err.

1 995.4 59.5 990.5 46.4

2 779.2 116.7 745.7 96.0

Bottle-neck1 Bottle-neck2

TCP Average Sending Rate, K=50

Class NS Mean

NS Std.

FFFM

Abs. Err.

1 42.5 0.28 41.6 0.90

2 42.3 0.31 41.2 1.09

3 16.7 0.25 18.2 1.48

Class1 Class2

Class3

Queue Length, K=50

Queue NS Mean NS Std. FFFM Abs. Err.

1 4875 100 4953 91.8

2 3849 290 3729 250

Bottle-neck1 Bottle-neck2

TCP Average Sending Rate, K=100

Class NS Mean

NS Std.

FFFM

Abs. Err.

1 41.8 0.21 41.6 0.22

2 41.6 0.19 41.2 0.38

3 17.4 0.17 18.2 0.83

Class1 Class2

Class3

Queue Length, K=100

Queue NS Mean NS Std. FFFM Abs. Err.

1 9942 162 9905 134

2 7790 248 7457 351

Bottle-neck1 Bottle-neck2

Computation Savings

2 7 m in .5 6 se c1 6 m in .2 3 se c2 m in .2 se c1 2 .5 se cN S

2 ,1 8 81 ,2 8 31 5 9 .31 6 .3 2S p e e d -u p

F F M

S c a le

0 .7 6 6 se c

1

0 .7 6 6 se c

1 0

0 .7 6 6 s e c

5 0

0 .7 6 6 se c

1 0 0

0.0 0.1

1.0

1.1

1.3

1.2

1.4

1.5

4

2.0 2.1

2.2 2.3

0.2

Net 0 Net 1

Net 2

5

3.13.0

3.2 3.3

Net 3

Topology of a Large IP Network

Computation Cost

0500

100015002000250030003500400045005000

5 10 15 20 25 30 35 40 45 50 55

SimulationTime

Integration with Packet Level Simulators

Fluid flow model can provide delay and loss information for packets passing fluid network segments. If traffic from packet segments is negligible to fluid segment, fluid model can be solved independently.

Simulated by FFFM

Packet LevelPacket Level

Integration into NS

FFFM has been integrated into NS by constructing Fluid Link and Fluid Network objects.

Access

Ns node

Ns node

Access

Access

Ns node

Fluid Network Segment

FluidNetwork

Topology of Hybrid NS Simulation

Packet Network Segment

Hybrid NS SimulationLink Bandwidth: (black) 100M, (red) 15M3 Background TCP Classes, 40 Flows per Class 3 Foreground TCP Sessions

Class1

Session3

Session1

Class3Class2

Session2

Fluid Network Segment

Packet Level Nodes

Background TCP Average Window Size

Class1

Class2 Class3

hybrid packet

Foreground TCP Sample Path

Session1

Session3

Session2

Bottle-neck Queue Evolution

Bottle-neck1 Bottle-neck2

Simulation time: Hybrid: 8.4s, Packet: 29.7sCPU: 800MHz, Memory: 256M

Open Issues

• Time-out, Slow Start

• Finite duration flows, unresponsive flows

• High interaction between packet network segments and fluid network segments

• Limitations of mean value fluid model

• Verify results for large networks