1 Colored GSPN Models for the QoS Design of Internet Subnets Marco Ajmone Marsan IEIIT-CNR and Politecnico di Torino - Italy Eindhoven – June 27, 2003

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Colored GSPN Models Colored GSPN Models for the QoS Design for the QoS Design of Internet Subnetsof Internet Subnets

Marco Ajmone MarsanMarco Ajmone MarsanIEIIT-CNR and Politecnico di Torino - Italy

Eindhoven – June 27, 2003

ICATPN 2003

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Venice 1988

My previous invited talk at ICATPN

Goal: convince researchers to use GSPN models

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Today

Original goal: publish a paper that I thought nobody would accept …

…but the paper was accepted!

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Today

New goal: explain why (IMO) GSPN models (and discrete-state models in general) are becoming inadequate for Internet modeling

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Colored GSPN Models Colored GSPN Models for the QoS Design for the QoS Design

of Internet Subnetsof Internet Subnets??Marco Ajmone MarsanMarco Ajmone Marsan

IEIIT-CNR and Politecnico di Torino - Italy

Eindhoven – June 27, 2003

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Outline

The Internet today

Dimensioning IP networks

GSPN and Queuing network models

Fluid approaches

Conclusions

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Outline

The Internet today



Fluid approaches

Conclusions

9Source: Internet Software Consortium (http://www.isc.org/)

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Source: Internet Traffic Report (http://www.internettrafficreport.com/)

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14Source: Sprint ATL (http://ipmon.sprint.com/packstat)April 7th 2003, 2.5 Gbps link

http://ipmon.sprint.com/packstat















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And still growing ...

Subject: [news] Internet still growing 70 to 150 per cent per yearDate: Mon, 23 Jun 2003 09:55:45 -0400 (EDT)From: [email protected]

...Andrew Odlyzko, director of the Digital Technology Center at the University of Minnesota, ... says Internet traffic is steadily growing about 70 percent to 150 percent per year. On a conference call yesterday to discuss the results, he said traffic growth slowed moderately over the last couple of years, but it had mostly remained constant for the past five years....

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Outline

The Internet today



Fluid approaches

Conclusions

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Over 90 % of all Internet traffic is due to TCP connections

TCP drives both the network behavior and the performance perceived by end-users

Analytical models of TCP are a must for IP network design and planning

Consideration

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A TCP Primer in 10 Slides• TCP is a reliable packet transfer protocol that

uses a variable window algorithm for:– Error control– Flow control– Congestion control

• Two main algorithms (and a number of gadgets):– Slow start– Congestion avoidance

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Slow Start Algorithm

• Idea:– The new segment (packet) transmission rate

adapts to the ACK reception rate– The TCP transmitter “tests” the link capacity

• At connection setup, cwnd = 1 segment (actually, cwnd=MSS)

• At every received ACK, cwnd = cwnd + 1

• The resulting growth is exponential

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Slow Start AlgorithmHost A

1 segment

RT

T

Host B

Time

2 segments

4 segments

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Slow Start: Sample Trace

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Congestion Avoidance Algorithm

• Idea:– Slower growth of cwnd

• At every ACK reception– cwnd = cwnd + 1/ cwnd – cwnd = cwnd + MSS*MSS/ cwnd (in bytes)

• The resulting growth is linear – cwnd grows by 1 MSS per RTT

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Congestion AvoidanceSample Trace

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When a Segment is Lost …

• …the transmitter rate has exceeded the available bandwidth

• Idea:– Reset the window size (cwnd=1)– Quickly recover the transmission rate

• The TCP transmitter detects the loss when the timeout expires, or 3 dupacks are received

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Graphically …

5

10

15

20

cwnd

Time [RTT]

ssthresh

slow start

congestionavoidance

RTO

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TCP Fairness

• The congestion control algorithm in TCP is AIMD (additive increase, multiplicative decrease)

• Fairness: N TCP connections sharing one bottleneck link of capacity C, obtain each C/N

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R

R

Fair bandwidth sharing

Throughput connection 1Th

roughput

connec t

i on 2

loss: window reduced by factor 2

congestion avoidance: AI

Fairness with 2 TCP connections

• AI: linear increase

• MD: proportional decrease

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AQM: RED

P(d)

Avgminth

maxth

1

Pmax

RED

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Consideration

Accurate TCP models must consider:

closed loop behavior

short-lived flows

multi-bottleneck topologies

AQM schemes (or droptail)

QoS approaches, two-way traffic, ...

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Developing accurate analytical models of the behavior of TCP is difficult.

A number of approaches have been proposed, some based on sophisticated modeling tools.

Consideration

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Outline

The Internet today



Fluid approaches

Conclusions

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T. Lakshman and U. Madhow, "The performance of TCP/IP for networks with high bandwidth-delay products and random loss," IEEE/ACM Transactions on Networking, vol. 5, no. 3, 1997.

M.Ajmone Marsan, E.de Souza e Silva, R.Lo Cigno, M.Meo, “An Approximate Markovian Model for TCP over ATM”, UKPEW '97

J. Padhye, V. Firoiu, D. Towsley, J. Kurose, "A Stochastic Model of TCP Reno Congestion Avoidance and Control“, UMASS CMPSCI Technical Report, Feb 1999.

Literature

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C.Casetti, M.Meo, “A New Approach to Model the Stationary Behavior of TCP Connections”, Infocom 2000

M.Ajmone Marsan, C.Casetti, R.Gaeta, M.Meo, “An Approximate GSPN Model for the Accurate Performance Analysis ofCorrelated TCP Connections”, SPECTS 2000

M.Garetto, R.Lo Cigno, M.Meo, E.Alessio, M.Ajmone Marsan, “Modeling Short-Lived TCP Connections with Open MulticlassQueueing Networks”, PfHSN 2002

A.Goel, M.Mitzenmacher, "Exact Sampling of TCP Window States", Infocom 2002

Literature

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R.Gaeta, M.Sereno, D.Manini, "Stochastic Petri Nets models for the performance analysis of TCP connections supporting finite data transfer", QOS-IP 2003

R.Gaeta, M.Gribaudo, D.Manini, M.Sereno, "On the Use of Petri Nets for the Computation of Completion Time Distributon for Short TCP Transfers", ICATPN 2003

Literature

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1 2

3

4...

N

URLs/sec

URLs/sec

greedy flows

4N F

23 F

finite flows (mice)

finite flows

greedy flows (elephants)

IP core

Problem statement

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Input variables: only primitive network parameters:

IP network: channel data rates, node distances, buffer sizes, AQM algorithms (or droptail), ...

TCP: number of elephants, mice establishment rates and file length distribution, segment size, max window size, ...

Output variables: IP network: link utilizations, queuing delays, packet loss probabilities, ...

TCP: average elephant window size and throughput, average mice completion times, ...

Problem statement

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IP networksub-model

TCPsub-model

1load

1

load N

packet loss probabilities, queuing delays

TCPsub-model

N

decomposition of the whole system into subsystems: sub-models are built for groups of homogeneous TCP connections (same TCP version, similar RTT and routing, ...) and for the IP network.

iterative solution with FPA (Fixed Point Algorithm).

Our modeling approach

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Our modeling approach

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GSPNs or . / G / queues describe states of the TCP protocol

tokens or customers stand for TCP connections

transition probabilities and service or firing times depend on TCP rules and network feedback (packet losses, round trip times, ...)

in the case of mice, colors or classes are introduced to represent the number of segments still to be transferred

TCP sub-model

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TCP sub-model (Elephants)

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TCP sub-model (Mice)

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The IP network sub-model is an open queuing network, where each queue represents an output interface of an IP router, with its buffer of finite capacity.

Different queuing models were tested:

M / M / 1 / B: very simple, but only suitable when dealing with elephants and heavy load links

M [D] / M / 1 / B: to better model the traffic burstiness of mice under variable link utilization

M [D] / M [D] / 1 / B: a very accurate model, capable of coping with complex multi-bottleneck topologies

IP network sub-model

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Bottleneck 1

Bottleneck 2

Numerical results: topology

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Numerical results: settings

0.1

0.5

10 20 100

0.4

length (segmen

ts)

probability

Packet size: 1000 bytesBuffer size: 64, 128, 512 packetsMaximum TCP window size: 64 segmentsTCP tic: 0.5 s

Flow length distribution (when mixing different flow lengths)

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modelsim

2040

6080

100120

N1

100200

300400

N2

2

3

4

5

6

Average window size

Elephants crossing both bottlenecks

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modelsim

20 40 60 80 100 120N1

100200

300400

N2

0.01

0.1

Packet loss probability

Elephants crossing both bottlenecks

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0200

400600

8001000N1

03000

60009000

12000

N2

0.01

0.1

Packet loss probability

Elephants with increased channel data rates (100 Mb/s -- 1 Gb/s)

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0.001

0.01

0.1

0.75 0.8 0.85 0.9 0.95 1Offered load

Bottleneck 1analysis - B = 128analysis - B = 64

Mice (NewReno)P

acke

t lo

ss

pro

bab

ilit

y

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0.2

0.5

1.0

2.0

5.0

10

0.75 0.8 0.85 0.9 0.95 1

Ave

rag

e co

mp

leti

on

tim

e (s

)

Offered load

10 packets20 packets100 packets

Mice (NewReno)

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Outline

The Internet today



Fluid approaches

Conclusions

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V. Misra, W. Gong, D. Towsley, "Stochastic Differential Equation Modeling and Analysis of TCP Windowsize Behavior“, Performance'99

T. Bonald, "Comparison of TCP Reno and TCP Vegas via FluidApproximation," INRIA report no. 3563, November 1998

V. Misra, W. Gong, D. Towsley, "A Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED“, SIGCOMM 2000

Literature

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Y.Liu, F.Lo Presti, V.Misra, D.Towsley, Y.Gu, "Fluid Models and Solutions for Large-Scale IP Networks", SIGMETRICS 2003

F. Baccelli, D.Hong, "Interaction of TCP flows as Billiards“, Infocom 2003

F.Baccelli, D.Hong, "Flow Level Simulation of Large IP Networks“, Infocom 2003

Literature

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Abandon a microscopic view of the IP network behavior, and model packet flows and other system parameters as fluids

The system is described with differential equations

Solutions are obtained numerically

Modeling approach

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A simple example:

One bottleneck link

RED buffer

Elephants only (no slow start)

Modeling approach

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TCP model

dWs(t)/dt = 1/Rs(t) – Ws(t) s(t) / 2

Where:

• Ws(t) is the average window • Rs(t) is the average round trip time

• s(t) is the congestion indication rate

of TCP sources of class s at time t

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IP network model

dQk(t)/dt = Σs Ws(t) (1-P(t)) / Rs(t)

– - C 1{Qk(t)>0}

Where:

• Qk(t) is the length of queue k at time t

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IP network model

Rs(t) = PDs + Qk(t)/C

Where:

• PDs is the propagation delay for source s

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IP network model

s(t+Rs(t)) = Ws(t)/Rs(t) P(t)

Where:

• P(t) is the loss probability at time t

P(t) = RED(Q(t))

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Fluid models – work in progress

• Slow start (mice)• Droptail buffers• Finite window• Threshold • Distributions • Fast recovery• Core network topologies

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Fluid models – results

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Baccelli and Hong obtained results for an access network with over one million TCP flows, about ten thousand routers, and link capacities from 6 Mb/s to 50 Gb/s.

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Outline

The Internet today



Fluid approaches

Conclusions

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Conclusions

Fluid models today seem the most promising approach to study large IP networks

Tools for the model development and solution are sought

Fluid Petri Nets may be helpful for the model construction

Efficient numerical techniques are a challenge

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Conclusions

The modeling paradigms to study the Internet behaviour are changing

This is surely due to scaling needs, but probably also corresponds to a new phase of maturity in Internet modeling

Reliable predictions of the behavior of significant portions of the Internet are within our reach

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A comment on model complexity

time

models used

understanding of mechanisms being modeled

models proposed

early middle late

modelcomplexity

Adapted from [Hluchyj 2001], [Kurose 2001]

We need to go down

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Thank You !

Documents

1 Colored GSPN Models for the QoS Design of Internet Subnets Marco Ajmone Marsan IEIIT-CNR and Politecnico di Torino - Italy Eindhoven – June 27, 2003