Traffic Engineering with AIMD in Traffic Engineering with AIMD in MPLS NetworksMPLS Networks

Jianping Wang* Stephen Patek** Haiyong Wang* Jorg Liebeherr*

*Department of Computer Science**Department of Systems and Information Engineeri

ngUniversity of Virginia

http://mng.cs.virginia.edu

MPLSMPLS

Multiprotocol Label Switching (MPLS) offers opportunities for improving Internet services through traffic engineering

– MPLS makes it possible for network engineers to set up dedicated label switched paths (LSPs) with reserved bandwidth for the purpose of optimally distributing traffic across a given network

MPLS NetworkMPLS Network

• Flows (traffic between source/destination pairs) may make use of multiple LSPs.– Primary vs. Secondary Paths

Cloud

source 1

destination 2source 2

source 3

source 4

IngressNodes

destination 4

destination 3

destination 1

EgressNodes

primary path

secondary paths

source1

source2

source4

LSP 1

LSP 2

LSP 4

source3

LSP 3

Simplified MPLS NetworkSimplified MPLS Network

• N sources and N LSPs• LSP i is the primary path for source i. Other LSPs (i j) are secondary paths• Source i has a load of i and a throughput of i • LSP i has a capacity of Bi

primary path

secondary path

secondary path

source1

source2

source4

LSP 1

LSP 2

LSP 4

source3

LSP 3

Simplified MPLS NetworkSimplified MPLS Network

• Problem: Given load i and capacity Bi

Assign flow from source i to primary path and secondary paths by satisfying a given set of objectives

primary path

secondary path

secondary path

Objectives for Flow AssignmentObjectives for Flow Assignment

• Efficiency: – all resources should be consumed or all

sources should be satisfied• Fairness:

– Satisfy given fairness criteria

• Primary Path First:– Minimize traffic on secondary paths

• Simple and Distributed Allocation:– Binary Feedback, Stability

BackgroundBackground

• Binary feedback rate control schemes (AIMD)– Jacobson (1988), Jain and Ramakrishnan

(1988, 1990, 1996), Chiu and Jain (1989)

• MATE, MPLS Adpative Traffic Engineering– Elwalid et al. (2001)

• Optimization-based end-to-end congestion control and fairness– Le Boudec (1999), Kelly (1997, 1998),

Massoulie and Roberts (1999), Vojnovic et al. (2000)

OutlineOutline

1. Fairness and Efficiency2. PPF Criterion3. AIMD algorithms4. NS-2 Experiments5. Conclusions

Bandwidth allocationBandwidth allocation

• Two allocation schemes

• Owned Resources: Each source can consume the entire capacity of its primary path (Bi), and it can obtain bandwidth on its secondary paths

• Pooled Resources: The aggregate capacity on all LSPs ( iBi) is distributed across all sources, without regard to the capacity on primary paths

Rate AllocationRate Allocation

• A rate allocation is a relation R = {i, ,i} (1 i N) such that both i i and 0 i i iBi

• A rate allocation is efficient if the following hold:

a) If i i < iBi then i i = i i

b) If i i iBi then i i = i Bi

If case b) holds, we say that the rate allocation is saturating

Fairness for pooled resourcesFairness for pooled resources

• A rate allocation for pooled resources is fair if there exists a value p > 0 (fair share) such that for each source i it holds that

i = min {i, p }

• The fair share p in a network with pooled resources is given by

where U = {j | j< p } and O = {j | j p }

otherwise

if

N

i j jp

,

0,1 OO

BUi

Fairness for owned resourcesFairness for owned resources

• A rate allocation for owned resources is fair if there exists a value o > 0 (fair share) such that for each source i it holds that

i = min {i, Bi+ o }

• Interpretation: Each source can use all of its primary bandwidth and a fair share of the surplus capacity

• Define:U’ = {j | j< Bi } O’ = {j | j Bi }C' = iU’ (Bi- i ) (total surplus

capacity) i' = i- Bi , if iO’

Fair share for ownedFair share for owned resources resources

• The fair share of the surplus is given by

where U” = {j O’ | ’i< o } and O” = {j O’ | ’i

o }

• The rate allocation is given by

otherwise

ifj jo

,

0,'

O"O"

C'U"

O"

U" U'

i

ioriifo

ii

,

,

iB

Example Example

source1

source2

LSP 1

LSP 2

source3

LSP 3

1= 5 Mbps

2= 20 Mbps

3= 25 Mbps

B1 = 10 Mbps

B2 = 10 Mbps

B3 = 20 Mbps

1= 5

2= 17.5

3= 17.5

pooled resource

s

p =17.51= 5

2= 12.5

3= 22.5

owned resource

s

o =2.5

Primary Path First (PPF) Primary Path First (PPF)

source1

source2

LSP 1

LSP 2

2 Mbps

2 Mbps

5 Mbps

5 Mbps

Sources “spread” the traffic on secondary paths even though there is enough capacity on primary paths

source1

source2

LSP 1

LSP 2

7 Mbps

7 Mbps

Traffic is concentrated on primary paths

The PPF objective maximizes traffic on primary paths

Primary Path First (PPF) Primary Path First (PPF)

• Define routing matrix Xxij amount of traffic sent by source i on path j.

ij xij : secondary traffic xii : primary traffic

• A saturating rate allocation is PPF-optimal if it solves the linear program

min i ij xij

subject to j xij = i , i= 1,2,…,N

i xij = Bj , j= 1,2,…,N

xij 0 , i,j= 1,2,…,N

Characterizing PPF Solutions Characterizing PPF Solutions

source1

source2

source4

LSP 1

LSP 2

LSP 4

source3

LSP 3

x12

x23

x34

• Chain: < i1 i2 … ik >, k >2

xi1i2 > 0, xi2i3 >0,

xi3i4 > 0, …,

xik-1ik > 0

• Cycle: < i1 i2 … ik >, k > 2, i1 = ik

xi1i2 > 0, xi2i3 >0,

xi3i4 > 0, …,

xik-1ik > 0

x12

x23

x31

Proposition: A routing matrix X is PPF-optimal if and only if there is no chain and no cycle

Distributed Rate Allocation: Multipath Distributed Rate Allocation: Multipath AIMD AIMD

source1

source2

LSP 1

LSP 2

Binary Feedback from LSPs:Each LSP j periodically sends messages to all sources containing a binary signal fj = {0,1} indicating its congestion state

• Utilization = Bj fj = 1

• Utilization < Bj fj = 0

Sources adapt rate using AIMD:

• fj = 1 multiplicative decrease (0 kr 1)

• fj = 0 additive increase (ka

0)

f1=0

f1=1

Additive increase on LSP 1Multiplicative decrease on LSP2

Multipath-AIMDMultipath-AIMD

For pooled resources:

1,1

0,

0,

1

1

jrij

jilij

jilaij

ij

fkx

fxx

fxkx

x

if

andif

andif

i

N

l

i

N

l

Multipath-AIMDMultipath-AIMD

For owned resources:

i = j:i Bi

i> Bi

i j:

1,,1

0,,,

0,,,

1

1

jiiirij

jiliiiaij

jiliiiiiiij

ij

fBxkx

fxBxkx

fxBxBxx

x

if

if

orif

i

N

l

i

N

l

i

ii

if

if

iirii

iiaiiii xkx

xkxx

,1

,,min

iaiiii Bkxx ,min

Feedback for PPF correctionFeedback for PPF correction

Extra feedback is required to enforce PPF

• Sources exchange bit vectors

• Exchange is asynchronous

• Bit vector of source i : mi = < mij, mij, …, miN>

mij = 0, if xij = 0mij = 1, if xij > 0

source1

source2

source4

LSP 1

LSP 2

LSP 4

source3

LSP 3

x34

x31

<1,0,0,1>

PPF correctionPPF correction

• After each multipath-AIMD adjustment, sources perform a PPF correction:

Conflict: PPF correction tends to push flow onto primary paths, interfering with the natural tendency of AIMD to arrive at a fair distribution of the load

otherwise

ifil

,

0,0,

ij

liijij

x

mKx maxx

ijiiii xK minxx ,

ij

ns-2 simulationns-2 simulation

• Packet level simulation• 5 sources, 5 LSPs• LSP Capacities

Bi=(50,40,30,30,30) Mbps

Access link bandwidth: 100 MbpsPropagation delay: 5 msFrequency of

congestion feedback LSP =5mssource update SRC =5ms

Packet size: 50 BytesAIMD parameters:

ka = 0.1 Mbps

kr = 0.01

B1

B2

B4

B3

S1

S2

S3

S4

I1

I2

I3

I4

I5 B5S5

Experiment 1: Experiment 1: Basic Multipath-AIMD with Basic Multipath-AIMD with Pooled ResourcesPooled Resources

• All sources are always backlogged (“Greedy Sources”)

• All sources converge within 90 seconds to the fair-share allocation

• The final routing matrix is not PPF optimal

Experiment 2: Basic Multipath-AIMDExperiment 2: Basic Multipath-AIMD

Initial scenario0 t < 80 sec

Final scenario80 t < 200 sec

Source i

Load i

Tput i

pooled

Tput i

owned

Load i

Tput i

pooled

Tput i

owned

1 10 10 10 10 10 10

2 30 30 30 50 46.7 50

3 50 50 50 50 46.7 45

4 60 60 60 60 46.7 45

5 30 30 30 30 30 30

Experiment 2: Pooled ResourcesExperiment 2: Pooled Resources

• Note convergence to new after load change of source 2 at 80 sec

• Solution not PPF optimal

Experiment 2: Owned ResourcesExperiment 2: Owned Resources

• Note convergence to new after load change of source 2 at 80 sec

• Solution is not PPF optimal

Experiments with PPF CorrectionExperiments with PPF Correction

• Loadsi=(50,40,30,30,30) Mbps

• Resources are pooled

• Sources exchange bit vector over a full-duplex link– Bandwidth: 100 Mbps– Propagation delay: 1 ms– Frequency PPF =5ms

• PPF parameters:K = 0.00001 Mbps

K=0.01 Mbps

Experiment 3: Experiment 3: Multipath-AIMD with PPFMultipath-AIMD with PPFcorrection with K = 0.00001 Mbpscorrection with K = 0.00001 Mbps

• Final allocation is fair, but not PPF-optimal

Experiment 3: Experiment 3: Multipath-AIMD with PPFMultipath-AIMD with PPFcorrection with K = 0.01 Mbpscorrection with K = 0.01 Mbps

• Final allocation is PPF-optimal, but not fair

ConclusionsConclusions

• We have proposed multipath-AIMD to achieve a fair and PPF-optimal rate allocation to flows in an MPLS network– Multipath-AIMD seeks to provide a fair allocation of

throughput to each source– Multipath-AIMD with PPF Correction seeks to

reduce the volume of secondary path traffic• Both algorithms rely upon binary feedback information

• Observation: Difficult (impossible?) to achieve PPF and fairness objectives simultaneously

• Open issues:– Relax restrictions on topology– (When) is it possible to be both fair and PPF optimal?