load sharing in networking systems
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Load Sharing in Networking Systems
Lukas KenclIntel Research Cambridge
Weiguang Shi, University of Alberta/KiyonJean-Yves Le Boudec, EPFLPatrick Droz, IBM Research
With citations from D. Thaler, R. Ravishankar and K. Ross.
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Outline
Load sharing in networking systems• Problem statement• Motivation• Imbalance due to traffic properties…………………. Break ………………………………….……• Inspiration: distributed Web caching• Solutions and properties:
– Adaptive HRW hashing– Adaptive Burst Shifting– Integrated: Hashing with Adaptive Burst Shifting
9. 10. 2006 L. Kencl, IR Cambridge – Load Sharing in Networking SystemsMFF UK, Praha
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Load Sharing in Networking Systems
Problem Statement
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Map packets to processors
Assumptions:Assumptions:•• Data arrives in packets.Data arrives in packets.•• Any processor can Any processor can process any packet.process any packet.HeterogenousHeterogenous
processor capacityprocessor capacity μμjj..
Incoming PacketsIncoming PacketsIncoming PacketsIncoming Packets
Multiple (M)Multiple (M)ProcessorsProcessors
11
22
33
MM
Multiple (N)Multiple (N)InputsInputs
11
22
33
44
NN
Task:Task:•• Map packets to processors so that load within some Map packets to processors so that load within some measure of balance.measure of balance.
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Map packets to multiple processorsFlows: avoid remapping or mis-sequencing!!!
Incoming PacketsIncoming Packets
Multiple (M)Multiple (M)ProcessorsProcessors
11
22
33
MM
Multiple (N)Multiple (N)InputsInputs
11
22
33
44
NN
Task:Task:•• Load on processors within some measure of balance.Load on processors within some measure of balance.•• SequenceSequence--preserving: preserving:
•• flow order flow order –– minimize reordering.minimize reordering.•• same flow to same processor (context) same flow to same processor (context) –– minimize remapping.minimize remapping.
Advantage:Advantage: system optimization.system optimization. Drawback:Drawback: complexity, overhead.complexity, overhead.
Assumptions:Assumptions:•• Data arrives in ordered Data arrives in ordered packetizedpacketized flows.flows.
•• Any processor can Any processor can process any packet.process any packet.HeterogenousHeterogenous processor processor
capacity capacity μμjj..
1111
11
11
22 22
22
22
22 11
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Measures of Balance
Processing load on processor j j (t)Capacity on processor j j
Workload intensity on processor j j(t) = j(t) / j
Total system workload intensity (t) = Σ j(t) / Σ j
“No single processor is overutilized if the system in total is not overutilized,and vice versa.”
Acceptable load sharing:if (t) [ 1 then ∀j, j(t) [ 1,if (t) > 1 then ∀j, j(t) > 1.
• Packet drops
• Acceptable Load Sharing:
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Coefficient of Variation (CV)as a measure of balance
Useful, as it takes the scale of measurements out of consideration.
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Reduce state maintenance of Flow-to-Processor Mapping
Multiple (N)Multiple (N)InputsInputs
11
22
33
NN
Multiple (M) Multiple (M) ProcessorsProcessors
11
22
33
44
MM
Incoming PacketIncoming Packet
flow flow identifier identifier vectorvector vv
v v
Upon packet arrival, a decision is made where to process the pacUpon packet arrival, a decision is made where to process the packet, based ket, based on the flow identifier. A on the flow identifier. A flowflow--toto--processor mapping processor mapping ff is thus established.is thus established.
f ( f ( vv ) = ) = 33
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Minimizing Disruption
Possible Goal:Possible Goal: Acceptable load sharing Acceptable load sharing withoutwithout maintaining maintaining flow stateflow stateinformation and yet information and yet minimizingminimizing the probability of the probability of mapping disruptionmapping disruption (flow (flow
remapping or reordering).remapping or reordering).
Special 0Special 0--1 Integer Programming Problem:1 Integer Programming Problem:
maxmax ΣΣvv Δ Δ vv(t(t) . ) . ΣΣjj (1{ (1{ f(tf(t--Δ Δ t)(vt)(v) = j} .) = j} . 1{ 1{ f(t)(vf(t)(v)= j})= j}),),whilewhile ΣΣvv aavv(t(t) .) . 1{ 1{ f(t)(vf(t)(v)= j})= j} = = jj (t)(t) [ [ jj , , ∀ ∀ j.j.
v v -- flow identifier vector in the packet header,flow identifier vector in the packet header,ff(t)(t)(v(v)) -- function mapping flows to processors, changing over time,function mapping flows to processors, changing over time,ΔΔvv(t)(t)cc {0,1}{0,1} -- indicator ifindicator if vv has appeared in the intervalshas appeared in the intervals (t(t--22ΔΔ t, tt, t--ΔΔ t) t) and and (t(t--ΔΔ t, t)t, t),,aavv(t(t)) -- how many times hashow many times has vv appeared in the intervalappeared in the interval (t(t--ΔΔ t, t),t, t),
tt -- iteration intervaliteration interval. .
We suspect an We suspect an NPNP--complete problem complete problem –– use use heuristicsheuristics..
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Summarize
Balance load
Avoid remapping - or packets out-of-sequence
Minimize overhead
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Load Sharing in Networking Systems
Motivation
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Practical Motivation:Multiprocessor Networking Systems
Distributed Router, or Parallel Forwarding Engine
Server Farm Load Balancer
Network Processor
Multicore Processor
Server FarmLoad Balancer
S1
S2
SM
Packet-to-server
mapping computation
Incoming Packet
Packet forwarding
Multiple (M) Servers
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Network Processor
NPNP
Pool of Microengines (ME)Pool of Microengines (ME)
GPPGPPSRAMSRAM DRAMDRAM
PacketsPackets
Network processor:• Pool of multi-threaded forwarding
engines• Integrated or attached GPP• Memories of varying bandwidth and
capacity
Large parallel programming problem• Concurrency• Packet order• Resource allocation• Load balancing
At 10 Gbps, packets arrive every 36 ns!!!
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Load Sharing in Networking Systems
Traffic properties make balancing difficult
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Traffic Properties
Address distribution – 32bit address space very unevenly assigned and populated
Burstiness
Power law
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TCP Traffic is Bursty
TCP behaviour: ideal and typical
Packets arrive in periodic bursts!
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Networking Traffic Exhibits Power-Law (Zipf-law) Properties
Flow popularities in traffic traces
P(R)~1/Ra
Frequency of an event as a function of its rank obeys power-law.
Network flows: a close to 1 (from above).
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Power-law leads to imbalance if static mapping (Shi et al, 2004)
m - number of processors,K - number of distinct object addresses or flow IDs,pi (0<i<K) - popularity of object i, qj (0<j<m) - number of distinct adresses or flow IDs mapped to processor j
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Conclusion Part I
Complex problem
Traffic properties work against static solutions
“Technology that just works”
“Technology that just works”
Concealing Complexity
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Break 5 minutes
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Load Sharing in Networking Systems
Inspiration: Distributed Web Caching and Web Server Load Balancing
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What is a Distributed Web Cache
Intranet
Internet
Proxy Cache stores Web objects locally
Collection of distributed Web caches
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HRW Mapping
Def.Def.: : ObjectObject--toto--Processor mapping functionProcessor mapping function f, f (v): Vf, f (v): V d d M :M :f (f (vv) = j) = j ww xxjj . g (. g ( v, v, jj ) = ) = maxmaxkk xxkk . g . g ((v, v, kk),),
wherewhere vv is the object identifier vector,is the object identifier vector, x x = (x= (x11, ... , x, ... , xmm)) is a weights' vector is a weights' vector and and g (g (vv, j), j)cc (0,1)(0,1) is a pseudorandom function of uniform distribution. is a pseudorandom function of uniform distribution.
Highest Random Weight (HRW) MappingHighest Random Weight (HRW) Mapping, , ThalerThaler, , RavishankarRavishankar, 1997, Ross, 1998, 1997, Ross, 1998, CARP Protocol, Windows NT LB, CARP Protocol, Windows NT LB
Minimal disruption of mappingMinimal disruption of mapping in case of processor addition or removal/failure.in case of processor addition or removal/failure.
Load balancing over Load balancing over heterogenousheterogenous processorsprocessors: weights: weights’’ vectorvector xx is in a 1is in a 1--toto--1 1 correspondence tocorrespondence to p p = (p= (p11, ... , p, ... , pmm)),, the vector of object fractions received the vector of object fractions received at each processor.at each processor.Pseudorandom function Pseudorandom function g (g (vv, , j)j)cc (0,1)(0,1) can be implemented as a fastcan be implemented as a fast--computable computable
hash function.hash function.
0
x1
x2
1 2 3
x2 . g (v, 2)Map to max of:
x3 x3 . g (v, 3)Example
x1 . g (v, 1)
: 3 processors
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HRW Minimal Disruption
Example: Add processor No. 4, vectors mapped either (i) as before addition or (ii) to the newly added processor – minimal number of vectors change mapping.
0 1 2 3
g (v, 3)g (v, 1)
Max of:g (v, 2)
1
4
g (v, 4)
0 1 2 3
g (v, 3)g (v, 1)
g (v, 4)
4
g (v, 2)
1Max of:
Partitioning into contiguous set HRW
Minimal disruption of mapping in case of processor addition:
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HRW Load Balancing
m - number of servers, S1, …, SmK - number of distinct object addresses or flow IDs, from the set of objects Opi (0<i<K) - popularity of object i, qj (0<j<m) - number of distinct adresses or flow IDs mapped to processor j , e.g. sum of the popularities of objects mapped to Sj
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Load Sharing in Networking Systems
Adaptive Methods- Adaptive HRW Hashing- Adaptive Burst Shifting
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Adaptive HRW Hashing(Kencl, Le Boudec 2002)
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Adaptive HRW mapping
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4. Download new4. Download newx := xx := x(t).(t).
2. Evaluate 2. Evaluate (t(t)) = (= ( 1 1 (t)(t), , 2 2 (t)(t), ... , , ... , mm (t)(t)))
(compare threshold).(compare threshold).
3. Compute new3. Compute newx x (t)(t) = (x= (x1 1 (t)(t), ..., , ..., xxmm (t)(t)).).
Adaptation through Feedback
Trigger definition targets Trigger definition targets preventing overload, preventing overload, if system in if system in total not overloaded, and vice total not overloaded, and vice versa.versa.A A threshold threshold triggers adaptation triggers adaptation
when close to load sharing when close to load sharing bounds. bounds. FlowFlow--toto--processor mapping processor mapping ff
becomes a becomes a function of timefunction of timef(t)(f(t)(vv))Adaptation may cause Adaptation may cause flowflow
remapping! remapping! How to minimize the How to minimize the amount remapped?amount remapped?
Multiple (N)Multiple (N)Input CardsInput Cards
11
22
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NN
Multiple (M)Multiple (M)processorsprocessors
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MM
CPCP
Control PointControl Point
1. Filtered workload 1. Filtered workload intensity ( j) =intensity ( j) = jj(t).(t).
Problem:Problem: incoming requests incoming requests are packets, not flows! Packets not evenly distributed over floware packets, not flows! Packets not evenly distributed over flows s -->> not evenly distributed over the request object spacenot evenly distributed over the request object space --> HRW mapping not sufficient for > HRW mapping not sufficient for acceptable load sharing boundsacceptable load sharing bounds ––> need to> need to adapt!adapt!
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Adaptation Algorithm
StartStart
TriggerTriggerAdaptationAdaptation
??
Wait time Wait time tt
Adapt Adapt weights' vector weights' vector xx
and uploadand upload
Triggering PolicyTriggering Policy Adaptation PolicyAdaptation Policy
YesYesNoNo
Compute filtered Compute filtered processor workload processor workload
intensity intensity (t(t))
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Triggering Policy
Dynamic workload intensityDynamic workload intensitythresholdthreshold
'' (t) = 1/2 (1+(t) = 1/2 (1+ (t))(t))
Triggering policyTriggering policy(i)(i) if if (t(t) ) [[ 1 1 andand maxmax jj (t) > (t) > (t) (t)
then then adaptadapt;;(ii) if(ii) if (t(t) > 1) > 1 andand minmin jj (t)(t) < < (t) (t)
then then adapt.adapt.
ExampleExample::(t) = (0.8, 0.2, 0.2), (t) = (0.8, 0.2, 0.2), (t) = 0.4(t) = 0.4
ee (t) = 0.7,(t) = 0.7,11 (t)(t) >> (t)(t) e e adapt.adapt.
0 10 20 30 40 50 60 70 80 90 1000.7
0.8
0.9
1
1.1
1.2
1.3
1.4
ρ(t), system in totalworkload intensity threshold
Triggering thresholdTriggering threshold
(t)(t) = = maxmax(( '' (t), upper)(t), upper)or vice versaor vice versa
0 10 20 30 40 50 60 70 80 90 1000.7
0.8
0.9
1
1.1
1.2
1.3
1.4
ρ(t), system in totaltriggering threshold
HysteresisHysteresis boundbound
upper: (1+upper: (1+ HH(t(t)) .)) . (t)(t)lower: (1 lower: (1 -- HH(t)) .(t)) . (t)(t)
0 10 20 30 40 50 60 70 80 90 1000.7
0.8
0.9
1
1.1
1.2
1.3
1.4
ρ(t), system in totalmax, min hysteresis bound
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Adaptation Policy:Minimal Disruption
•• A, B A, B -- mutually exclusive subsets ofmutually exclusive subsets of M={1,...,m}M={1,...,m}, , M=AM=A 44 B.B.•• α α c c (0, 1).(0, 1).•• f, f'f, f' –– two HRW mappings with the weights' vectorstwo HRW mappings with the weights' vectors xx, , x'x'::
x'x'jj = = αα . . xxjj,, ∀ ∀ jj c c A,A,x'x'jj = = xxjj,, ∀ ∀ jj c c BB..
•• ppjj , , p'p'jj -- fraction of objects mapped to nodefraction of objects mapped to node j j usingusing ff, , f'f'..
1) 1) p'p'jj [ [ ppjj , , jj c c AA,,p'p'jj m m ppjj , j, j c c BB..
2) Fraction of objects mapped to a different node by each mapp2) Fraction of objects mapped to a different node by each mappingingisis MINIMAL, MINIMAL, that is, equal tothat is, equal to | | p'p'jj -- ppjj | . |V | | . |V | at every nodeat every node j. j.
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• reduced receives less, unaltered receives more, if reduction by a single, invariable multiplier.• minimal disruption of the mapping.
0
x1
x2
1 2 3
x2 . g (v, 2)
x1 . g (v, 1)Max of:
1 2 3
x3
02/3.x1
2/3.x2
x3 . g (v, 3)
2/3 . x2 . g (v, 2)
2/3 . x1 . g (v, 1)Max of:
x3 x3 . g (v, 3)
Adaptation Policy: Minimal Disruption Example (3 proc.)
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Adaptation Policy
Let Let (t(t)) [ [ 11.. Then:Then:
xxjj (t) : = (t) : = c(t)c(t) . x. xj j (t(t-- t) ,t) , ifif jj (t)(t) >> (t) (t) (( jj exceeds thresholdexceeds threshold (t(t)))),,xxjj (t) : = (t) : = xxjj (t(t-- t),t), ifif jj (t)(t) [[ (t) (t) (( jj does not exceed thresholddoes not exceed threshold (t(t))))..
IfIf (t) > 1(t) > 1,, the adaptation is carried out in a symmetrical manner.the adaptation is carried out in a symmetrical manner.
The weights' The weights' multiplier coefficient multiplier coefficient c(tc(t)) ::
( )( )(t)(t)minmin {{ jj(t(t)) | | jj(t(t)) >> (t)(t)}}c(t) =c(t) =
1/m1/m
FactorFactor c(t)c(t) is proportional to the minimal error and to the number of nodes.is proportional to the minimal error and to the number of nodes.
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Adaptive Burst Shifting(Shi, MacGregor, Gburzynski 2005)
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Adaptive Burst Shifting
Insight: the periodicity of bursts may allow shifting flows in-between bursts, without affecting order within flows.
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Adaptive Burst Shifting
Burst Distributor Algorithm
Flow Table monitors packets in system
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Performance evaluation
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Adaptive HRW on generated traffic
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Expectations
•• Workload intensity on individual processors close to that of thWorkload intensity on individual processors close to that of the e system in total system in total (acceptable load sharing);(acceptable load sharing);•• Packet loss probability lowered Packet loss probability lowered (acceptable load sharing);(acceptable load sharing);•• Persistent flows (appearing in two consecutive iterations) Persistent flows (appearing in two consecutive iterations) seldom remapped seldom remapped (minimize disruption).(minimize disruption).
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AHH Keeps Per-processor Workload Intensity Close to Ideal
0 50 100 150 2000
0.5
1
1.5
2
2.5W
orklo
ad in
tens
ity
Time
ρ(t), system in total
Naive, no LS.Naive, no LS.
0 50 100 150 2000
0.5
1
1.5
2
2.5
Wor
kload
inte
nsity
Time
ρ(t), system in total
Static HRW Static HRW
0 50 100 150 2000
0.5
1
1.5
2
2.5
Wor
kload
inte
nsity
Time
ρ(t), system in total
Adaptive HRWAdaptive HRW
0 50 100 150 2000
0.5
1
1.5
2
2.5
Wor
kload
inte
nsity
Time
ρ(t), system in totalMax, min ρj(t), no LSMax, min ρj(t), static LSMax, min ρj(t), adaptive LS
Max and min of all.Max and min of all.
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Packet Loss Significantly Reducedwith the Adaptive Control Loop
0 50 100 150 2000
2
4
6
8
10
x 104
Pac
kets
dro
pped
s
Time
System in totalNo LSStatic LSAdaptive LS
Packet loss: Naive, Static, Adaptive, Ideal. Packet loss: Naive, Static, Adaptive, Ideal.
0 50 100 150 2000
0.5
1
1.5
2
2.5
3
3.5x 10
4
Pac
kets
dro
pped
Time
Static LSAdaptive LS
Packet loss in excess of Ideal: Static, Adaptive.Packet loss in excess of Ideal: Static, Adaptive.
Adaptive HRW saves on average 60% Adaptive HRW saves on average 60% of packets dropped in by the static load sharing.of packets dropped in by the static load sharing.
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Minimal Disruption Property Ensures Few Flow Remappings
0 50 100 150 20010
1
102
103
104
105
Flo
ws
Time
Flows appearingFlows persistentFlows remapped
Flows, per iteration: appearing, Flows, per iteration: appearing, persitentpersitent and remapped.and remapped.
Adaptive control loop Adaptive control loop leads on average to:leads on average to:•• less than 0.05% less than 0.05% of the of the appearing flowsappearing flowsremapped per iteration;remapped per iteration;•• less than 0.2% less than 0.2% of the of the persistent flowspersistent flowsremapped per iteration.remapped per iteration.
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AHH and ABS on traffic traces
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Adaptive HRW and Adaptive Burst Switching
Packet drop rates.Packet drop rates. Packet reordering.Packet reordering.
Packet remapping.Packet remapping.
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Conclusion: AHH and ABS
•• ABS better in preventing packet drop ABS better in preventing packet drop •• AHH better in preventing remapping and reordering, AHH better in preventing remapping and reordering, although larger table would improve ABSalthough larger table would improve ABS•• ABS works on much smaller timeABS works on much smaller time--scale scale –– can address can address packet burstspacket bursts•• AHH converges to optimal allocation, but timescale too AHH converges to optimal allocation, but timescale too long for burstslong for bursts•• hybrid solution?hybrid solution?
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Just in: HABS – a hybrid solution(Kencl, Shi - ANCS 2006)
Good performance in all three metrics of drop rates, Good performance in all three metrics of drop rates, remapping and reordering.remapping and reordering.
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The End
Thank you!
Seminar @ 10:40
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