Modelling a supercomputer with the model

Tuan V. Dinh, Lachlan Andrew and Yoni Nazarathy

Modelling a supercomputer with the model

Australia and New Zealand Applied Probability Workshop

http://caia.swin.edu.au/cv/tdinh 10 July 2013 Slide 2 Australia and New Zealand Applied Probability Workshop

Supercomputer clusters

large scale simulation: climate, genome, astronomy, etc.

foundation of cloud computing

BIG DATAEXASCALE

COMPUTINGMORE COMPUTING POWER DESIRED

Electricity bills

Heat – thermal management

Investment – cooling systems,

hardware, etc.

http://caia.swin.edu.au/cv/tdinh




Power proportionality

Load

Pow

er

ideal

reality

60% peak

single server(1)

(1) Bassoro, “The case for energy proportional”, 2007.

idle server ~ 60% peak

power

turn off idle servers

challenges: switching cost

(setup, wear-and-tear), performance impacts ?

Swinburne Supercomputer





An energy saving framework

CONTROL FRAMEWORK

system congestion

model

number of active servers needed ?

historical implications

?ongoingsystem states ?

arrival characteristics ?

job elapsed times ?

min ( )energyperformance

penaltyswitching+ +

Objective:





Congestion model

CONTROL FRAMEWORK



?ongoingsystem states ?


job elapsed times ?


penaltyswitching+ +

Objective:





Congestion model -

1

2

3

…

batch Poisson, rate function

batch size distributionwith c.d.f

i.i.d service time

WHY ?

jobs arrive in “batch” manner,

i.e within seconds, from same user

system mostly under-utilized,

using infinite server approximation

substantial daily variations





Discrete-time cost

timeT+tt

: current running jobs

t +k

{jobs arriving in (t,t+k],

still around at t+k} {jobs arriving before t, still around at t+k}

C(k) = n(k) + |n(k) – n(k-1)| +

C1(k):energy C3(k):performance penaltyC2(k):switching





Optimization formulationC(k) = n(k) + |n(k) – n(k-1)|+


(*)

solving (*): load estimation in far future.

the system can feedback the ACTUAL load U(s) for s

< k





A Model Predictive Control framework

CONTROL FRAMEWORK



?

ongoingsystem states ?


job elapsed times ?


penaltyswitching+ +

Objective:

MPC





Model Predictive Control execution

timeT+tt

T

Solve (**), obtain {n*(0), n*(1),…}.ONLY “execute” n*(0).

t +1

T

T+t+1

Solve (**), obtain {n*(0), n*(1),…}.ONLY “execute” n*(0).

(**)

Limited look-ahead

1. less sensitive to load estimation accuracy2. Use “on-going” information

know how many jobs actually arrived in (t,t+1]





Solving the optimization problem

{ n(k) + |u(k)| } (***)

s.t: ,

k =0,1…,K-1

Normal approximation

C(k) = n(k) + |n(k) – n(k-1)|+


k =0,1…,K-1

solved numerically using LP





X(k): new arrivals

[Carrillo,89]: is a compound Poisson RV, with batch rate:

, where s = (k+1/2)Δ; Δ: slot-time.

even if the arrival process is NOT Poisson, [Whitt,99].

{jobs arriving in (t,t+k],

still around at t+k}

N ~ Poisson( )

bi: i.i.d batch size, mean and variance





U(k): existing jobs

[Carrillo,91]: is a binomial RV, with parameters:

and , where s = (k+1/2)Δ; Δ: slot-time.

Hence:

{jobs arriving before t, still around at t+k}

one can use job elapsed runtimes to calculate

[Whitt,99]





Summary of analytical framework

CONTROL FRAMEWORK



?



job elapsed times ?

Objective:

MPC

LP optimization



penaltyswitching+ +





Numerical evaluation

supercomputer simulator CONTROLLER

system states

control decision

Swinburne supercompute

rlogs

cost performance





Scheme 1: All up (no turn off)

supercomputer simulator

system states

control decision

cost performanceNO CONTROL


rlogs





Scheme 2: twait heuristic


system states

control decision

cost performancetwait heuristic

Server idle for twait

=> turn OFF


rlogs





Scheme 3: predictive control


system states

control decision

cost performanceMPC

estimated from historical

data


rlogs





S.3: rate function

time of day

rate

arr

ivals

2010 2011

use daily periodic rates





S.3: service time & batch size

[Lublin et al.,2003]: Hyper-Gamma, Log-uniform

[Li et al.,2005]: Log Normal, Weibull

Empirical (2010)

Gamma

time(sec)

c.d

.f

size(CPU)

c.d

.fOur approximations only concern MEAN and VARIANCE of X

X: batch size

G: service time

(2010)





S.3: cost performance

ε ~ service availability

norm

alis

ed c

ost

Cost 1 = total cost when there is NO CONTROL (energy only)

Simulation period: 1 year





Cost performance: all schemes

“offline”

optimal cost[Lu et al., 12].

No perf. penalty

S.1 S.2 S.3, ε = 0.58

consider predictive settings (S.3) whose demand penalty cost is the same as twait

heuristic (S.2)

after all, model is to estimate

θ(k)s.

still > 20% to gain





Remarks and considerations

1. Room for improvement: ~20% to gain!

2.Examining our estimations ?

rate function not accurate

Use job elapsed times


?

3. Fundamental bound on what to achieve given uncertainty ?

[Dinh,Andrew and Branch,CCgrid13]





Thank you

CONTROL FRAMEWORK



?



job elapsed times ?

Objective:

MPC

LP optimization



penaltyswitching+ +




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Modelling a supercomputer with the model