IEEE GLOBECOM 2005 Autnmic Pwer Management Schemes fr Internet Servers and Data Centers L. Mastrlen, N. Bambs, C. Kzyrakis, D. Ecnmu December 2005 St Luis, MO
Outline Mtivatin The System Mdel and the DP Frmulatin A Justified Heuristic Simulatin and Evaluatin Cnclusins & Future Wrk 2
Mtivatin Typical Internet Server Typical Data Center The System Mdel and the DP Frmulatin A Justified Heuristic Outline Simulatin and Evaluatin Cnclusins & Future Wrk 3
Typical Internet Server Internet Server has multiple resurces (e.g. CPUs) Incming jbs are placed in a buffer Other tasks need als t be cmpleted Server has t apprpriately allcate its resurces Temperature f peratin is imprtant Incming Jb Traffic Internet Server Jb Buffer Other tasks requiring resurces Multiple Resurces e.g. CPUs 4
Typical Data Center At an apprpriately high level f mdeling abstractin, an internet server can be viewed as a caricature f a data center Jb Buffer Multiple Resurces e.g. Servers Incming Jb Traffic Other jbs requiring resurces 5
Outline Mtivatin The System Mdel and the DP Frmulatin The Mdel CPU Allcatin Envirnment & Thermal Envirnment Assciated Csts The Optimizatin Prblem Bellman s Equatin A Justified Heuristic Simulatin and Evaluatin Cnclusins & Future Wrk 6
The mdel Sltted time CPU Pl f Size M Thermal State Set T Jb Buffer f Size B Jb Buffer CPU Pl a CPU Allcatin Envirnment (respnsive) At the beginning f a slt: c is the# f CPUs used by buffer a is the # f available CPUs (M-a-c) is the # f unavailable CPUs u is the # f CPUs t use during this slt b c Thermal Envirnment (respnsive) 7
CPU Allcatin Envirnment & Thermal Envirnment CPU Allcatin Envirnment At the beginning f a slt the state is a After decisins the state is a * =(a+c-u) At the beginning f the next slt the state will be a The transitins a * a will be Markvian p a*a u Thermal Allcatin Envirnment State remains the same within a time slt Current state is t Next state will be t The transitins t t will be Markvian q tt (c,a,u) Statistically Independent Envirnments 8
Assciated Csts Csts incurred in each time slt: Backlg Cst C b (b) Increasing in b Pwer Cst (& Thermal Stress) C ut (u,t) Increasing in u & t (temperature) Recnfiguratin Cst C uc (u,c) Depends n the difference (u-c) 9
The Optimizatin Prblem At time 0: System starts with a full Buffer Objective: Empty the buffer with minimum verall cst At any time slt: The state is: (b, t, c, a) The management decisin is: u At mst ne jb will finish with prbability s(u) This is a transient prblem The slutin depends n the state but nt the specific time slt 10
Bellman s Equatin J(b,t,c,a) cst-t-g beginning frm state (b,t,c,a) J(b,t,c,a)=min u {ξc b (b) + (1-ξ)(C ut (u,t) + C uc (u,c)) +s(u) Σ q tt (c,a,u) p a*a u J(b-1,t,u,a ) +(1-s(u)) Σ q tt (c,a,u) p a*a u J(b,t,u,a ) } buffer state thermal state CPUs used CPUs available CPUs t use : b {0,..,B} : t T S=(b, t, c, a) : c {0,..,M} : a {0,..,M-c} Backlg cst Pwer cst : u {0,..,c+a} u Recnfiguratin cst ξ [0,1] : C b (b) : C ut (u,t) : C uc (u,c) 11
Outline Mtivatin The System Mdel and the DP Frmulatin A Justified Heuristic Key Insights The Frmula Simulatin and Evaluatin Cnclusins & Future Wrk 12
Key Insights u (c+a) b=0 u=0 u 1 if b>0 and (c+a) 1 (nt necessarily true) u(b+1,t,c,a) u(b,t,c,a) u(b,t,c,a) u(b,t,c,a ) if a a(nt necessarily true) The heuristic shuld incrprate the parameter ξ 13
The frmula The heuristic is described by the fllwing frmula: u(b,t,c,a)=min{h(c+a,t), b a 1 {b>0} (1+rund(f(ξ)h(c+a,t) ))} B M-c+1 h(c+a,t) limits the CPUs based n t f(ξ)=2 (3ξ-1) Nte f([0.0 0.5 1.0])=[0.5 1.4 4.0] 14
Outline Mtivatin The System Mdel and the DP Frmulatin A Justified Heuristic Simulatin and Evaluatin Simulatin Envirnment Simulatin Details Simulatin Results Cnclusins & Future Wrk 15
Simulatin Envirnment Evaluatin with simulatins using: OMNET++ Tw cases f arrivals: Cnstant Rate inter-arrival time ~ exp( 2 ) Bursty sequential cnstant rate and idle cycles with length ~ exp( 100 ) Executed ur simulatin fr ξ {0.1, 0.3, 0.5, 0.7, 0.9} Our benchmark was a cnstant CPU usage plicy 16
Simulatin Details In ur simulatin scenari we assumed the fllwing: Size f buffer : B=20 Set f thermal states : T={1,2,3,4,5} # f CPUs : M=8 s(u) : s(u)=exp(-0.2u) C b (b) : Cb(b)=b C ut (u,t) : Cut(u,t)=u t C uc (u,c) : Cuc(u,c)=0.2[u-c] + +0.1[u-c] - 17
s b s b j l a t T / d e j l a t T / d e p t s C r e w P p p p l a t T r r d d b b J J g i n eu r a g e A v e ξ Simulatin Results Cnstant Rate arrivals 9.E+05 8.E+05 7.E+05 6.E+05 5.E+05 4.E+05 3.E+05 2.E+05 1.E+05 0 10 20 30 40 50 60 70 80 90 100 110 Q u e Ti m Optimal Heuristic Cnstant 18.00 16.00 14.00 12.00 10.00 8.00 6.00 4.00 2.00 Optimal Heuristic 0.00 0.0 0.2 0.4 0.6 0.8 1.0 70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 Cnstant 0 2 4 6 18
s b s b j l a t t s C T r / d j l a t T / d e p p e w e p P p r d l a r t d b T b J J ξ g i n eu r a g e A v e Simulatin Results Bursty arrivals 9.E+05 8.E+05 7.E+05 6.E+05 5.E+05 4.E+05 3.E+05 2.E+05 1.E+05 Optimal Heuristic Cnstant 0 10 20 30 40 50 60 70 80 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 Optimal Heuristic 0.00 0.0 0.2 0.4 0.6 0.8 1.0 50.00 45.00 40.00 35.00 30.00 25.00 20.00 15.00 10.00 5.00 0.00 Cnstant 0 2 4 6 Ti m Q u e 19
Outline Mtivatin The System Mdel and the DP Frmulatin A Justified Heuristic Simulatin and Evaluatin Cnclusins & Future Wrk Cnclusins Future Wrk 20
Cnclusins Presented a nvel pwer management mdel fr internet servers and data centers Frmulated a DP that is agnstic t the arrival rate Created a lw cmplexity justified heuristic Simulated fr varius arrival patterns Substantial benefits especially when the arrivals exhibited strng tempral variatins 21
Future Wrk Future wrk will fllw in tw directins: Evaluatin with actual system parameters Traffic estimatin 22
Thank Yu! 23