Amdahl s Law in the Datacenter Era! A Market for Fair Processor Allocation!

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1 Amdahl s Law in the Datacenter Era! A Market for Fair Processor Allocation! Seyed Majid Zahedi* (Duke University), Qiuyun Llull* (VMware/ Duke University), Benjamin C. Lee (Duke University)! *Equal Contributions! 1

2 Sharing in Federated Data Centers! Users pool resources in non-profit data centers! E.g., research groups within university! Users are entitled to portion of resources! Based on contributions to shared pool! 2

3 Challenges for Modern Data Centers! u 1 u 2 u 3 u 4 m 3 m 1 m 2 m 4 m 5 m 6 m 7 m 8 m 9 m 10 Computing resources are physically distributed across servers! Users run complex jobs with diverse characteristics! Users jobs are assigned to different servers! Users prefer specific allocations on specific servers! 3

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sha1_base64="pomo6cyeo/pqmhvbduxnjuw3ifi=">aaab8nicbvdlssnafl3xweur2qwbybfcsendqlucg5cvjc00ouymn+3qystmtiqssvej3lhqcevxubd8a7/blzo2c209mha4517umrmkncntoj/w0vlk6tp6aao8ubw9s1vz279vcsopujtmsewercfnal3nnmdoipfeacd2mlos/pydssvicaphcforgqgwmkq0ktwvinoyhbn2wn6r1jy6m4g9sbozumtwp77vv/ktvq/y7vvjmkyonoveqw7dsbsfeakz5zixvvrhquiidlbrqcarkj+bzm7ti6p07tcw5gltt9tfgxmjlbphgzksmqp5rxd/87qpds/9jikk1sjo9fcyclvhdlga3wcsqezjqwivzgs16zbiqrwpqwxkamx/ezg4p/wlunntymjcfcu4gem4hgacqrouoauuuejgaz7g2uqtr+vfep2ollmznsr8gfx2a2/bleg=</latexit> <latexit sha1_base64="pomo6cyeo/pqmhvbduxnjuw3ifi=">aaab8nicbvdlssnafl3xweur2qwbybfcsendqlucg5cvjc00ouymn+3qystmtiqssvej3lhqcevxubd8a7/blzo2c209mha4517umrmkncntoj/w0vlk6tp6aao8ubw9s1vz279vcsopujtmsewercfnal3nnmdoipfeacd2mlos/pydssvicaphcforgqgwmkq0ktwvinoyhbn2wn6r1jy6m4g9sbozumtwp77vv/ktvq/y7vvjmkyonoveqw7dsbsfeakz5zixvvrhquiidlbrqcarkj+bzm7ti6p07tcw5gltt9tfgxmjlbphgzksmqp5rxd/87qpds/9jikk1sjo9fcyclvhdlga3wcsqezjqwivzgs16zbiqrwpqwxkamx/ezg4p/wlunntymjcfcu4gem4hgacqrouoauuuejgaz7g2uqtr+vfep2ollmznsr8gfx2a2/bleg=</latexit> Management Properties! Work Conservation! Never leave servers idle if there are unsatisfied user demands! Sharing Incentives! Guarantee users at least the utility from their entitlements! u i ( ) u <latexit sha1_base64="nux5he22fct/qypbk6q4xzzpfdc=">aaab8nicbvdlssnafl2pr1pf1s7ddbbbhztejboruhfzwdhce8pkommhtizhzikwki0f4cafilu/xoxgh/gnrpy0xwjrgyhdofdyz5wg4uxp2/60skvlk6tr5fxkxubw9k51d+9gxakk1cuxj2unwipyjqirmea0k0iko4dtdjc6kpz2lzwkxejajxpqr3ggwmgi1kbyvajryrbmdz2w96p1u2fpgbajmyp1zu3j+/4rp271qu9epyzpriumhcvvdexe+xmwmhfo84qxkppgmsid2jvu4igqp5tkztghufoojkv5qqoj+nsjw5fs4ygwk0vgne8v4n9en9xhmz8xkasacji9fkyc6rgvbaa+k5ropjyee8lmvksgwgkitu0vu4iz/+vf4p40zhv2lsmjcvouyr8o4agcoiumxeilxccqwam8wbovwo/wi/u6hs1zs50a/ih19gomzzx7</latexit> i ( ) x i e i 4

5 Management Questions! How can we model users demands for processors?! How can we fairly allocate processors?! Fig. downtownrecruiting.com! 5

6 Roadmap! Model user utilities! Operationalize Amdahl s Law for data center workloads! Propose Amdahl utility using Karp-Flatt metric! Design market mechanism! Design market for processor allocation! Propose Amdahl bidding procedure using closed-form equations! Find market equilibrium to guarantee fair division! Conclude! 6

7 Amdahl s Law! [G. Amdahl 1967]! Architects use it to estimate upper bounds on speedups! Speedup(x) = T 1 T x = T 1 (1 F )T 1 + F T 1 x = x x(1 F )+F 7

8 <latexit sha1_base64="f9zvgm5q2uujumfw66uwofcxkic=">aaacaxicbvdlsgnbeoynrxhfuu+ih8egjihh14t6uakb4dgcawljemyns8mq2qczs5kwbc/+ihcpkl79c2/e/bqnj4mmfjquvd10d7krz1kz5perwlhcwl5jr2bw1jc2t7lbo3cyjawhngl5kooulpszgnqkku7rkadydzmtub3yyk/duyfzgnyqquqdh3cc5jgclzza2t2z7xfqjwp6apokp0z6eeukujiudfvznfk0x0dzxjqsxonqopwnanvw9rpzdkns00arjqvswgaknaqlxqinw0wzljtcpic7tkfpgh0qnwt8whadaawnvfdochqaq78neuxlofbd3elj1zwz3kj8z2veyjt3ehzesaibmszyyo5uiez5odytlcg+0aqtwfstihsxdkpp1di6bgv25xlinxyviuandqmee6rhhw4hdxacqqmuoqo2ehiaj3ibv+predbejpdja8qyzuzchxgfp08slyy=</latexit> sha1_base64="1dlfmwgm00v+igotyomlaizgrte=">aaacaxicbvdlssnafj34rpuvdswkdbahrsxjn+pckrskywrwftpqj9njo3qyctmtaqnbjb/ixowkw//cnr/gfzh9llt1wixdofdy7z1uykhulvvlzm0vlc4tp1bsq2vrg5vm1vatdckbsruhlbb1f0nckcdvrruj9vaq5lum1nxeaejx7omqnoa3ahasx0cdtj2kkdjsy9yv2x4oxscmjxco+0ncz9on5dxxowmzgstvjqbnit0hmellfum7chbxazmfzxaai59whrmssmfboxjijbtfjctpzirjihapduhdu458ip149eicj7tshl4gdhefr+rvirj5ug58v3f6shxltdcu//makflonjjymfke4/eil2jqbxcyb2xtqbbia00qfltfcnex6tcuti2tq7cnx54l1ul+pg9d6zckyiwu2aohiatscaqk4apuqbvg8acewat4nr6nz+pneb+3zhmtmr3wb8bhd0awl9s=</latexit> What Portion of Code is Parallelizable?! [Allen Karp and Horace Flatt 1990]! Expert programmers may not know! Fortunately, we can measure speedup! Measure! Set! Calculate! s(x) = x x(1 F )+F Karp-Flatt! 1 1 F = 1 1?! Metric! s(x) x 8 Fig. criticallyrated.files.wordpress.com

9 Karp-Flatt Metric in Practice! decision correlation gradient svm F Number of Cores F Number of Cores Number of Cores F Number of Cores For many Spark and PARSEC workloads, Karp-Flatt has low variance! Abundant, fine-grained parallelism! Few serial bottlenecks! Constant Karp-Flatt metric indicates accuracy of Amdahl s Law! 9

Small dataset: limited parallelism Var(F) 0.

12 Parallel Fraction (Variance) 1 3 5 7 9 11

Multi-threaded: Scheduling and intensive

10 Limitations of Karp-Flatt Metric! Graph processing: overhead increases with x Small dataset: limited parallelism Var(F) Parallel Fraction (Variance) Application ID Multi-threaded: Scheduling and intensive inter-thread communication overhead There are some exceptions! High correlation between serial and parallel portion! High scheduling and inter-thread communication! Very limited parallelism! 10

11 Amdahl s Law in Practice! Execution Time Prediction Accuracy for Decision Tree Execution Time (s) Measured Estimated Core Allocation Measured performance tracks estimated speedup! Amdahl s Law can drive processor allocation! 11

12 !!! <latexit sha1_base64="ifpnje6nxycxowpjq/81wmswyco=">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</latexit> sha1_base64="dhojcdhqws/7sorj6lncsqykgxc=">aaacphicbvc7tsmwfhv4lviqmmjgusevhiphaqakchbgiruuqsmr4zrfycer7uark/wm/ailc//axsbcaiivgtdlanorwffo3hn1fy4fmyqvbt9by+mtk1ptuzn87nz8wmjhafleronapi4jfolth0ncaejqiipgtmnbepczafixh/1544oisaowpnoxaxhucwlamvkg8gq1xkmllyn17ge669f0e+5dnxaia1cm3nmx+056pnl67wl6kd7irjw6wdtmr4psr1c0y3zwcbg4p6byodhau727b1s9wppbjndcsagwq1i2httwly2eopirno8mksqix6ioaroyik5ks2fuu7hhmdymimfeqgdg/t7qievz475r9n3k/7m+owrwtfsw29i0jbnfqjw4fcqmqgj2o4rtkghwrgcawokav0j8jkx0ygsenye4/y0pg/p2ea9sh5swkmbqobak1kejogahvmarqii6woabvia38g49wq/wh/u5ki5zpzsr4e9zx99d0brq</latexit> <latexit sha1_base64="fb45zasxggtvlwmazb5mikaw550=">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</latexit> <latexit sha1_base64="e1owbqg67/jcchk0grg0zs3mkxg=">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</latexit> <latexit sha1_base64="e1owbqg67/jcchk0grg0zs3mkxg=">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</latexit> Amdahl Utility! Measures normalized progress across servers! Work completed for user i Speedup ij (x ij )= in unit of time on one core of server j u i (x i )= P m j=1 w ij s ij (x ij ) P m j=1 w ij x ij F ij +(1 F ij )x ij 12

13 Roadmap! Model user utilities! Operationalize Amdahl s Law for data center workloads! Propose Amdahl utility using Karp-Flatt metric! Design market mechanism! Design market for processor allocation! Propose Amdahl bidding procedure using closed-form equations! Find market equilibrium to guarantee fair division! Conclude! 13

14 !!! <latexit sha1_base64="jv1doaxj8l0xdk8fgkjhper2gs4=">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</latexit> Market for Fair Allocation! Users receive budgets in proportion to their entitlements! Market sets prices for processors on each server! Users demand processors that maximize their utility! max. u i (x i ), s.t. mx x ij p j apple b i j=1 At equilibrium prices, market clears! nx x ij = C j i=1 14

15 !! <latexit sha1_base64="tougdpwschzghr9mig6oc5yuu8c=">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</latexit> <latexit sha1_base64="2pvliw9qwwuqkqnkowepn0wy+9u=">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</latexit> <latexit sha1_base64="2pvliw9qwwuqkqnkowepn0wy+9u=">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</latexit> <latexit sha1_base64="57tnqvnpae4kca3itbcl07yl4a4=">aaacdhicbzc7tgjbfibp4g3xhlrateqtbgdxri1isggsmrehadzmdgmmzm5uzmznygzlgxtfxczcjymvd2dn2zhccgx/zjiv/zknz87vhzwpbdvfvmppewv1lb2e2djc2t7j7u7dqccshnziwapz8lcinala00xz2gglxb7had0bvsb1+h2vigxiwo9c2vzxt7aui1gby80ehe4gr09qcbvu5lsxkznjbsws5bkejkiiku7azebsgj0rwgrnbrly7r74aqbvn/vv6gqk8qnqhgolmo4d6nampwae0yttihqnmrnihm0afninqh1prknqsxe6qbti84rge/f3rix9pua+zzp9rptqvjy2/6s1i909b8dmhjgmgkwxdsoodidg0aaok5ropjkaiwtmr4j0scremwazjgrn/urfqj0wlgr2lzmrl2gqnbzaietbgtmowyvuoqyehuajxudversertfrfdqasmyz+/bh1ucpbn+b/q==</latexit> sha1_base64="ighuhzc5fdxkcyiwumqqotcz/vg=">aaacdhicbzc7tsmwfiydrqxcaowsfggplg3cagyvinvhlbkhldosoa7bunwcyhaqqigjcwuvwsiacayghocnt8g9dndys5y+/ecchz8/ibmvyra/jyxfpewv1dxafn1jc2vb3nm9lleimpfwxcjrd5akjhlikaoyqcecodbgpbymkqn67zyissn+pyyxaywoy2mhyqs05zuhsd8vqgnyhk2zhh5ky052k/imbpr7gszbit/3tcsu2mpbexcmylnwxemd9n+rvvnvbec4cqlxmcepg44dq1akhkkykszftcsjer6glmlo5cgkspwor8ngkxbasbmj/bicy/f3ripckydhodtdphpytjyy/6s1etu5a6wux4kihe8wdrigvqrh0ca2fqqrntsaskd6rxd3keby6qdzogrn9ur58e6k50x70rfcf0yua/vgabsaa06bcy5afxgag3vwcj7bi/fgpbmvxtukdcgyzuybpzi+fwayi52m</latexit> Amdahl Bidding Procedure! Users iteratively bid for processors using closed-form equation! q b ij (t + 1) / f ij p j (t) w ij s ij (x ij (t)) Market sets prices based on bids! p j (t) = P n i=1 b ij/c j Iterate until prices are stationary! 15 Fig. searchengineland.com

16 ! Properties of Amdahl Bidding Procedure! Allocations are work-conserving! Market guarantees sharing incentives! Users bid truthfully in large, competitive systems! Market does all of these with low overhead! 16

17 Mechanisms for Evaluation! Proportional Sharing (PS)! Allocate cores in proportion to entitlements on each server! Upper-Bound (UB)! Allocate cores to maximize system progress! 17

18 Sharing Incentives! Normalized Performance PS AB UB Class 1 Class 2 Class 3 Class 4 Class 5 PS provides SI by definition! UB treats users unfairly, starves users with low entitlements! AB provides SI with market equilibrium, low overhead! 18

19 System Performance! Normalized Performance PS AB UB 4 App/Ser 8 App/Ser 12 App/Ser 16 App/Ser 20 App/Ser 24 App/Ser PS ignores demands! UB achieves highest performance! AB outperforms PS, low overhead! 19

20 Computational Overheads! Updating bids: 0.1ms! Termination check and setting prices: 0.85ms! Convergence rate of 10 iterations, on average! Overhead of 12.5ms with 0.25ms network delay! 20

21 Summary and Future Direction! Amdahl utility measures progress using Karp-Flatt metric! Amdahl bidding procedure finds market equilibrium! Allocations are work-conserving! Market guarantees sharing incentives! Users bid truthfully in large, competitive systems! 21

22 Thank You! 22

Amdahl s Law in the Datacenter Era: A Market for Fair Processor Allocation

Amdahl s Law in the Datacenter Era: A Market for Fair Processor Allocation Seyed Majid Zahedi, Qiuyun Llull, Benjamin C. Lee Duke University, Durham, NC, USA VMware Inc., Palo Alto, CA, USA {seyedmajid.zahedi,