Robust Resource Allocation in Parallel and Distributed Computing Systems (tentative)

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1 Robust Resource Allocatio i Parallel ad Distributed Computig Systems (tetative) Ph.D. cadidate V. Shestak Colorado State Uiversity Electrical ad Computer Egieerig Departmet Fort Collis, Colorado, USA shestak@colostate.edu

2 V. Shestak: Progress Toward Ph.D. start: August 2003 research completed: 75% (3 parts out of 4) publicatios: 510 accepted (9 cofereces, oe joural) 5oe uder review (joural) 5oe draft i preparatio (joural) patets: oe filed, two i process graduatio: December

3 Outlie part 1: two-stage approach to resource allocatio for periodic strigs of applicatios part 2: resource allocatio i IBM cluster-based pritig system part 3: stochastic robustess metric ad its use for static resource allocatios part 4: robust resource allocatio uder radom ode failures ad recoveries i progress 3

4 PART 1: Shipboard Computig Eviromet computatio resources 5 heterogeeous set of machies 5 multitaskig eabled commuicatio etwork 5 idepedet virtual poit-to-poit commuicatio routes 5 fixed available badwidth o each route resource mapper 5 cetralized approach 5 iitial static resource allocatio 5 robust agaist icreases i workload 4

5 PART 1: Workload periodic cotiuously ruig applicatios orgaized i strigs strig QoS costraits 5 throughput = 1/P (where P is time iterval betwee iput arrivals) 5 ed-to-ed latecy L P P strigs have priority factors tc [1] t t [1] L t [ 1] t [ ] t c 5

6 PART 1: Performace Goal for Iitial Allocatio primary objective: maximize the sum of priority factors of strigs allocated i the system secodary objective: maximize system slackess 5 system slackess is the miimum uused utilizatio across all machies ad commuicatio routes i the system 5 system slackess quatitatively reflects the system s potetial to absorb upredictable icreases i workload 6

7 PART 1: Resource Utilizatio b a b b a b b a 7

8 PART 1: Two-Stage Solutio Approach first stage: Geitor-based global search algorithm coupled with low-level greedy heuristic 5 global search algorithm operates i the permutatio space 5 greedy heuristic maps chromosomes ito the solutio space solut io passed secod stage: Brach-ad-Boud depth first search algorithm 5 Iteger Liear Programmig (ILP) formulatio 5 cotiuous lower boud tighteig over time 8

9 9 PART 1: Results 1 Trial

10 10 PART 1: Results 50 Trials

11 PART 1: Refereces V. Shestak, E. K. P. Chog, A. A. Maciejewski, H. J. Siegel, L Bemohamed, I. J. Wag, R. Daley, Resource allocatio for periodic applicatios i a shipboard eviromet, 14th Heterogeeous Computig Workshop (HCW 2005), i proceedigs of 19th Iteratioal Parallel ad Distributed Processig Symposium (IPDPS 2005), Apr. 2005, pp V. Shestak, E. K. P. Chog, A. A. Maciejewski, H. J. Siegel, L. Bemohamed, I-J. Wag, ad R. Daley, A two-stage approach to resource allocatio for periodic strigs of applicatios i a shipboard eviromet, submitted to Joural of Parallel ad Distributed Computig (JPDC). Uder review. 11

12 Outlie part 1: two-stage approach to resource allocatio for periodic strigs of applicatios part 2: resource allocatio i IBM cluster-based pritig system part 3: stochastic robustess metric ad its use for static resource allocatios part 4: robust resource allocatio uder radom ode failures ad recoveries i progress 12

13 PART 2: IBM Priter System Layout processig must be doe i distributed fashio pritheads cosume bitmaps i page order 13

14 PART 2: Goals for Cluster Cotroller Project algorithm for assigig sheetsides to blades 5mathematical model of the eviromet 5optimized sheetside workload distributio algorithm system performace simulatio 5evaluate algorithm s efficiecy 5determie cost effective system cofiguratio g miimize umber of blades g miimize memory sizes 14

15 PART 3: IBM Cluster Cotroller Project: Results bitmap lifetime (sec.) how log bitmap exists i the system mi RIP completio time roud robi radom 15

16 PART 2: Refereces J. Smith, V. Shestak, H. J. Siegel, S. Price, L. Teklits, ad P. Sugavaum Resource allocatio i cluster-based imagig systems, 2007 Iteratioal Coferece o Parallel & Distributed Techiques ad Applicatios (PDPTA 07). Accepted, to appear. patet: V. Shestak, S. Price, J. Smith, L. Teklits, H. J. Siegel, ad P. Sugavaam, Methods ad Systems for Improved Pritig System Sheet Side Dispatch i a Clustered Priter Cotroller, filed as IBM Docket BLD US1, Sep

17 Outlie part 1: two-stage approach to resource allocatio for periodic strigs of applicatios part 2: resource allocatio i IBM cluster-based pritig system part 3: stochastic robustess metric ad its use for static resource allocatios part 4: robust resource allocatio uder radom ode failures ad recoveries i progress 17

18 PART 3: QoS-Costraied Resource Allocatio establish system performace metric develop mathematical model that provides fuctioal depedece betwee performace metric, iput parameters, ad ucertaities i the system itegrate this model ito adapted or developed optimizatio techique evaluate quality of the received sub-optimal solutio(s) 18

19 PART 3: QoS-Costraied Example System Λ a 11 a 1 1 a 1M a M M periodic data sets processig of each data set to be completed withi time uits Λ 19

20 PART 3: Stochastic Robustess Metric for a give resource allocatio S = { a, a,..., a } 5 set of applicatios o compute ode j T j 1j 2 j j 5 (radom variable) executio time of o compute ode j ψ ij 5 (radom variable) makespa β 5 ad specify acceptable rage for mi β max j ψ a ij 1 M = max{ T,..., T } i1 i= 1 i= 1 ψ im stochastic robustess metric is the probability that the performace characteristic is cofied to the iterval : P[ β ψ β ] mi [ β, β ] max mi max 20

21 PART 3: Stochastic Resource Allocatio applicatio assiged to: ode 1 ode 2 probability desity fuctio est. makespa (mea) makespa costrait time probability of exceedig makespa time 21

22 PART 3: Idepedece amog local performace characteristics allows stochastic robustess metric to be computed as ψ j j = T i= 1 ij M P[0 ψ Λ ] = P[0 ψ j Λ] j= 1 amog radom variables allows covolutio to be applied to fid pdf of T ij i= 1 5 Fast Fourier Trasform (FFT) method ca be used j T ij if depedecies, apply bootstrap approximatio method 22

23 PART 3: Compariso Aalysis stochastic robustess (%) makespa (sec.) based o mea values 1,000 radomly geerated resource allocatios T ij discrete distributios costructed radomly i the same rage 23

24 PART 3: Heuristics allocate N idepedet applicatios across M odes miimize period betwee data sets while maitaiig P[ ψ Λ] value heuristics two-phase greedy 5 basic, coflict resolutio oe-phase greedy 5 sortig, mea load balacig global search 5 steady-state geetic algorithm 5 at coloy optimizatio 5 simulated aealig 24

25 PART 3: Greedy Heuristics: Results value was set to 0.9 P[ ψ Λ] results are based o 50 experimetal trials 25

26 PART 3: Global Search Heuristics: Results value was set to 0.9 P[ ψ Λ] results are based o 50 experimetal trials 26

27 PART 3: Refereces V. Shestak, J. Smith, A. A. Maciejewski, ad H. J. Siegel, A stochastic approach to measurig the robustess of a resource allocatio i distributed systems, 2006 Iteratioal Coferece o Parallel Processig (ICPP 06), Aug. 2006, pp V. Shestak, J. Smith, R. Umlad, J. Hale, P. Moraville, A. A. Maciejewski, ad H. J. Siegel, Greedy approaches to stochastic robust resource allocatio i sesor drive distributed systems, 2006 Iteratioal Coferece o Parallel & Distributed Techiques ad Applicatios (PDPTA 06), Jue 2006, pp V. Shestak, J. Smith, A. A. Maciejewski, ad H. J. Siegel, Iterative algorithms for stochastically robust static resource allocatio i periodic sesor drive clusters, 8th IASTED Iteratioal Coferece o Parallel ad Distributed Computig ad Systems (PDCS 2006), Nov

28 Outlie part 1: two-stage approach to resource allocatio for periodic strigs of applicatios part 2: stochastic robustess metric ad its use for static resource allocatios part 3: resource allocatio i IBM cluster-based pritig system part 4: robust resource allocatio uder radom ode failures ad recoveries i progress 28

29 PART 4: System Prototype task pool workload heterogeeous cluster 29 cluster cotroller system log

30 PART 4: System Prototype heterogeeous cluster l o g l o g cluster cotroller l o g l o g 30 stage i time

31 PART 4: Kow Parameters & Assumptios each task has a importace factor estimated time to compute each task is kow ode failure & recovery statistics is kow total time to execute task batch is T o ew arrivals durig T stage legth: λ time uits (fixed) system log is received at the ed of each stage mappig decisio is geerated per stage o credit is give for partial task executio if ode recovers i stage i it will be used i stage i

32 PART 4: Goal for Cluster Cotroller maximize reveue, i.e., expected sum of importace factors of the tasks completed over T maximize sum of importace factors of the tasks completed per each stage λ 32

33 PART 4: Off-Lie Policy Geeratio (Hypothetical Solutio) off-lie geerated policy: 5 result lookup table 5 optimal cotrol selectio at each stage 5 fiite horizo DP cluster cotroller 5 itractable eve for medium-scale problems 0 λ produce mappig execute tasks 33

34 PART 4: O-lie Policy Geeratio o-lie policy geeratio: cluster cotroller 5 Mote Carlo simulatio 5 limited horizo DP time to select cotrol varies 0 λ produce mappig execute tasks 34

35 PART 4: Estimatig Expected Reveue from Future States N x i i i total umber of stages MDP state ux ( ) cotrol applied to x imp[ x, u( x )] accumulated importace i stage i i [ ] [ ] ( ) ( ( )) reveue = E imp x, u( x ) + E imp x, u( x ) + E N stages i compute compute estimate compute 35

36 PART 4: Estimatig Expected Reveue from Future States certai umber of stages iput method output curret state cotrol probabilities machie learig: regressio, eural etworks expected accumulated importace from future states Ca we achieve the desired accuracy? For how may stages? 36

37 Outlie part 1: two-stage approach to resource allocatio for periodic strigs of applicatios part 2: stochastic robustess metric ad its use for static resource allocatios (doe joitly with J. Smith, ad will appear i his thesis) part 3: resource allocatio i IBM cluster-based pritig system (doe joitly with J. Smith, ad will appear i his thesis) part 4: robust resource allocatio uder radom ode failures ad recoveries 37

38 Summary part 1: desiged two-stage approach to static resource allocatio for periodic strigs of applicatios i QoS-costraied system part 2: desiged workload distributio algorithm for IBM priter cluster cotroller part 3: preseted a methodology for derivig stochastic robustess metric for resource allocatio 5illustrated methodology for example distributed system part 4: propose a idea for resource allocatio i distributed systems with radom ode failures ad recoveries 38

Scheduling under Uncertainty using MILP Sensitivity Analysis

Scheduling under Uncertainty using MILP Sensitivity Analysis Schedulig uder Ucertaity usig MILP Sesitivity Aalysis M. Ierapetritou ad Zheya Jia Departmet of Chemical & Biochemical Egieerig Rutgers, the State Uiversity of New Jersey Piscataway, NJ Abstract The aim