Resource Allocation with a Budget Constraint for Computing Independent Tasks in the Cloud

Transcription

1 Resource Allocaton wth a Budget Constrant for Computng Independent Tasks n the Cloud Wemng Sh and Bo Hong School of Electrcal and Computer Engneerng Georga Insttute of Technology, USA 2nd IEEE Internatonal Conference on Cloud Computng Technology and Scence Nov. 30 Dec 3, 200 Indanapols, USA

2 Outlne Introducton System Model Problem Formulaton Soluton Smulaton Concluson and Dscusson December 20, 200 CloudCom 200 2

3 Introducton Motvaton: Explore the resource allocaton scheme from the perspectve of the cloud users. How to acheve the maxmum return under the lmted budget? Approach: Consder the problem of runnng a large number of ndependent equal-szed tasks on the cloud nfrastructure under the budget constrant. Formulate and solve the problem based on a modeled cloud nfrastructure. December 20, 200 CloudCom 200 3

4 Introducton Centralzed work paradgm Master Tasks An applcaton consstng of a large amount of ndependent, equal-szed tasks The granularty of the applcaton s one task Compute Nodes One-round dstrbuton fashon Vrtualzed compute nodes wth dfferent CPU frequency, nterconnect bandwdth and monetary charge rate December 20, 200 CloudCom 200 4

5 Introducton Prevous works try to optmze ther doman-specfc utlty functon over the system parameters such as the CPU frequency, the memory sze, the network bandwdth. The bandwdth-centrc allocaton scheme favors the compute nodes wth the maxmum nterconnect bandwdth. Thngs change when a new metrc: the monetary charge rate s taken nto account. December 20, 200 CloudCom 200 5

6 Introducton The applcaton under our consderaton embodes the dvsble workload model. Fundamental bass of the potental applcatons that can be ported to run on the cloud A natural approach to the problem s to mnmze the makespan or the total-completon-tme of all the tasks under the budget constrant. Cloud users are usually charged by tme However, these problems proved to be NP-complete. An alternatve approach s to maxmze the steadystate throughput of the system. December 20, 200 CloudCom 200 6

7 Introducton A system wth a one-round dstrbuton fashon typcally undergoes three stages: Start-up stage Some compute nodes are dle because they have not receved the tasks to be processed Steady-state stage (Perodc stage) All the compute nodes are all fed wth tasks and the amount of tme spent on communcaton and computaton become stable Clean-up stage Some compute nodes become dle agan after fnshng the assgned tasks whle other compute nodes are stll busy workng on the assgned tasks December 20, 200 CloudCom 200 7

8 Introducton The steady-state throughput the number of tasks that can be completed by the allocated computng resources per tme perod n the steady state wthout takng nto account the start-up and the clean-up stages of the applcaton The budget-constraned steady-state throughput maxmzaton problem s a reasonable approxmaton of the budget-constraned makespan mnmzaton problem. the amount of tasks to be processed s huge the tme spent on the start-up and the clean-up stages become neglgble compared wth the overall computng tme spent n the steady state December 20, 200 CloudCom 200 8

9 Outlne Introducton System Model Problem Formulaton Soluton Smulaton Concluson and Dscusson December 20, 200 CloudCom 200 9

10 System Model A cloud computng nfrastructure typcally conssts of the underlyng data centers wth vrtualzed computng resources the storage nodes that host the tasks and the assocated data to be processed nterconnect network equpments Assume that there s only one edge (communcaton lnk) between the master node and any compute node. December 20, 200 CloudCom 200 0

11 System Model The cloud nfrastructure can be modeled as a node-weghted edge-weghted star-shaped graph G = ( V, E, B, P) V = { C } 0} : the set of allocated compute nodes E = { e : the set of edges (communcaton lnks) between C 0 and C B = { b } : the maxmum # of tasks transmtted from C 0 to C per tme unt, whose value captures the dfference n the communcaton bandwdths between C 0 and C P = { p } : the maxmum # of tasks fnshed by C per tme unt, whose value captures the dfference n the computng power of the compute nodes December 20, 200 CloudCom 200

12 Communcaton/Computaton Model Master node Mult port communcaton model would turn the problem to be NPcomplete agan! The sngle port communcaton No computaton on the master node Compute nodes Non-overlap communcaton model No communcaton between each other as the tasks are assumed to be ndependent December 20, 200 CloudCom 200 2

13 Cost/Budget Model The cost model Lnear: The monetary charge rate m s proportonal to the computng power p Logarthm cost model: Model the scenaro when the cloud servce provder tres to promote the use of compute nodes wth the better computaton performance The budget model Proportonal: the budget (per tme perod) s proportonal to the number of avalable compute nodes Constant: the budget (per tme perod) s held constant regardless of the number of avalable compute nodes December 20, 200 CloudCom 200 3

14 Outlne Introducton System Model Problem Formulaton Soluton Smulaton Concluson and Dscusson December 20, 200 CloudCom 200 4

15 Problem Formulaton Constrants under consderaton: the conservaton property of the steady state,.e., all the tasks receved from the master node by any allocated compute node should be consumed by tself. b t = p t ' the non-overlap communcaton and computaton model,.e., the communcaton tme and the computaton tme of any compute node can not overlap, and the sum of whch can not exceed one tme perod t + t ' T the sngle-port communcaton model of the master node ndcates that the sum of the communcaton tme of the allocated compute nodes can not exceed one tme perod. k = t T December 20, 200 CloudCom 200 5

16 Problem Formulaton Constrants under consderaton (contnued): the lmted nterconnect bandwdth of the master node,.e., the number of tasks that the master node can transmt to the allocated compute nodes durng one tme perod s lmted k = b t B the monetary constrant mposed by the lmt of avalable budget,.e., the money spent on the allocated compute nodes should not exceed the avalable budget per tme perod k ' = ( t + t ) m M December 20, 200 CloudCom 200 6

17 Problem Formulaton The steady-state throughput can be expressed as The set of constrants:, the throughput contrbuted by compute node C, the rato of the cost of fnshng one task on C to the avalable budget M per tme perod December 20, 200 CloudCom t R = b m p b M h ) ( + = = = k R R B R h R R b k p b R k k k + = = = (4) (3) (2) for ) ( ()

18 Outlne Introducton System Model Problem Formulaton Soluton Smulaton Concluson and Dscusson December 20, 200 CloudCom 200 8

19 Soluton A lnear programmng problem generally does not have the analytc (closed-form) soluton No straghtforward heurstc exsts Under certan crcumstances, the analytc solutons do exst We dentfy two modes of the system wheren the analytc solutons exst These solutons gve us the straghtforward heurstcs to allocate compute nodes December 20, 200 CloudCom 200 9

20 Soluton The soluton to the orgnal problem can be shown to be R = m mn( Rs, B) R s s the soluton to the auxlary problem: Maxmze R = k = R, subject to: () R ( b + p ) for k (2) k = b R (3) k = h R December 20, 200 CloudCom

21 Soluton Based on the relatonshp between the communcaton-to-computaton rato λ and the monetary charge rate m, we dentfy two modes where closed-formed solutons exst. Budget-bound: λ > M / m, k Communcaton-bound: λ < M / m, = b / k p December 20, 200 CloudCom 200 2

22 Soluton When the system s budget-bound (resp. communcaton-bound) : Sort the compute nodes by the beneft-frst heurstc h (resp. communcaton-frst heurstc b ) The maxmum steady-state throughput can be obtaned by sendng the tasks to nodes n the order of ncreasng h (resp. decreasng b ) December 20, 200 CloudCom

23 Outlne Introducton System Model Problem Formulaton Soluton Smulaton Concluson and Dscusson December 20, 200 CloudCom

24 Smulaton Setup Smulaton s done n Matlab The smulated star-shaped graph conssts of one master node and k compute nodes. To test the scalablty of the heurstcs, k s set to be 0 2 l (l = 0,,,8) Four dfferent computng powers are smulated by randomly pckng the values from the set {v p, 2v p, 4v p, 8v p } wth equal probablty Trgger the dfferent modes of the system by settng the values of the correspondng bandwdths Compare the smulaton results of our proposed heurstcs wth other straghtforward heurstcs December 20, 200 CloudCom

25 Proportonal (resp. Constant) Budget and Lnear Cost Model December 20, 200 CloudCom

26 Proportonal (resp. Constant) Budget and Logarthm Cost Model December 20, 200 CloudCom

27 Outlne Introducton System Model Problem Formulaton Soluton Smulaton Concluson and Dscusson December 20, 200 CloudCom

28 Concluson and Dscusson Our ntal goal has been reduced to the problem of maxmzng the steady-state throughput of the allocated compute nodes n the cloud under the budget constrant. Ths problem can be formulated and solved effcently as a lnear programmng problem under our model. We dentfy two modes of the system: budget-bound and communcaton-bound The allocaton scheme should be beneft-aware. When the system s budget-bound, the beneft-frst heurstcs s the best When the system s communcaton-bound, the communcaton-frst heurstc s the best December 20, 200 CloudCom

29 Concluson and Dscusson The communcaton capacty has not been ncluded n the cost model. Our model dd not drectly consder the dynamc nature of the cloud computng platform and cost spent on the start-up and clean-up stages. Yet, we provde an analytcal framework and hghlght an mportant metrc that needs to be ncorporated nto the resource allocaton scheme for the beneft of the cloud users. December 20, 200 CloudCom

30 Q&A December 20, 200 CloudCom