Balanced Ant Colony Algorithm for Scheduling DAG to Grid Heterogeneous System

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1 Internatonal Journal of Scentfc & Engneerng Research Volume 2, Issue 6, June Balanced Ant Colony Algorthm for Schedulng DAG to Grd Heterogeneous System Mrs. Smtha Jha Abstract- Ant Colony Optmzaton can be used for schedulng tasks on resources n Grd. In earler work ths technque has been appled for ndependent task schedulng. Ths paper apples the above technque for dependent task schedulng. Here a hybrd algorthm by Sakellarou can be appled, where tasks n DAG (Drected acyclc graph) are upward ranked and sorted decreasngly. Then the sorted tasks are grouped along the sorted sequences and n every group, tasks are ndependent. Then ndependent task groups can be scheduled to resources usng algorthm specfed by author Chang. Index Terms Grd System, Drected Acyclc graph(dag),independent, Dependent task schedulng, Ant Colony Optmzaton, Groupng, Rankng. 1 INTRODUCTION C urrent scentfc problems are very complex and need huge computng power and storage space. The past technologes such as dstrbuted or parallel computng are unsutable for current scentfc problems wth large amounts of data. Processng and storng massve volumes of data may take a very long tme. Grd computng [3] s a new paradgm for solvng those complex problems. In grds, we need to consder the condtons such as network status and resources status. If the network or resources are unstable, obs would be faled or the total computaton tme would be very large. So we need an effcent ob schedulng algorthm for these problems n the grd envronment. Because the envronment status may change frequently, tradtonal ob schedulng algorthm such as Frst Come Frst Serve (FCFS), Shortest Job Frst (SJF), etc., may not be sutable for the dynamc envronment n grds. Mrs Smtha Jha s currently pursung Ph.D degree program n Computer Scence from BIRLA INSTITUTE OF TECHNOLOGY,EXT. CENTER NOIDA,UP,INDIA, PH E-mal: s,ha@btmesra.ac.n In grds, users may face hundreds of thousands of computers to utlze. It s mpossble for anyone to manually assgn obs to computng resources n grds. Therefore, grd ob schedulng s a very mportant ssue n grd computng. Please refer to a survey [3], whch also poses some open ssues. A good schedule would adust ts schedulng strategy accordng to the changng status of the entre envronment and the types of obs. Therefore, a dynamc algorthm n ob schedulng such as Ant Colony Optmzaton (ACO) [4,5] s approprate for grds. ACO s a heurstc algorthm wth effcent local search for combnatoral problems. ACO mtates the behavor of real ant colones n nature to search for food and to connect to each other by pheromone lad on paths traveled. Many researches use ACO to solve NP-hard problems such as travelng salesman problem [6],graph colorng problem [7], vehcle routng problem [8], andso on. In [1] ths technque has been appled for ndependent task schedulng. Ths paper apply the above technque for dependent task schedulng. Here a hybrd algorthm by Sakellarou[2] can be appled,where tasks n DAG(Drected acyclc graph) are upward ranked and sorted decreasngly. Then the sorted tasks are grouped along the sorted sequences and n every group,tasks are ndependent. We assume each ob s an ant and the algorthm sends the ants to search for resources. We also modfy the global and local pheromone update functons n ACO algorthm n order to balance the load for each grd resource. The rest of the paper s organzed as follows. Secton 2 ntroduces the related work about many knds of ACO algorthm and ob schedulng n grds. Secton 3 detals the proposed ACO optmzaton algorthm, ts pseudocode and

2 Internatonal Journal of Scentfc & Engneerng Research Volume 2, Issue 6, June algorthm analyss n ob schedulng for dependent task schedulng. Secton 4 gves the comparson of proposed algorthm wth other exstng methods n terms of tme complexty. Secton 5 concludes paper and Secton 6 lsts references. 2.RELATED WORK: 2.1. Ant algorthms There are many dfferent knds of ACO algorthm,.e., AntColony System (ACS) [6], Max-Mn Ant System (MMAS) [9],Rank-based Ant System (RAS) [10], Fast Ant System (FANT) [11] and Eltst Ant System (EAS) [12]. ACS uses the pseudorandomproportonal rule to replace state transton rule for decreasng computaton tme of selectng paths and update the pheromone on the optmal path only. It s proved that t helps ants search the optmal path.mmas s based on the basc ACO algorthm but lmtng the pheromone range to be greater than or equal to the low bound value (Mn) and smaller than or equal to the upper bound value(max). The low bound and upper bound are defned by the user.accordng to the low bound and upper bound values, MMAS could avod ants to converge too soon n some ranges. In the desgn of RAS, t sorts the ants by ant s tour length n ascendng order after all ants completed ther tours. It means that the frst ant fnds the shortest path to complete the tour and the last ant takes the longest tour. They gve each ant a dfferent densty of pheromone to update ther path by the ascendng order: the hgher the poston of the ant, the more pheromone t could update; the lower the poston of the ant, the less pheromone t has. By the dea of RAS, the shortest length gets more pheromone to attract more ants to follow and the system could get the optmal soluton very soon, and t updates pheromone after each teraton. In order to avod the sub-optmal soluton, t apples a reset pheromone functon.eas update more pheromone on the best-so-far tour found norder to attract more ants to follow the best-so-far tour. 2.2 Job schedulng n grds Job schedulng s well studed wthn the computer operatng systems [13]. Most of them can be appled to the grd envronment wth sutable modfcatons. In the followng we ntroduce several methods for grds. The FPLTF (Fastest Processor to Largest Task Frst) [14] algorthm schedules tasks to resources accordng to the workload of tasks n the grd system. The algorthm needs two man parameters such as the CPU speed of resources and workload of tasks. The scheduler sorts the tasks and resources by ther workload and CPU speed then assgns the largest task to the fastest avalable resource. If there are many tasks wth heavy workload, ts performance may be very bad. Dynamc FPLTF (DPLTF) [15] s based on the statc FPLTF, t gves the hghest prorty to the largest task.dpltf needs predcton nformaton on processor speeds and taskworkload. The WQR (Work Queue wth Replcaton) s based on the workqueue (WQ) algorthm [15]. The WQR sets a faster processor wth more tasks than a slower processor and t apples FCFS and random transfer to assgn resources. WQR replcates tasks n order to transfer to avalable resources. The amount of replcatons s defned by the user. When one of the replcaton tasks s fnshed,the scheduler wll cancel the remanng replcaton tasks. The WQR s shortcomng s that t takes too much tme to execute and transfer replcaton tasks to resource for executon. Mn-mn [16] set the tasks whch can be completed earlest wth the hghest prorty. The man dea of Mn-mn s that t assgns tasks to resources whch can execute tasks the fastest. Maxmn[16] set the tasks whch has the maxmum earlest completon tme wth the hghest prorty. The man dea of Max-mn s that t overlaps the tasks wth long runnng tme wth the tasks wth short runnng tme. For nstance, f there s only one long task, Mn-mn wll execute short tasks n parallel and then execute long task. Max-mn wll execute short tasks and long task n parallel.the RR (Round Robn) algorthm focuses on the farness problem. RR uses the rng as ts queue to store obs. Each ob n queue has the same executon tme and t wll be executed n turn.if a ob can t be completed durng ts turn, t wll store back to the queue watng for the next turn. The advantage of RR algorthm s that each ob wll be executed n turn and they don t have to wat for the prevous one to complete. But f the load s heavy, RR wll take long tme to complete all obs. Prorty schedulng algorthm gves each ob a prorty value and uses t to dspatch obs. The prorty value of each ob depends on the ob status such as the requrement of memory szes, CPU tme and so on. The man problem of ths

3 Internatonal Journal of Scentfc & Engneerng Research Volume 2, Issue 6, June algorthm s that t may cause ndefnte blockng or starvaton f the requrement of a ob s never beng satsfed.the FCFS (Frst Come Frst Serve) algorthm s a smple ob schedulng algorthm. A ob whch makes the frst requrement wll be executed frst. The man problem of FCFS s ts convoy effect [13].If all obs are watng for a bg ob to fnsh, the convoy effect occurs.the convoy effect may lead to longer average watng tme and lower resource utlzaton. 3 BALANCED ANT COLONY ALGORITHM FOR DEPENDENT TASK SCHEDULING 3.1 ARCHITECTURE OF THE SCHEDULING SYSTEM Model Descrpton: G G G G... Gn Wth the condton that all the tasks n G 1 wll be executed after all the tasks n G has been executed for all =0 to n-1. SCHEDULING SYSTEM G G G G... Gn ] Input- [ Output- MACHINES(A cluster of Workstatons) Fg-2 Schedulng Archtecture Suppose Drected acyclc graph(dag) below represents a set of dependent tasks. T1 gven Ths can be solved by takng a cluster of workstatons connected by nternet as shown n Fg-3 G, G, G... n G can be appled to these workstatons wth a condton that there should be synchronzaton among them,so that G 1 group uses the result of tasks completed n G group T2 T3 0ton 1.Each group G tasks can be executed usng Balanced Ant Colony Optmzaton. T4 T5 G T T T 1, 2,... CWS CWS 1, 2,... CW Fg-1(Gven Drected Acyclc graph representng set of dependent tasks) The DAG s dvded nto n no. of groups contanng ndependent sets of tasks. T6 Fg-4 Assgnng tasks to cluster of workstatons. Here each of the task s modelled as an ant and each of the machne n the cluster of workstaton s

4 Internatonal Journal of Scentfc & Engneerng Research Volume 2, Issue 6, June the food. Each ant select food through shortest path.e. where the pheromone densty s more. The balanced antcolony algorthm for schedulng tasks to resources s descrbed n the next secton. 3.1 Proposed algorthm:. and. W=weght of the node. S=the set of mmedate successor of node C=Weght of the edge connectng nodes In ths secton we are presentng the algorthm for the dependent task schedulng n Grd heterogeneous system usng Ant Colony Optmzaton technque. Step 1: Input the Drected acyclc graph(dag) G depctng how dfferent tasks are dependent to each other.[in the graph each node representng task node and the edges between them represents the dependency among them] Step 2: Rank the nodes n the graph usng Rankng() method. Step 3:Usng GroupCreaton() method,a set of groups of ndependent tasks are made. Step 4:for Groupno=1;Groupno<n;Groupno++ [for n no. of groups of ndependent tasks] GroupCreaton() method algorthm 1.Sort nodes n descendng order of ther rank values. G0=,=0; 2.Scan nodes n descendng order of the rank values If current node has a dependence wth a node G Then ++; and G=; Add node to G 3.Repeat step 2 untl there are no more nodes. Apply method on each group. AntColony(Groupno.) SchedulngAntColony(Group no.) algorthm Rankng() method algorthm 1. Assgn a weght to each node as the average computaton cost across all machnes. 2. Assgn a weght to each edge as the average communcaton cost across all machnes. 3. Use upward rankng to compute the rank value for each node, The rank value R of a node I s recursvely defned as follows R= W + max(c +R) for all present n S [An Ant n the Ant system s a ob n the Grd system. Pheromone value on a path n the Ant system s a weght for a resource n the Grd system. A resource wth a large weght value means that the resource has a better computng power. The scheduler collects data from nformaton server and uses the data to calculate a weght value of the resource. The pheromone(weght) of each resource s stored n the scheduler and the scheduler uses t as the parameter for the Balanced Ant Colony Optmzaton algorthm. At last the selects the resource accordng to the algorthm.] Where

5 Internatonal Journal of Scentfc & Engneerng Research Volume 2, Issue 6, June The pheromone ndcator(pi)(the ntal pheromone value of each ob to the resource) PI M T BW CS *(1 LD) (1) 4. The global pheromone update s to recalculate the entre PI matrx,after the resource completes the ob. 3.2 Pseudocode of the proposed algorthm Where M =Sze of a gven ob. In ths secton we are presentng the pseudocode for the dependent task schedulng usng Ant Colony Optmzaton technque. BW =Network Bandwdth between scheduler and the resource. T =CPU tme needed for the ob. Procedure Graph G) SchedulngDependenttask_Antcolony( LD =Current load at resource. CS=CPU speed of resource. The load,bandwdth and CPU speed can be obtaned by NWS(Network Weather Servce). 1. Do steps 2 to 4 untl all the tasks are assgned 2. The resource status(how many obs are there n resource,. e. how much s t busy,the program executon tme and the sze of obs) s told by PI. The larger the value of PI, the more effcent t s to assgn ob to the resource. 3. The PI matrx s as follows for m resources and n obs. P P... PI P P... P P P P n n m1 m2 mn (2) The largest entry from the PI matrx s chosen say P,then the th ob assgned to the resource th. After ths equaton (2) s updated usng equaton (1) for m resources and (n-1) obs. Ths s called local pheromone update. Procedure MakngIndependent taskgroup(); For(=1;<groupno.;++) Procedure SchedulngAntcolony(groupno.); Procedure Makngndependent taskgroup() ( Procedure Rankng(); Procedure GroupCreaton(); Procedure Rankng() 1.Assgn a weght to each node as the average computaton cost across all machnes. 2.Assgn a weght to each edge as the average communcaton cost across all machnes. 3.Use upward rankng to compute the rank value for each node. Procedure GroupCreaton()

6 Internatonal Journal of Scentfc & Engneerng Research Volume 2, Issue 6, June Sort nodes n descendng order of ther rank values. G0=,=0; 2.Scan nodes n descendng order of the rank values If current node has a dependence wth a node G Then ++; and G=; Add node to G 3.Repeat step 2 untl there are no more nodes. The rank value R of a node I s recursvely defned as follows R= W + max(c +R) for all present n S Where W=weght of the node. S=the set of mmedate successor of node. C=Weght of the edge connectng nodes and. Procedure SchedulngAntColony(Group no.) [An Ant n the Ant system s a ob n the Grd system. Pheromone value on a path n the Ant system s a weght for a resource n the Grd system. A resource wth a large weght value means that the resource has a better computng power. The scheduler collects data from nformaton server and uses the data to calculate a weght value of the resource. The pheromone(weght) of each resource s stored n the scheduler and the scheduler uses t as the parameter for the Balanced Ant Colony Optmzaton algorthm. At last the selects the resource accordng to the algorthm.] The pheromone ndcator(pi)(the ntal pheromone value of each ob to the resource) PI M T BW CS *(1 LD) Where M =Sze of a gven ob. (1) BW =Network Bandwdth between scheduler and the resource. T =CPU tme needed for the ob. LD =Current load at resource. CS=CPU speed of resource. The load,bandwdth and CPU speed can be obtaned by NWS(Network Weather Servce). No_of_tasks_assgned=0; Do 1.The resource status(how many obs are there n resource,. e. how much s t busy,the program executon tme and the sze of obs) s told by PI. The larger the value of PI, the more effcent t s to assgn ob to the resource. 2.The PI matrx s as follows for m resources and n obs. P P... PI P P... P P P P (2) n n m1 m2 mn The largest entry from the PI matrx s chosen say P,then the th ob assgned to the resource th. After ths equaton (2) s updated usng equaton (1) for m resources and (n-1) obs. Ths s called local pheromone update. 3.The global pheromone update s to recalculate the entre PI matrx,after the resource completes the ob. No_of_tasks_assgned++;

7 Internatonal Journal of Scentfc & Engneerng Research Volume 2, Issue 6, June whle(no_of_ tasks _assgned<totalno_tasks) 3.3 Algorthm analyss Let T represent the Tme complexty of the proposed algorthm. T =T(Rankng)+T(Groupng)+T(ACO) Where ACO s Ant Colony Optmzaton algorthm. T(Rankng)=O(logn) T(Groupng)=O(nlogn)[Tasks are sorted usng heap sort) T(ACO)= 2 ( np) 4 COMPARISON WITH OTHER METHODS: There exst other clusterng heurstcs for dependent task schedulng[3].domnant Sequence Clusterng(DSC) algorthm proposed by Yang et al[4] has tme complexty for a DAG as O(( e n)log n) whch s equal to O n 2 ( log ) n for a dense graph.. Smlarly CLASS- II,a cluster algorthm proposed by Lou et al [5] has tme complexty as O( e nlog n) whch s equal to O n n n 2 ( log ) for a dense graph. The fg-5 depcts a comparson of these methods wth respect to no. of tasks to be assgned. 5 CONCLUSION From above algorthm analyss t s concluded that ACO gves better performance wth respect to DSC and CLASS II clusterng heurstc methods for a fxed no. of processors. In ths paper pseudocode of the proposed algorthm s wrtten whch has to be coded n C n next paper. 6 REFERENCES [1] An ant algorthm for balanced ob schedulng n grds Ruay-Shung Chang_, Jh-Sheng Chang, Po- Sheng Ln Department of Computer Scence and Informaton Engneerng, Natonal Dong Hwa Unversty, Shoufeng Hualen, 974 Tawan, ROC [2].A Hybrd heurstc for DAG Schedulng on Heteorogeneous Systems. Rzos Sakellaro and Henan Zhao,Department of Computer Scence,Unversty of Manchester,Oxford Road,Manchester M13 9PL,U.K. [3]. Fangpeng Dong and Selm G. Akl Schedulng Algorthms for Grd Computng: State of the Art and Open Problems Techncal Report No [4]. M. Dorgo, C. Blum, Ant colony optmzaton theory: A survey, Theoretcal Computer Scence 344 (2 3) (2005) [5]. M. Dorgo, Ant colony optmzaton, [6]. M. Dorgo, L.M. Gambardella, Ant colony system: A cooperatve learnng approach to the travelng salesman problem, IEEE Transactons on Evolutonary Computaton 1 (1) (1997) [7]. E. Salar, K. Eshgh, An ACO algorthm for graph colorng problem, n: Congress on Computatonal Intellgence Methods and Applcatons, Dec. 2005, p. 5. [8]. Xaoxa Zhang, Lxn Tang, CT-ACO hybrdzng ant colony optmzaton wth cycle transfer search for the vehcle routng problem, n: Congress on Computatonal Intellgence Methods and Applcatons, Dec. 2005, p. 6. [9]. T. Stutzle, MAX-MIN Ant System for Quadratc Assgnment Problems Techncal Report AIDA-97-04, Intellectcs Group, Department of Compute Scence, Darmstadt Unversty of Technology, Germany, July [10]. B. Bullnhemer, R.F. Hartl, C. Strauss, A new rank-based verson of the ant system: A computatonal study, Central European Journal for Operatons Research and Economcs 7 (1) (1999)

8 Internatonal Journal of Scentfc & Engneerng Research Volume 2, Issue 6, June [11]. E.D. Tallard, L.M. Gambardella, Adaptve memores for the quadratc assgnment problem, Techncal Report IDSIA-87-97, IDSIA, Lugano, Swtzerland, [12]. M. Dorgo, V. Manezzo, A. Colorn, The ant system: Optmzaton by a colony of cooperatng agents, IEEE Transactons on Systems, Man, and Cybernetcs, Part B 26 (1) (1996) [13]. Abraham Slberschatz, Peter Baer Galvn, Greg Gagne, Operatng System Concepts, 7th edton, John Wley & Sons, [14]. D. Saha, D. Menasce, S. Porto, Statc and dynamc processor schedulng dscplnes n heterogeneous parallel archtectures, Journal of Parallel and Dstrbuted Computng 28 (1) (1995) [15]. D. Paranhos, W. Crne, F. Braslero, Tradng cycles for nformaton: Usng replcaton to schedule bag-of-tasks applcatons on computatonal grds, n: Internatonal Conference on Parallel and Dstrbuted Computng (Euro- Par), n: Lecture Notes n Computer Scence, vol. 2790, 2003, pp [16]. M. Maheswaran, S. Al, H.J. Segel, D. Hensgen, R. Freund, Dynamc matchng and schedulng of a class of ndependent tasks onto heterogeneous computng system, Journal of Parallel and Dstrbuted Computng 59 (1999) CWS1 Router CWS2 CWS3 CWS4 Fgure-3

9 Internatonal Journal of Scentfc & Engneerng Research Volume 2, Issue 6, June X AXIS-NO. OF TASK Y AXIS-TIMECOMPLEXITY Fg-5

10 Internatonal Journal of Scentfc & Engneerng Research Volume 2, Issue 6, June