制度:新 ; 報告番号:甲2691号 ; 学位の種類:博士(国際情報通信学) ; 授与年月日:2008/7/30 ; 早大学位記番号:新486

Ghatpande Abhay

English

制度:新 ; 報告番号:甲2691号 ; 学位の種類:博士(国際情報通信学) ; 授与年月日:2008/7/30 ; 早大学位記番号:新4866textthesi

Ghatpande, Abhay

33886

Waseda University Repository

Divisible load scheduling on heterogeneous distributed systems =Ishu bunsan shisutemu ni okeru kabun tasuku no sukejulingu

DSpace at Waseda University

Graduate School of Global Information andTelecommunication Studies, Waseda UniversityAbstract of Doctoral DissertationDivisible Load Scheduling onHeterogeneous Distributed Systems??????????????????????????Abhay Ghatpande????????Global Information and Telecommunication StudiesAudiovisual Information Creation Technology IIJuly 2008With the proliferation of the Internet, volunteer computing is rapidly becoming feasible and gainingpopularity. Volunteer computing is a form of distributed computing in which a large number of av-erage users offer their computers to serve as processing and storage resources for scientific researchprojects or what are known as grand challenge problems. Similarly, grid computing and cloud computing,which provide mechanisms for users and applications to submit and execute computationally inten-sive workflows on remote resources, are being used for wide variety of applications today.The jobs that can be submitted to these systems are limited because they use open and shared re-sources that introduce three important challenges: (a) heterogeneity, (b) uncertainty, and (c) networklatency and delay. If an application has a complex structure, then a lot of time is spent waiting for datato be transferred between the participating nodes. This makes divisible loads ideally suited for execu-tion on volunteer and grid computing systems. Divisible loads are perfectly parallelizable and can bearbitrarily partitioned into independently and identically processable load fractions.Divisible loads usually follow the master-slave model of computation: a master node holds theentire (divisible) load and distributes it to the slave nodes; the slave nodes perform requisite processingon the allocated load fractions, and send the results back to the master. This research considers twoof the above mentioned issues: (a) the slaves are heterogeneous, i.e., they differ in computation speedand the bandwidth of the network that links them with the master node, and (b) the networks havehigh latency, i.e., the bandwidths can be considerably lower than the computation speeds.Under these conditions, the focus of this research is to minimize the makespan, i.e., the total timefrom the point that the master begins sending out load fractions to the point where result collectionfrom all slaves is complete. This involves finding the optimal number of slaves to be used, the size ofthe load fractions to be allocated to each, the order (sequence) in which the fractions are sent to theslaves, and the order in which the slaves send the results back to the master. This is referred to as theDLSRCHETS (Divisible Load Scheduling with Result Collection on HETerogeneous Systems) problem.Divisible Load Theory (DLT), the mathematical framework for the optimization of Divisible LoadScheduling (DLS) has been studied for over ten years. Most of the work has concentrated on the casewhere no results are returned to the master. This simplifies the analysis to a great extent, and allowsfor derivation of optimal load fractions and sequence of distribution to the slaves. The addition of re-sult collection and system heterogeneity breaks down this simplicity. The complexity of DLSRCHETSis an open problem and there is no known polynomial-time algorithm for an optimal solution to DL-SRCHETS. Before this research, the only proposed solutions to DLSRCHETS were FIFO (First In, FirstOut) and LIFO (Last In, First Out) type of schedules, which are not always optimal.This work considers the most general form of DLSRCHETS. No assumptions are made regarding thenumber of slaves allocated load, both the network and computation speeds of the slaves are heteroge-neous, and idle time can be present in the schedule if it reduces the makespan. The overall structureof this thesis is as follows. The theoretical basis of DLSRCHETS is first established, and it is definedin terms of a linear program for analysis. The optimal schedule for a system with two slaves is exten-sively explored because the proposed algorithms are built on it. Two new polynomial-time algorithms,namely ITERLP (ITERative Linear Programming) and SPORT (System Parameters based Optimized Re-sult Transfer) are proposed as solutions to DLSRCHETS. The performance of traditional and new algo-rithms is compared using a large number of simulations and the proposed algorithms are shown tohave superior performance.1The thesis is organized into five main chapters, preceded by an introduction, and terminated by aconclusion. All the chapters are described below.Chapter 1. Introduction establishes the research context that forms the basis for this thesis. It in-troduces the application areas of volunteer and grid computing, and the problems faced in schedul-ing applications on these platforms. Next, divisible loads and divisible load scheduling are introducedalong with the important results to date. The shortcomings of traditional DLT and the research objec-tives are laid out. Traditional methods are compared with the new approaches in this thesis, and thecontributions of this thesis are elaborated. The organization of the thesis is explained.Chapter 2. System Model defines the system model upon which this thesis is built. There are severalimportant constraints and assumptions that are used in the problem definition. The first one is thatthe communication and computation times are linearly increasing functions of the size of data. Simi-larly, the size of result data generated by a processor is directly proportional to the size of its allocatedinput load data. The constant of proportionality depends only on the application under considerationand is the same for all the processors. It is assumed that a processor can do only one thing at a time,i.e., communication and computation cannot overlap in a processor. Further, a processor can commu-nicate with only one other processor at a time. This is known as the one-port model. All operationsincluding data transmission, reception, and computation follow the atomic or block-based model, i.e.,they proceed uninterrupted in a single installment until the end. In this chapter, justification is givenfor all these assumptions considering the target applications and environment.Chapter 3. Analysis of DLSRCHETS provides a detailed derivation of the DLSRCHETS problem def-inition. After first laying the theoretical basis, the DLSRCHETS problem is defined in terms of a linearprogram. The analysis of the optimal solution to DLSRCHETS is presented. Two important proofs aregiven — one for the allocation precedence condition and the other for the idle time theorem. The allocationprecedence condition is necessary to limit the number of possible schedules of DLSRCHETS to a finitenumber. It argues that there always exists an optimal solution to DLSRCHETS in which the entire loadis first distributed to the slaves before the master starts to receive results from the slaves. The proofuses rearrangement of the timing diagram to substantiate the claim.The proof of the idle time theorem is more complicated as it uses the geometry of linear programming.A brief introduction to linear programming is included in the chapter for this reason. The idle timetheorem states that not all slaves may be allocated load in the optimal solution, and irrespective of thenumber of slaves that are allocated load, at most one slave can have idle time in the optimal solution.In linear programming, some solutions can be degenerate. Analysis proves that the idle time theoremis true for both non-degenerate and degenerate cases.Chapter 4. The ITERLP Algorithm proposes the new polynomial time ITERLP algorithm. The com-plexity of DLSRCHETS is an open problem and finding the optimal solution is difficult. Thus, one hasto resort to heuristic algorithms under the circumstances. The proposed ITERLP algorithm reducesthe number of possible allocation and collection sequences to m each instead of the usual m!. Therationale behind the pruning of possible schedules in ITERLP is explained.The computation cost of ITERLP is still quite high — in the worst caseO(m3) linear programs have to besolved. The simulations show that ITERLP performance is much better than LIFO and FIFO over a wide2range of parameter values. The performance of the algorithm is quite stable; schedules generated byITERLP have execution time close to the optimal in most of the cases. In the simulations, the maximumdeviation of processing time with respect to the optimal is 0.8% for 5 processors, and it takes about 3to 5 minutes to find the schedule. As the number of processors increase, the time required to computethe solution increases. For example, it takes around 80 minutes to compute the ITERLP schedule for 65processors. Because the expected error is low, even though computation cost is high, ITERLP allowscomparison of other heuristic algorithms when it is impractical to find the optimal solution.Chapter 5. The Two-Slave System lays the foundation of the two-slave system that forms the basisfor the SPORT algorithm. Several important concepts are introduced in this chapter. It begins with thethree types of possible optimal schedules in a two-slave system and the related derivations. This is fol-lowed by the derivation of the optimal schedule for two processors using simple if-then-else clauses.This derivation includes two important results: (a) the condition for optimality of the LIFO and FIFOschedules, which shows that whether LIFO (resp. FIFO) is faster for a system depends only on the com-munication speeds of the links, and (b) the condition for the existence of idle time in a FIFO schedulethat shows a relationship between the presence of idle time and the computation and communicationspeeds of the two processors, and the type of divisible load. Next, the equivalent processor for LIFOand FIFO schedules in a two-slave system is derived. The equivalent processor enables the combinationof two processors into a single virtual processor. Next, the equivalent processor concept is extendedto an arbitrary number of processors, and its applications are explained. A method to determine thenumber of processors to allocate load is derived using the equivalent processor concept.Chapter 6. The SPORT Algorithm introduces the SPORT algorithm as a solution to the DLSRCHETSproblem. Along with the allocation and collection sequences, the SPORT algorithm finds: (a) the num-ber of processors to use for computation, and (b) the load fractions to be allocated to the participants.The important point is that this is done without solving time consuming linear programs. The numberof possible allocation and collection sequences is limited to a few, potentially optimal permutations.Because of this, the complexity of SPORT isO(m), wherem is the number of available processors. Thealgorithm is robust to system composition and it provides good schedules for both homogeneous andheterogeneous types of systems. In the simulations, the maximum deviation of processing time withrespect to optimal is 1.5% for 5 processors. SPORT is very fast — it takes less than a second to find thesolution for 500 processors.The basic idea behind SPORT is very simple — to use two processors at a time and build a piecewiselocally optimal schedule. However it is not very straightforward to be able to do this directly, andseveral necessary tools are designed. Detailed explanation regarding the working of the algorithm isgiven. The method of deriving load fractions using binary tree traversal is explained. Results of thecomprehensive simulation testing of the algorithms are presented.Chapter 7. Conclusion summarizes the various points covered in the thesis and presents severalideas for future work. It is proposed that future work can proceed in the following main directions:(a) Theoretical analysis of complexity and other optimality results, (b) Extensions to the current sys-tem model, (c) Modifying the nature of DLSRCHETS itself, and (d) Development of applications andphysical testing.3LIST OF ACADEMIC ACHIEVEMENTSArticles inrefereed journals• A. Ghatpande, H. Nakazato, O. Beaumont, and H. Watanabe. SPORT: An al-gorithm for divisible load scheduling with result collection on heteroge-neous systems. IEICE Transactions on Communications, E91-B(8), Aug. 2008.(To be published)• A. Ghatpande, H. Nakazato, O. Beaumont, and H. Watanabe. Analysis of di-visible load scheduling with result collection on heterogeneous systems.IEICE Transactions on Communications, E91-B(7), July 2008.Presentations atinternationalconferences• A. Ghatpande, O. Beaumont, H. Nakazato, and H. Watanabe. Divisible loadscheduling with result collection on heterogeneous systems. In Proc. Het-erogeneous Computing Workshop (HCW 2008) held in the IEEE Intl. Parallel andDistributed Processing Sysmposium (IPDPS 2008), Miami, FL., Apr. 2008.H. Watanabe, A. Ghatpande, and H. Nakazato. Distributed computing forreal-time video processing. In Proc. 1st International Conference on Ubiqui-tous Computing (ICUC 2003), pages 207–213, Seoul, Korea, Oct. 2003.Presentations atdomesticacademicmeetingsS. Iwasaki, A. Ghatpande, H. Nakazato, H. Kanemitsu, T. Hoshiai, andH. Tominaga. A study of resource information exchange method on P2P-Grid. Technical Report NS2007-53, IEICE, Sept. 2007.K. Kondou, A. Ghatpande, H. Nakazato, H. Kanemitsu, T. Hoshiai, andH. Tominaga. A study of data transferring for job execution time opti-mization on P2P-Grid. Technical Report NS2007-54, IEICE, Sept. 2007.Presentations atdomesticconferencesB. Volodya, A. Ghatpande, and H. Nakazato. Regression based executiontime estimation for scheduling in distributed computing systems. In Proc.2007 Forum on Information Technology (FIT 2007), L-025, Sept. 2007.A. Ghatpande, H. Nakazato, and H. Watanabe. SPORT: Extended simula-tion results for divisible load scheduling on heterogeneous systems. InProc. 2006 IEICE Society Conference, BS-15-3, Sept. 2006.A. Ghatpande, H. Nakazato, and H. Watanabe. SPORT: A near-optimalsolution to divisible load scheduling on heterogeneous systems. In Proc.2005 IEICE Society Conference, BS-9-4, Sept. 2005.A. Ghatpande, H. Nakazato, and H. Watanabe. Distributed video encodingon heterogeneous processor trees. In Proc. 19th Picture Coding Symposiumof Japan (PCSJ 2004), P-5.11, Nov. 2004.A. Ghatpande, H. Nakazato, and H. Watanabe. An architecture for dis-tributed video encoding on the Internet. In Proc. 18th Picture Coding Sym-posium of Japan (PCSJ 2003), P-2.02, Nov. 2003.1PosterpresentationsA. Ghatpande and H. Nakazato. Bandwidth measurement in broadbandnetworks for QoS guarantees. In Wabot-House Symposium, Gifu, Japan, Nov.2007.A. Ghatpande and H. Nakazato. Server architecture and HNML for net-worked home appliances. In Wabot-House Symposium, Gifu, Japan, Nov.2007.A. Ghatpande, H. Nakazato, and H. Watanabe. Grid over P2P systems:Issues and concepts. In 2006 Global Information and Telecommunication Re-search Workshop, Saitama, Japan, Oct. 2006.A. Ghatpande, H. Nakazato, and H. Watanabe. Distributed computing onP2P systems. In Spring Symposium of the 21st Century COE Productive ICTAcademia Program, Tokyo, Japan, Mar. 2006.A. Ghatpande, H. Nakazato, and H. Watanabe. Adaptive load schedulingusing autonomous learning agents. In 2005 Global Information and Telecom-munication Research Workshop, Saitama, Japan, Nov. 2005.A. Ghatpande, H. Nakazato, and H. Watanabe. Wide area distributed com-puting. In 2004 Global Information and Telecommunication Research Workshop,Saitama, Japan, Nov. 2004.2

Ishu bunsan shisutemu ni okeru kabun tasuku no sukejulingu

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Ishu bunsan shisutemu ni okeru kabun tasuku no sukejulingu

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