Scheduling multiple divisible loads on a linear processor network

Min, Veeravalli, and Barlas have recently proposed strategies to minimize the overall execution time of one or several divisible loads on a heterogeneous linear network, using one or more installments. We show on a very simple example that their approach does not always produce a solution and that, when it does, the solution is often suboptimal. We also show how to find an optimal schedule for any instance, once the number of installments per load is given. Then, we formally state that any optimal schedule has an infinite number of installments under a linear cost model as the one assumed in the original papers. Therefore, such a cost model cannot be used to design practical multi-installment strategies. Finally, through extensive simulations we confirmed that the best solution is always produced by the linear programming approach, while solutions of the original papers can be far away from the optimal

Comments on "Design and performance evaluation of load distribution strategies for multiple loads on heterogeneous linear daisy chain networks''

Min, Veeravalli, and Barlas proposed strategies to minimize the overall execution time of one or several divisible loads on a heterogeneous linear network, using one or more installments. We show on a very simple example that the proposed approach does not always produce a solution and that, when it does, the solution is often suboptimal. We also show how to find an optimal scheduling for any instance, once the number of installments per load is given. Finally, we formally prove that under a linear cost model, as in the original paper, an optimal schedule has an infinite number of installments. Such a cost model can therefore not be sed to design practical multi-installment strategies

The effect of start-up delays in scheduling divisible loads on bus networks: An alternate approach

AbstractIn this paper, scheduling of divisible loads in a bus network is considered. The objective is to minimize the processing time by including the overhead component due to start-up time that could degrade the performance of the system, in addition to the inherent communication and computation delays. These overheads are considered to be constant additive factors to the communication and computation components. A closed-form expression for optimal processing time is derived. Using this closed-form expression, this paper analytically proves significant results regarding the optimal sequence of load distribution and optimal number of processors. Numerical examples are presented to illustrate the analysis

Optimizing Data Intensive Flows for Networks on Chips

Data flow analysis and optimization is considered for homogeneous rectangular mesh networks. We propose a flow matrix equation which allows a closed-form characterization of the nature of the minimal time solution, speedup and a simple method to determine when and how much load to distribute to processors. We also propose a rigorous mathematical proof about the flow matrix optimal solution existence and that the solution is unique. The methodology introduced here is applicable to many interconnection networks and switching protocols (as an example we examine toroidal networks and hypercube networks in this paper). An important application is improving chip area and chip scalability for networks on chips processing divisible style loads

Scheduling Real-time Divisible Loads in Cluster Computing Environment

The significance of cluster computing in solving massively parallel workloads is tremendous. Divisible Load Theory has proven to be very successful in optimizing the usage of the system resources by partitioning the arbitrarily divisible loads adequately among the cluster nodes. Arbitrarily divisible loads have significant real-world applications in high energy and particle physics. In this thesis, various algorithms for a cluster computing environment are studied including the ones dealing with divisible load theory confirming DLT based algorithms performing better in most cases. The loads that are considered in this thesis are hard real-time tasks with associated deadlines. Specifically, a comparison is made between clusters with one where the head node doesn't participate in processing of the work-loads with the other where the head node does participate in processing of the work-loads. A new mathematical formula is derived for the task execution time corresponding to the new scenario of head node possessing front-end processing capability. The existing algorithms corresponding to Real-Time Divisible Load Theory are then implemented using this new formula to examine the scheduling performance in this new scenario compared to the conventional scenario where the head node lacks front-end processing capability

Scheduling divisible loads with time and cost constraints

In distributed computing, divisible load theory provides an important system model for allocation of data-intensive computations to processing units working in parallel. The main task is to define how a computation job should be split into parts, to which processors those parts should be allocated and in which sequence. The model is characterized by multiple parameters describing processor availability in time, transfer times of job parts to processors, their computation times and processor usage costs. The main criteria are usually the schedule length and cost minimization. In this paper, we provide the generalized formulation of the problem, combining key features of divisible load models studied in the literature, and prove its NP-hardness even for unrestricted processor availability windows. We formulate a linear program for the version of the problem with a fixed number of processors. For the case with an arbitrary number of processors, we close the gaps in the study of special cases, developing efficient algorithms for single criterion and bicriteria versions of the problem, when transfer times are negligible

Ishu bunsan shisutemu ni okeru kabun tasuku no sukejulingu

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