Dual Objective Min-Min Algorithm for Meta Task Scheduling in Grid Computing
D. I. George Amalarethinam
5. Experiments and Results
The experiments are conducted for twelve different types of ETC matrices which were produced using benchmark simulation model [1]. The simulated values of ETC and memory requirements are shown in figure 2. The ETC matrix produced considers three factors: Consistency of resources, heterogeneity of resources and heterogeneity of tasks. The task heterogeneity and resource heterogeneity take two values: high and low. The characteristics of the ETC matrices have been further varied to simulate more aspects of realistic situations. Three different types of ETC matrices are generated based on consistency.
The resources considered here may be consistent, partially consistent or inconsistent. An ETC matrix is said to be consistent in which if a resource Ri executes a task Ti faster than a resource Rj then the resource Ri should execute all tasks faster than resource Rj. Inconsistent matrices contain resources which execute some tasks faster and some tasks slower. Partially-consistent matrices contain a sub matrix of consistent resources and other resources in the matrix are inconsistent.
DOMM is analyzed by generating 12 different types of ETC matrices. Table 1 shows a sample ETC matrix generated for 5 inconsistent resources. In this table the tasks and resources have high
We have simulated the memory availability of different resources by generating a memory availability table. Table 3 shows the memory capacity of each resource.
Table 3: Memory Availability Table
Resources Memory Size
R0 431
R1 815
R2 150
R3 436
R4 953
Table 4 shows the makespan produced by Min-Min algorithm and DOMM algorithm for consistent ETC matrices. Table 5 shows the makespan produced by Min-Min algorithm and DOMM algorithm for partially consistent ETC matrices. Table 6 shows the makespan produced by Min-Min algorithm and DOMM algorithm for inconsistent ETC matrices. The instances in all the three Tables are labeled using three alphabets. The first alphabet represents the consistency of the matrix which may take any one of the following values
C Consistent matrix (or)
P Partially-consistent matrix (or) I Inconsistent matrix
The second alphabet shows the task heterogeneity which may take the value L for low or H for high heterogeneity. Similarly the third alphabet represents resource heterogeneity which use L for low or H for High heterogeneity. All the results show that DOMM outperforms the traditional Min-Min algorithm. Since the Min-Min algorithm does not consider the memory requirements of a task, the tasks may suffer during scheduling because of the unavailability of the memory during run time. Thus DOMM contains fault tolerance mechanism by identifying the problem before scheduling. The results are analyzed using graphs shown in the following figures. Figure 3 shows the chart for consistent matrices, figure 4 shows the chart for partially-consistent matrices and figure 5 shows the chart for inconsistent matrices.
Table 4: Makespan values of Min-Min and DOMM algorithms for various consistencies and heterogeneity of resources.
Instances Makespan produced by Min-Min Makespan produced by DOMM
CLL 446 244
CLH 210.77 1034.75
CHL 2715.49 1523.09
CHH 3309.6 2380.41
PLL 283.21 160.43
PLH 1551.98 762.53
PHL 2227.42 1996.41
PHH 4129 3488
ILL 291.94 214.99
ILH 1324.92 887.22
IHL 1983.6 1583.59
IHH 3230.41 1738.78
Figure 2: Sample values of ETC and memory requirement
Figure 3: Makespan produced by Consistent Resources
Figure 4: Makespan produced by Partially Resources Consistent
Figure 5: Makespan produced by Inconsistent Resources
The values given in the table clearly show that for all types of consistencies and heterogeneity DOMM gives reduced makespan. This result is achieved by balancing the load and using the resources efficiently. From the table we can observe that the resources with high heterogeneity produce more makespan whereas resources with low heterogeneity produce less makespan irrespective of the consistency.
6. Conclusion
Scheduling a task on the appropriate resource is difficult in a distributed environment like Grid. For static scheduling algorithms, the tasks may suffer during execution because of the various parameters.
Memory requirement is one of the important parameters to be considered during execution. The Min-Min algorithm considers only the execution time of the tasks for scheduling and it does not balance the load. In this paper, a new algorithm Dual Objective Min is proposed based on the traditional Min-Min algorithm. The newly proposed algorithm produces better results for various consistency and heterogeneity of tasks and resources. The new DOMM algorithm proposed in this paper tries to balances the load as well as provides fault tolerance mechanism by considering the memory requirement as a parameter for scheduling the tasks. The results show that DOMM outperforms the traditional Min-Min algorithm for all cases. The work may be further extended by considering other factors like network bandwidth, communication delay and so on in the future.
References
[1] Buyya, R., D. Abramson, J. Giddy and H.Stockinger, 2002, “Economic models for resource management and scheduling in grid computing”, J. Concurrency and Computation: Practice and Experience, pp.1507-1542.
[2] Foster, I., C. Kesselman and S. Tuecke, 2002, “The anatomy of the Grid: Enabling scalable virtual organizations”, International Journal of High Performance Computing Applications.
[3] H. Casanova, G. Obertelli, F. Berman, R. Wolski, 2003, “The AppLeS parameter sweep template: user-level middleware for the grid”, Proceedings of the ACM/IEEE Conference on Supercomputing.
[4] Rajkumar Buyya, David Abramson, Jonathan Giddy and Heinz Stockinger, 2002, “Economic models for resource management and scheduling in Grid computing”, Concurrency and Computation: Practice and Experience, pp. 1507 – 1542.
[5] B. Yagoubi and Y. Slimani, 2007, “Task Load Balancing Strategy for Grid Computing”, Journal of Computer Science, pp.186-194.
[6] Braun, T.D., Siegel, H.J., Beck, N., Boloni, L.L., Maheswaran, M., Reuther, A.I., Robertson, J.P., et al. 2001, “A comparison of eleven static heuristics for mapping a class of independent tasks onto heterogeneous distributed computing systems”, Journal of Parallel and Distributed Computing, Vol. 61, No. 6, pp.810–837.
[7] Singh. M and Suri. P.K, 2008, “QPS A QoS Based Predictive Max-Min, Min-Min Switcher Algorithm for Job Scheduling in a Grid”, Information Technology Journal, Volume: 7, Issue: 8, pp. 1176-1181.
[8] Sameer Singh Chauhan,R. Joshi. C, 2010, “QoS Guided Heuristic Algorithms for Grid Task Scheduling”, International Journal of Computer Applications (0975 – 8887), Volume 2, No.9, pp 24-31.
[9] Saeed Parsa, Reza Entezari-Maleki, 2009, “RASA: A New Grid Task Scheduling Algorithm”, International Journal of Digital Content Technology and its Applications Volume 3, Number 4.
[10] Saurabh Kumar Garg 1, Rajkumar Buyya1 and H. J. Siegel2, 2009, “Scheduling Parallel Applications on Utility Grids: Time and Cost Trade-off Management”, Proc. 32nd Australasian Computer Science Conference (ACSC ‘09), pp 151 -159.
[11] G. K. Kamalam and V. Murali Bhaskaran, 2010, “An Improved Min-Mean Heuristic Scheduling Algorithm for Mapping Independent Tasks on Heterogenous Computing Environment”, International Journal Of Computational Cognition, Vol. 8, No. 4.
[12] He. X, X-He Sun, and Laszewski. G.V, 2003, "QoS Guided Minmin Heuristic for Grid Task Scheduling," Journal of Computer Science and Technology, Vol. 18, pp. 442-451.
[13] Kokilavani.T and George Amalarethinam.D.I, 2010, “Applying Non-Traditional Optimization Techniques to Task Scheduling in Grid Computing”, International Journal of Research and Reviews in Computer Science, Vol. 1, No. 4, pp. 34 – 38
[14] Kokilavani.T and George Amalarethinam.D.I, 2011, “Load Balanced Min-Min Algorithm for Static Meta-Task Scheduling in Grid Computing”, International Journal of Computer Applications (0975 – 8887) Volume 20– No.2, pp. 42 – 48.
[15] Kokilavani. T and George Amalarethinam.D.I, 2012, “An Ant Colony Optimization Based Load Sharing Technique for Meta Task Scheduling in Grid Computing”, Proceedings of the Second International Conference on Advances in Computing and Information Technology, AISC 177, Springer, Vol. 2, pp. 395 – 404.
http://www.europeanjournalofscientificresearch.com