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Scheduling Divisible Loads on Heterogeneous Linear Daisy Chain Networks with Arbitrary Processor Release Times
March 2004 (vol. 15 no. 3)
pp. 273-288

Abstract—The problem of distributing and processing a divisible load in a heterogeneous linear network of processors with arbitrary processors release times is considered. A divisible load is very large in size and has computationally intensive CPU requirements. Further, it has the property that the load can be partitioned arbitrarily into any number of portions and can be scheduled onto processors independently for computation. The load is assumed to arrive at one of the farthest end processors, referred to as boundary processors, for processing. The processors in the network are assumed to have nonzero release times, i.e., the time instants from which the processors are available for processing the divisible load. Our objective is to design a load distribution strategy by taking into account the release times of the processors in such a way that the entire processing time of the load is a minimum. We consider two generic cases in which all processors have identical release times and when all processors have arbitrary release times. We adopt both the single and multi-installment strategies proposed in the divisible load scheduling literature in our design of load distribution strategies, wherever necessary, to achieve a minimum processing time. Finally, when optimal strategies cannot be realized, we propose two heuristic strategies, one for the identical case, and the other for nonidentical release times case, respectively. Several conditions are derived to determine whether or not optimal load distribution exists and illustrative examples are provided for the ease of understanding.

[1] G.D. Barlas, Collection Aware Optimum Sequencing of Operations and Closed Form Solutions for the Distribution of a Divisible Load on Arbitrary Processor Trees IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 5, pp. 429-441, May 1998.
[2] V. Bharadwaj, D. Ghose, and V. Mani, Multiinstallment Load Distribution in Tree Networks With Delays IEEE Trans. Aerospace and Electronic Systems, vol. 31, no. 2, pp. 555-567, 1995.
[3] V. Bharadwaj, D. Ghose, V. Mani, and T.G. Robertazzi, Scheduling Divisible Loads in Parallel and Distributed Systems. IEEE Computer Soc. Press, 1996.
[4] V. Bharadwaj, H.F. Li, and T. Radhakrishnan, Scheduling Divisible Loads in Bus Networks with Arbitrary Processor Release Times Computers and Math. with Applications, vol. 32, no. 7, 1996.
[5] V. Bharadwaj, X. Li, and K.C. Chung, On the Influence of Start-Up Costs in Scheduling Divisible Loads on Bus Networks IEEE Trans. Parallel and Distributed Systems, vol. 11, no. 12, pp. 1288-1305, Dec. 2000.
[6] V. Bharadwaj and G. Barlas, Access Time Minimization for Distributed Multimedia Applications Multimedia Tools and Applications, vol. 12, nos. 2/3, pp. 235-256, Nov. 2000.
[7] V. Bharadwaj, D. Ghose, and T.G. Robertazzi, Divisible Load Theory: A New Paradigm for Load Scheduling in Distributed Systems Cluster Computing, vol. 6, no. 1, Jan. 2003.
[8] J. Blazewicz and M. Drozdowski, Distributed Processing of Divisible Jobs with Communication Startup Costs Discrete Applied Math., vol. 76, nos. 1-3, pp. 21-41, June 1997.
[9] J. Blazewicz, M. Drozdowski, and M. Markiewicz, Divisible Task Scheduling Concept and Verification Parallel Computing, pp. 87-98, Jan. 1999.
[10] S.K. Chan, V. Bharadwaj, and D. Ghose, Experimental Study on Large Size Matrix-Vector Product Computations using Divisible Load Paradigm on Distributed Bus Networks #TR-OSSL/BV-DLT/01, Nov. 2000.
[11] Y.C. Cheng and T.G. Robertazzi, Distributed Computation with Communication Delays IEEE Trans. Aerospace and Electronic Systems, vol. 24, no. 6, pp. 700-712, Nov. 1988.
[12] M. Drozdowski and P. Wolniewicz, Experiments with Scheduling Divisible Tasks in Clusters of Workstations Proc. Euro-Par 2000, pp. 311-319, 2000.
[13] D. Ghose and H.J. Kim, Load Partitioning and Trade-Off Study for Large Matrix-Vector Computations in Multicast Bus Networks with Communication Delays J. Parallel and Distributed Computing, vol. 54, 1998.
[14] K. Hwang and Z. Xu, Scalable Parallel Computing: Technology, Architecture, Programming. McGraw-Hill, Feb. 1998.
[15] K. Li, Managing Divisible Loads in Partitionable Networks High Performance Computing Systems and Applications, J. Schaeffer and R. Unrau, ed., pp. 217-228, Kluwer Academic Publishers, 1998.
[16] X. Li, V. Bharadwaj, and C.C. Ko, Scheduling Divisible Tasks on Heterogeneous Single-level Tree Networks with Finite-Size Buffers IEEE Trans. Aerospace and Electronic Systems, vol. 37, Jan. 2001.
[17] M. Michael, How Useful Is Old Information? IEEE Trans. Parallel and Distributed Systems, vol. 11, no. 1, pp. 6-20, Jan. 2000.
[18] L. Pangfeng and N.B. Sandeep, Experiences with Parallel N-Body Simulation IEEE Trans. Parallel and Distributed Systems, vol. 11, no. 12, pp. 1306-1323, Dec. 2000.
[19] D.A.L. Piriyakumar and C.S.R. Murthy, Distributed Computation for a Hypercube Network of Sensor-Driven Processors with Communication Delays Including Setup Time IEEE Trans. Systems, Man, and Cybernetics Part A: Systems and Humans, vol. 28, no. 2, pp. 245-251, Mar. 1998.
[20] T.G. Robertazzi, "Processor Equivalence for a Linear Daisy Chain of Load Sharing Processors," IEEE Trans. Aerospace and Electronic Systems, vol. 29, no. 4, pp. 1,216-1,221, Oct. 1993.
[21] B.A. Shirazi, A.R. Hurson, and K.M. Kavi, Scheduling and Load Balancing in Parallel and Distributed Systems. IEEE Computer Soc. Press, 1995.
[22] J. Sohn and T.G. Robertazzi, A Multi-Job Load Sharing Strategy for Divisible Jobs on Bus Networks CEAS Technical Report 665, State Univ. of New York at Stony Brook, Apr. 1993.
[23] J. Sohn and T.G. Robertazzi, Optimal Load Sharing for a Divisible Job on a Bus Network IEEE Trans. Aerospace and Electronic Systems, vol. 32, no. 1, pp. 34-40, Jan. 1996.
[24] K.Y. Tieng, F. Ophir, and L.M. Robert, Parallel Computation in Biological Sequence Analysis IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 3, pp. 283-294, Mar. 1998.

Index Terms:
Linear networks, release times, divisible loads, communication delays, processing times, finish times.
Citation:
Bharadwaj Veeravalli, Wong Han Min, "Scheduling Divisible Loads on Heterogeneous Linear Daisy Chain Networks with Arbitrary Processor Release Times," IEEE Transactions on Parallel and Distributed Systems, vol. 15, no. 3, pp. 273-288, March 2004, doi:10.1109/TPDS.2004.1264811
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