This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
On the Influence of Start-Up Costs in Scheduling Divisible Loads on Bus Networks
December 2000 (vol. 11 no. 12)
pp. 1288-1305
ASCII Text
x 
 
Bharadwaj Veeravalli, Xiaolin Li, Chi Chung Ko, "On the Influence of Start-Up Costs in Scheduling Divisible Loads on Bus Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 12, pp. 1288-1305, December, 2000.
 
 
BibTex
x
 
@article{ 10.1109/71.895794,
author = {Bharadwaj Veeravalli and Xiaolin Li and Chi Chung Ko},
title = {On the Influence of Start-Up Costs in Scheduling Divisible Loads on Bus Networks},
journal ={IEEE Transactions on Parallel and Distributed Systems},
volume = {11},
number = {12},
issn = {1045-9219},
year = {2000},
pages = {1288-1305},
doi = {http://doi.ieeecomputersociety.org/10.1109/71.895794},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Parallel and Distributed Systems
TI - On the Influence of Start-Up Costs in Scheduling Divisible Loads on Bus Networks
IS - 12
SN - 1045-9219
SP1288
EP1305
EPD - 1288-1305
A1 - Bharadwaj Veeravalli,
A1 - Xiaolin Li,
A1 - Chi Chung Ko,
PY - 2000
KW - Divisible loads
KW - communication delay
KW - processing time
KW - optimal sequence
KW - bus networks.
VL - 11
JA - IEEE Transactions on Parallel and Distributed Systems
ER -
 

Abstract—Optimal distribution of divisible loads in bus networks is considered in this paper. The problem of minimizing the processing time is investigated by including all the overhead components that could penalize 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 respective communication and computation components. Closed-form solution for the processing time is derived and the influence of overheads on the optimal processing time is analyzed. We derive a necessary and sufficient condition for the existence of the optimal processing time. We then study the effect of changing the load distribution sequence on the time performance. Through rigorous analysis, an optimal sequence to distribute the load among the processors is identified, whenever it exists. In case such an optimal sequence fails to exist, we present a greedy algorithm to obtain a suboptimal sequence based on some important properties of the overhead factors. Then, the effect of granularity of the data that is divisible is considered in the analysis for the case of homogeneous networks. An integer approximation algorithm capable of generating integer values of the load fractions in time $O(m)$, where $m$ is the number of processors in the network, is proposed. We then show that the upper bound on the suboptimal solution generated by our algorithm lies within a radius given by the sum of the computation and communication delays. Several numerical examples are presented to illustrate the concepts.

[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] S. Bataineh and T.G. Robertazzi, “Ultimate Performance Limits for Networks of Load Sharing Processors” Proc. Conf. Information Sciences and Systems, Princeton Univ., Princeton, N.J., pp. 794-799, Mar. 1992.
[3] S. Bataineh and M. Al-Ibrahim, “Effect of Fault-Tolerance and Communication Delay on Response Time in a Multiprocessor System with a Bus Topology,” Computer Comm., vol. 17, pp. 843-851, 1994.
[4] S. Bataineh and B. Al-Asir, “An Efficient Scheduling Algorithm for Divisible and Indivisible Tasks in Loosely Coupled Multiprocessor Systems,” Software Eng. J., vol. 9, no. 1, pp. 13-18, 1994.
[5] D.P. Bertsekas and J.N. Tsitsiklis, Parallel and Distributed Computation.Englewood Cliffs, N.J.: Prentice Hall International, 1989.
[6] V. Bharadwaj, D. Ghose, and V. Mani, "Optimal Sequencing and Arrangement in Distributed Single-Level Tree Networks with Communication Delays," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 9, pp. 968-976, Sept. 1994.
[7] V. Bharadwaj, “Distributed Computation with Communication Delays: Design and Analysis of Load Distribution Strategies,” PhD thesis, Faculty of Eng., Indian Inst. of Science, Bangalore, India, June 1994.
[8] 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.
[9] V. Bharadwaj, D. Ghose, V. Mani, and T.G. Robertazzi, Scheduling Divisible Loads in Parallel and Distributed Systems.Los Alamitos, Calif.: IEEE CS Press, 1996.
[10] V. Bharadwaj, H.F. Li, and T. Radhakrishnan, “Scheduling Divisible Loads in Bus Networks with Arbitrary Processor Release Times,” Computers and Mathematics with Applications, vol. 32, no. 7, pp. 57-77, 1996.
[11] J. Blazewicz and M. Drozdowski, "Distributed Processing of Divisible Jobs with Communication Startup Costs," Discrete Applied Mathematics, vol. 76, issues 1-3, pp. 21-41, June 1997.
[12] S.H. Bokhari, Assignment Problems in Parallel and Distributed Computing.Boston: Kluwer Academic, 1987.
[13] K. Boryczko, M. Bubak, M. Gajecki, J. Kitowsk, J. Moscinski, and M. Pogoda, “Transmission Rates and Performance of a Network of Computers,” High-Performance Computing and Networking, Volume II: Networking and Tools, W. Gentzsch and U. Harms, eds., pp. 142-149. Berlin: Springer-Verlag, 1994.
[14] S. Charcranoon, T.G. Robertazzi, and S. Luryi, “Cost Efficient Load Sequencing in Single Level Tree Networks” Proc. 1998 Conf. Information Sciences and Systems, Princeton Univ., 1998.
[15] 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.
[16] M. Drozdowski, “Selected Problems of Scheduling Tasks in Multiprocessor Computer Systems,” Wydawnictwa Politechniki Poznanskiej, no. 321,Poznan, Poland, 1997.
[17] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness.New York: W.H. Freeman, 1979.
[18] A. Gerasoulis and T. Yang,"On the granularity and clustering of directed acyclic task graphs," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 6, pp. 686-701, June 1993.
[19] D. Ghose and V. Mani, "Distributed Computation with Communication Delays: Asymptotic Performance Analysis," J. Parallel and Distributed Computing, vol. 23, pp. 293-305, Nov. 1994.
[20] 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. 55, pp. 32-59, 1998.
[21] A. Gupta, V. Kumar, and A. Sameh, “Performance and Scalability of Preconditioned Conjugate Gradient Methods on Parallel Computers,” IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 5, pp. 455-469, May 1995.
[22] J.F. Jeng and S. Sahni, “Reconfigurable Mesh Algorithms for the Hough Transform,” J. Parallel and Distributed Computing, vol. 20, pp. 69-77, 1994.
[23] H.J. Kim, G.I. Jee, and J.G. Lee, "Optimal Load Distribution for Tree Network Processors," IEEE Trans. Aerospace and Electronic Systems, vol. 32, no. 2, pp. 607-612, Apr. 1996.
[24] C. Lee, Y.F. Wang, D. Uecker, and Y. Wang, “Image Analysis for Automated Tracking in Robot-Assisted Endoscopic Surgery,” Proc. 12th Int'l Conf. Pattern Recognition, Jerusalem, Israel, pp. 88-92, Sept. 1994.
[25] C. Lee, Y.F. Wang, and T. Yang, “Static Global Scheduling for Optimal Computer Vission and Image Processing Operations on Distributed-Memory Multiprocesors,” Technical Report TRC 94-23, Univ. of California, Santa Barbara, Dec. 1994.
[26] C.H. Lee and K.G. Shin, “Optimal Task Assignment in Homogeneous Networks,” IEEE Trans. Parallel and Distributed Systems, vol 8, no. 2, pp. 119-129, Feb. 1997.
[27] D. Ghose and V. Mani, "Distributed Computation in a Linear Network: Closed-form Solutions and Computational Techniques," IEEE Trans. Aerospace and Electronic Systems, vol. 30, no. 2, pp. 471-483, Apr. 1994.
[28] 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.
[29] S. Sahni and V. Thanvantri, “Performance Metrics: Keeping the Focus on Runtime,” IEEE Parallel and Distributed Technology, pp. 43-56, Spring 1996.
[30] H.J. Siegel, J.B. Armstrong, and D.W. Watson, "Mapping Computer-Vision-Related Tasks onto Reconfigurable Parallel Processing Systems," Computer, vol. 25, no. 2, pp. 54-63, Feb. 1992.
[31] J. Sohn and T. G. Robertazzi, “Optimal Load Sharing for a Divisible Job on a Bus Network,” Proc. Conf. Information Science and Systems, pp. 835-840, Mar. 1993.
[32] 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.
[33] J. Sohn and T.G. Robertazzi, “An Optimum Load Sharing Strategy for Divisible Jobs with Time-Varying Processor Speed and Channel Speed,” Proc. ISCA Int'l Conf. Parallel and Distributed Computing Systems, pp. 27-32, Sept. 1995.
[34] 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.
[35] J. Sohn, T.G. Robertazzi, and S. Luryi, Optimizing Computing Costs Using Divisible Load Analysis IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 3, pp. 225-234, Mar. 1998.
[36] J.A. Stankovic, M. Spuri, M. Di Natale, and G. Buttazzo, “Implications of Classical Scheduling Results for Real-Time Systems,” IEEE Computer, vol. 28, no. 6, June 1995.
[37] J. Xu, “Multiprocessor Scheduling of Processes with Release Times, Deadlines, Precedence, and Exclusion Relations,” IEEE Trans. Software Eng., vol. 19, no. 2, pp. 139-154, Feb. 1993.

Index Terms:
Divisible loads, communication delay, processing time, optimal sequence, bus networks.
Citation:
Bharadwaj Veeravalli, Xiaolin Li, Chi Chung Ko, "On the Influence of Start-Up Costs in Scheduling Divisible Loads on Bus Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 12, pp. 1288-1305, Dec. 2000, doi:10.1109/71.895794
Usage of this product signifies your acceptance of the Terms of Use.