Abstract
Parallel computer architectures utilize a set of computational elements (CE) to achieve performance that is not attainable on a single processor, or CE, computer. A common architecture is the cluster of otherwise independent computers communicating through a shared network. To make use of parallel computing resources, problems must be broken down in to smaller units that can be solved individually by each CE while exchanging information with CEs solving other problems.
Effective utilization of a parallel computer architecture requires the computational load to be distributed more or less evenly over the available CEs. The qualifier “more or less” is used because the communications required to distribute the load consume both computational resources and network bandwidth. A point of diminishing returns exists.
In this work, a nonlinear deterministic dynamic time-delay systems is developed to model load balancing in a cluster of computer nodes used for parallel computations. This model is then compared with an experimental implementation of the load balancing algorithm on a parallel computer network.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abdallah, C.T., Hayat, M., Birdwell, J.D. and Chiasson, J.: “Dynamic Time Delay Models for Load Balancing,” Part II: A Stochastic Analysis of the Effect of Delay Uncertainty, in Advances in time-delay systems (S.-I. NICULESCU, K. Gu, EDS.) (this volume) (2003).
Abdallah, C.T., Alluri, N., Birdwell, J.D., Chiasson, J., Chupryna, Y., Tang, Z. and Wang, T.: “A Linear Time Delay Model for Studying Load Balancing Instabilities in Parallel Computations,” International Journal of System Science (2003) (to appear).
Abdallah, C.T., Dorato, P., Benitez-Read, J. and Byrne, R.: “Delayed positive feedback can stabilize oscillatory systems,” Proceedings of the American Control Conference, San Francisco CA (1993) 3106–3107
Abdallah, C.T., Birdwell, J.D., Chiasson, J., Chupryna, V., Tang, Z. and Wang, T: “Load Balancing Instabilities due to Time Delays in Parallel Computation,” Proceedings of the 3rd IFAC Conference on Time Delay, Systems, Santa Fe, NM (2001).
Altman, E. and Kameda, H.: “Equilibria for Multiclass Routing in Mull-Agent Networks,” Proceedings of the 2001 IEEE Conference on Decision and Control, Orlando. FL. USA, December 2001.
Bellman, R. and Cooke, K.L.: Differential-Difference Equations, (Academic Press New York, 1963).
Birdwell, J.D., Horn, R.D., Icove, D.J., Wang, T.W., Yadav, P. and Niezgoda, S.: “A hierarchical database design and search method for CODIS,” in Proc. Tenth International Symposium on Human Identification, Orlando, FL, September, 1999.
Birdwell, J.D., Wang, T.-W. and Rader, M.: “The University of Tennessee’s new search engine for CODIS,” in Proc. 6th CODIS Users Conference, Arlington, VA, February, 2001
Birdwell, J.D., Wang, T.W., Hom, R.D., Yadav, P. and Icove, D.J.: “Method of Indexed Storage and Retrieval of Multidimensional Information,” in Proc. Tenth SIAM Conference on Parallel Processing for Scientific Computation, U. S. Patent Application 09/671,304, September, 2000.
Birdwell, J.D., Chiasson, J., Abdallah, C.T., Tang, Z., Alluri, N., Churpryna, V. and Wang T.W.: “Load Balancing Instabilities due to Time Delays in Parallel Computation,” Automatica (Submitted for Publication, 2002).
Birdwell, J.D., Chiasson, J., Tang, Z., Abdallah, C.T., Hayat, M., and Wang, T.W.: “Dynamic Time Delay Models for Load Balancing Part I: Deterministic Models,” in Proc. CNRS-NSF IVorkshop: Advances in Control of Time-Delay Systems, Paris France, 2003.
Birdwell, J.D., Chiasson, J., Abdallah, C.T., Tang, Z., Alluri, N., and Wang, T.W.: “Load Balancing Instabilities due to Time Delays in Parallel Computation,” submitted to the 42nd Conference on Decision and Control (2003).
Cavendish, D., Mascolo, S. and Ceria, M.: “SP-EPRCA: an ATM rate based congestion control scheme based on a Smith predictor,” Preprint (1996).
Chiasson, J.N., Brierley, S.D. and Lee, E.B.: “A simplified derivation of the Zeheb-Walach 2-D stability test with applications to time-delay systems,” IEEE Transactions on Auomatic Control, (1985).
Chiasson, J.: “A method for computing the interval of delay values for which a differential-delay system,” IEEE Transactions on Automatic Control, 33 (1988) 1176–1178.
Chiasson, J. and Abdallah, C.T.: “A Test for Robust Stability of Time Delay Systems,” in Proceedings of the 3rd IFAC Conference on Time Delay Systems, Sante Fe, NM, 2001.
Cooke, K.L. and Ferreira, J.M.: “Stability conditions for linear retarded functional differential equations,” Journal of Mathematical Analysis and Applications 96 (1983).
Corradi, A., Leonardi, L. and Zambonelli, F.: “Diffusive load-balancing polices for dynamic applications,” IEEE Concurrency 22 (no. 31) (1999) 979-993
Cybenko, G.: “Journal of Parallel and Distributed Computing,” IEEE Transactions on Automatic Control, 7 (1989) 279-301
Dasgupt P., Performance Evaluation of Fast Ethernet, ATM and Myrinet under PVM, MS Thesis, 2001, University of Tennesse.
Dasgupta, P., Birdwell, J.D. and Wang, T.W.: “Timing and congestion studies under PVM,” in Proc. Tenth SIAM Conference on Parallel Processing for Scientific Computation, Portsmouth, VA, March 2001.
Datko, R.: “A procedure for determination of the exponenti al stabil ity of certain differential-difference equations,” in Quarterly Applied Mathematics, 36 (1978) 279–292.
Dickmann, O., van Gils, S.A., Verduyn Lunel, S.M. and Walther, H.-O.: Delay Equations (Springer-Verlag New York, 1995
Hale, J.K. and Verduyn Lunel, S.M.: Introduction to Functional Differential Equations. Springer-Verlag: 1993
Hertz, D., Jury, E.I. and Zeheb, E.: “Simplified analytic stability test for systems with commensurate time delays,” in IEE Proceedings, pari D, 131 (1984).
Hertz, D., Jury, E.I. and Zeheb, E.: “Stability independent and dependent of delay for delay differential systems,” J. Franklin Institute (1984).
Kameda, H., Li, J., Kim, C. and Zhang, Y.: Optimal Lead Balancing in Distributed Camputer Systems (Springer London, 1997).
Kameda, H., El-Zoghdy Said Fathy, Ryu, I. and Li, J.: “A Performance Comparison of Dynanmic versus Static Load Balancing Policies in a Mainframe,” in Proceedings of the 2000 IEEE Conference on Decision and Control, Sydney, Australia, pp. 1415–1420, December, 2000.
Kamen, E.W.: “Linear systems with commensurate time delays: Stability and stabilization independent of delay,” IEEE Transactions on Automatic Control, 27 (1982) 367–375.
Kleinrock, L.: Queuing Systems Vol I: Theory (John Wiley & Sons New York, 1975).
Mascolo, S.: “Smit“s Principle for Congestion Control in High-Speed Data Network.” IEEE Transactions on Automatic Control, 45 (2000) 358–364.
Niculescu, S.-I.: Delay Effects on Stability. A robust control approach (Springer-Verlag Heidelberg, 2001).
Niculescu, S.-I. and C. T. Abdallah, “Delay effccts on static ouput feedback stabilization,” Proceedings of the IEEE Conf. Dec. Contr., Sydney, Australia (2000).
Ataşlar, B., Quet, P.F., Üftar, A., Özbay, H., Kang, T. and Kalyanaraman, S.: “Robust Rate-based now controllers for high-speed networks: the care of uncertain time-varying multiple time-delays.” Preprint, 2001.
Petterson, B.J., Robinett, R.D. and Werner, J.C.: “Lag-stabilized force feedback damping,” Intenal Report SAMD91-0194, UC-406, 1991.
Power, H.M. and Simpson, R.J.: Introduction to Dynamics and Control (McGraw-Hill: 1978).
Smith, O.J.M.: “Closed Control of Loops with Dead Time,” Chemical Engineering Progress, 57 (1957) 217–219.
Spies, F.: “Modeling of optimal load balancing strategy using queuing theory,” Microprocessors and Microprogramming, 41 (1996) 555–570.
Wang, T.W., Birdwell, J.D., Yadav, P., Icove, D.J., Niezgoda, S. and Jones, S.: “Natural clustering of DNA/STR profiles,“ in Proc. Tenth International Symposium on Human Identification, Orlando, FL, September, 1999.
Willebcek-LeMair, M.H. and Reeves, A.P.: “Strategies for dynamic load balancing on highly parallel computers,” IEEE Transactions on Parallel and Distributed Systems, (1993) 979–993.
Xu, C. and Lau, F.C.M.: Load Balancing in Parallel Computers: Theory and Practice (Kluwer BostOn, 1997).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Douglas Birdwell, J., Chiasson, J., Tang, Z., Abdallah, C., Hayat, M.M., Wang, T. (2004). Dynamic Time Delay Models for Load Balancing. Part I: Deterministic Models. In: Niculescu, SI., Gu, K. (eds) Advances in Time-Delay Systems. Lecture Notes in Computational Science and Engineering, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18482-6_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-18482-6_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20890-7
Online ISBN: 978-3-642-18482-6
eBook Packages: Springer Book Archive