Hisao Kameda
Abstract
In completely symmetric systems that have homogeneous nodes (hosts, computers, or processors) with identical arrival processes, an optimal static load balancing scheme does not involve the forwarding of jobs among nodes. Using an appropriate analytic model of a distributed computer system, we examine the following three decision schemes for load balancing: completely distributed, intermediately distributed, and completely centralized. We show that there is no forwarding of jobs in the completely centralized and completely distributed schemes, but that in an intermediately distributed decision scheme, mutual forwarding of jobs among nodes is possible, leading to degradation in system performance for every decision maker. This result appears paradoxical, because by adding communication capacity to the system for the sharing of jobs between nodes, the overall system performance is degraded. We characterize conditions under which such paradoxical behavior occurs, and we give examples in which the degradation of performance may increase without bound. We show that the degradation reduces and finally disappears in the limit as the intermediately distributed decision scheme tends to a completely distributed one.
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This file is a corrigendum submitted by the authors in 2009 to their 2002 article "Paradoxes in distributed decisions on optimal load balancing for networks of homogeneous computers" and approved by the JACM Editor-in-Chief
- Arora, N., and Sen, S. 1997. Resolving social dilemmas using genetic algorithms: Initial results. In Proceedings of the 7th International Conference on Genetic Algorithms. Michigan State University, 689--695.Google Scholar
- Braess, D. 1968. Über ein Paradoxen aus der Verkehrsplanung. Unternehmensforschung 12, 258--268.Google Scholar
- Calvert, B., Solomon, W., and Ziedins, I. 1997. Braess's paradox in a queueing network with state-dependent routing. J. Appl. Prob. 34, 134--154.Google Scholar
- Cohen, J. E., and Jeffries, C. 1997. Congestion resulting from increased capacity in single-server queueing networks. IEEE/ACM Trans. Netw. 5, 1220--1225. Google Scholar
- Cohen, J. E., and Kelly, F. P. 1990. A paradox of congestion in a queuing network. J. Appl. Prob. 27, 730--734.Google Scholar
- Frank, M. 1981. The Braess paradox. Math. Prog. 20, 283--302.Google Scholar
- Haurie, A., and Marcotte, P. 1985. On the relationship between Nash--Cournot and Wardrop equilibria. Networks 15, 295--308.Google Scholar
- Kameda, H. 2002. How harmful the paradox can be in the Braess/Cohen--Kelly--Jeffries networks. In Proceedings of IEEE INFOCOM 2002 (New York, NY). IEEE Computer Society Press, Los Alamitos, Calif.Google Scholar
- Kameda, H., Altman, E., Kozawa, T., and Hosokawa, Y. 2000. Braess-like paradoxes in distributed computer systems. IEEE Trans. Automatic Contr. 45, 1687--1691.Google Scholar
- Kameda, H., Hosokawa, Y., and Pourtallier, O. 2001a. Effects of symmetry on Braess-like paradoxes in distributed computer systems---A numerical study --. In Proceedings of the 40th IEEE Conference on Decision and Control (Orlando, Fl.) IEEE Computer Society Press, Los Alamitos, Calif., 831--836.Google Scholar
- Kameda, H., Kozawa, T., and Li, J. 1997a. Anomalous relations among various performance objectives in distributed computer systems. In Proceedings of the 1st World Congress on Systems Simulation. IEEE Computer Society Press, Los Alamitos, Calif., 459--465.Google Scholar
- Kameda, H., Li, J., Kim, C., and Zhang, Y. 1997b. Optimal Load Balancing in Distributed Computer Systems. Springer-Verlag, New York. Google Scholar
- Kameda, H., Ohta, M., and Hosokawa, Y. 2001b. Effects of symmetry on paradoxical cost degradation in a Nash non-cooperative network system. In Proceedings of IFAC Symposium on Modeling and Control of Economic Systems (SME 2001) (Klagenfurt, Austria).Google Scholar
- Kim, C., and Kameda, H. 1990. An algorithm for optimal static load balancing in distributed computer systems. IEEE Trans. Comput. 41, 381--384. Google Scholar
- Kleinrock, L. 1976. Queueing Systems, Volume II: Computer Applications. Wiley, New York.Google Scholar
- Korilis, Y. A., Lazar, A. A., and Orda, A. 1995. Architecting noncooperative networks. IEEE J. Sel. Areas Commun. 13, 1241--1251. Google Scholar
- Korilis, Y. A., Lazar, A. A., and Orda, A. 1999. Avoiding the Braess paradox in noncooperative networks. J. Appl. Prob. 36, 211--222.Google Scholar
- Koutsoupias, E., and Papadimitriou, C. 1999. Worst-case equilibria. In Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science. 404--413. Google Scholar
- Li, J., and Kameda, H. 1998. Load balancing problems for multiclass jobs in distributed/parallel computer systems. IEEE Trans. Comput. 47, 322--332. Google Scholar
- Murchland, J. D. 1970. Braess's paradox of traffic flow. Transpn. Res. 4, 391--394.Google Scholar
- Orda, A., Rom, R., and Shimkin, N. 1993. Competitive routing in multiuser communication networks. IEEE/ACM Trans. Netw. 1, 614--627. Google Scholar
- Rosen, J. B. 1965. Existence and uniqueness of equilibrium points for concave n-person games. Econometrica 33, 153--163.Google Scholar
- Roughgarden, T., and Tardos, É. 2000. How bad is selfish routing? In Proceedings of the 41th IEEE Annual Symposium on Foundation of Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., 93--102. Google Scholar
- Samuelson, P. 1992. Tragedy of the open road: Avoiding paradox by use of regulated public utilities that charge corrected Knightian tolls. J. Int. Comparat. Econ. 1, 3--12.Google Scholar
- Shapiro, J. F. 1979. Mathematical Programming, Structures and Algorithms. Wiley, New York.Google Scholar
- Tantawi, A. N., and Towsley, D. 1985. Optimal static load balancing in distributed computer systems. J. ACM 32,2 (Apr.), 445--465. Google Scholar
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- Paradoxes in distributed decisions on optimal load balancing for networks of homogeneous computers
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