The Convergence of Realistic Distributed Load-Balancing Algorithms

We give a general model of partially asynchronous, distributed load-balancing algorithms for the discrete load model in parallel computers, where the processor loads are treated as non-negative integers. We prove that all load-balancing algorithms in this model are finite. This means that all load-balancing algorithms based on this model are guaranteed to reach a stable situation at a certain time (which depends on the particular algorithm) at which no load will be sent from one processor to another. With an additional assumption, we prove that the largest load difference between any two processors, in the final stable situation of the load-balancing algorithms in this model, is upper-bounded by the diameter of the topology.

[1]  Ana Cortés,et al.  On the stability of a distributed dynamic load balancing algorithm , 1998, Proceedings 1998 International Conference on Parallel and Distributed Systems (Cat. No.98TB100250).

[2]  J. Song.  A partially asynchronous and iterative algorithm for distributed load balancing , 1993, [1993] Proceedings Seventh International Parallel Processing Symposium.

[3]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[4]  Anthony P. Reeves,et al.  Strategies for Dynamic Load Balancing on Highly Parallel Computers , 1993, IEEE Trans. Parallel Distributed Syst..

[5]  Jacques E. Boillat,et al.  Load Balancing and Poisson Equation in a Graph , 1990, Concurr. Pract. Exp..

[6]  Francis C. M. Lau,et al.  Load balancing in parallel computers - theory and practice , 1996, The Kluwer international series in engineering and computer science.

[7]  S. Muthukrishnan,et al.  Dynamic Load Balancing by Random Matchings , 1996, J. Comput. Syst. Sci..

[8]  George Cybenko,et al.  Dynamic Load Balancing for Distributed Memory Multiprocessors , 1989, J. Parallel Distributed Comput..

[9]  Franco Zambonelli,et al.  Diffusive load-balancing policies for dynamic applications , 1999, IEEE Concurr..

[10]  Ana Cortés,et al.  An asynchronous and iterative load balancing algorithm for discrete load model , 2002, J. Parallel Distributed Comput..

[11]  Ralf Diekmann,et al.  Efficient schemes for nearest neighbor load balancing , 1999, Parallel Comput..

[12]  Seyed Hossein Hosseini,et al.  Analysis of a Graph Coloring Based Distributed Load Balancing Algorithm , 1990, J. Parallel Distributed Comput..

[13]  Y. F. Hu,et al.  An improved diffusion algorithm for dynamic load balancing , 1999, Parallel Comput..

[14]  Yuval Rabani,et al.  Local divergence of Markov chains and the analysis of iterative load-balancing schemes , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[15]  S. Muthukrishnan,et al.  First- and Second-Order Diffusive Methods for Rapid, Coarse, Distributed Load Balancing , 1996, Theory of Computing Systems.