An interacting particle model for load transferring in parallel architectures is defined. In the case of an infinite lattice the model is proved to be ergodic and to converge exponentially fast to its equilibrium. When the architecture is that of a complete graph, the total number of loads behaves as a birth and death process, and explicit upper bounds on the benefits that can be expected from a transferring policy are derived. Experimental results for different types of architectures are presented and compared to the solution of the mean field equations. There is fairly good agreement between the two for quantities of practical interest.
"The load transfer model." Ann. Appl. Probab. 8 (2) 337 - 353, May 1998. https://doi.org/10.1214/aoap/1028903530