Theoretical Analysis of the Heterogeneous Dynamic Load-Balancing Problem Using a Hydrodynamic Approach

This paper presents a hydro-dynamic framework to solving the dynamic load balancing problem on a network of heterogeneous computers. In this approach, each processor is viewed as a liquid cylinder where the cross-sectional area corresponds to the capacity of the processor, the communication links are modeled as liquid channels between the cylinders, the workload is represented as liquid, and the load balancing algorithm describes the ow of the liquid. It is proved that all algorithms under this framework converge geometrically to the state of equilibrium, in which the heights of the liquid columns are the same in all the cylinders. In this way, each processor obtains an amount of workload proportional to its capacity. The parameters that a ect the convergence rate of the algorithms are also identi ed and discussed.