Load balancing on generalized hypercube and mesh multiprocessors with LAL

A typical nearest neighbor balancing strategy, called LAL (local average load), in which the workload of a processor is averaged among its nearest neighbors at discrete time steps is investigated. The underlying systems considered are multiprocessor systems interconnected by generalized hypercube (GHC), mesh and loop structures. It is assumed that the amount of computation tasks arriving at or finished by a processor at each time step can be described by a random variable with some general distribution. With some general assumptions about these random variables, it is shown that the expected difference between the actual load of a processor and the average load of the system is zero and the variance of this difference is bounded by a constant independent of time