Cycle-Time Configuration for Parallel Processing Systems via Max-Plus Algebra

In this article, cycle-time configuration is realized using max-plus algebra for a parallel processing system via a synchronous feedback controller. As a key efficiency metric of parallel processing systems, throughput is determined by cycle time, which is threatened by clock asynchrony and the curse of dimensionality. Using instruction dependency and weak linear independence, the parallel processing system is equivalent to a max-plus nonautonomous system to mitigate the curse of dimensionality caused by numerous processing tasks. Based on the max-plus nonautonomous system, the cycle-time configuration is achieved via a synchronous feedback controller while adhering to time restrictions of the parallel processing system. Numerical simulations validate the effectiveness of the proposed cycle-time configuration in parallel processing systems.