Stochastic Cellular Automata Model to Reduce Rule Space Cardinality Applied to Task Scheduling with Many Processors

Task scheduling consists of allocating the parallel program tasks into the processors of a multiprocessing system. This paper investigates cellular automata (CA) based models for solving the scheduling problem. A standard genetic algorithm (GA) is employed to evolve appropriate CA rules, that is transition rules able to schedule parallel programs. We identified that the state-of-art CA-based schedulers suffer when trying to manage eight or more processors. This difficulty is mainly due to the severe increment in the rule space cardinality when the number of states per cell are increased to represent more processors. We propose a non-standard cellular automata model able to minimize this problem. A new definition of local neighborhood is proposed here, which is denominated as Mapping-Reduce. In addition, the transition rule related to the mapping-reduce neighborhood uses a nondeterministic output, which printed a stochastic characteristic for the new CA model. By using the new CA model we were able to simplify the complexity of the transition rules employed in the proposed CA-based scheduler model. Simulations based on the new model were carried out using a family of four parallel programs that solve equations by Gaussian elimination. Based on the experiments using 4, 8 and 16 processors, it was noted that the results of the CAbased scheduling approach were improved for architectures with a higher number of nodes. Moreover, the evolved rules had shown a better generalization ability when applied to schedule new parallel programs which is a critical point related to the main motivation for the employment of CA in scheduling.