the use of Linux-based clusters is a strategy for the development of multiprocessor systems. These types of systems face the problem of efficiently executing the planning and allocation of tasks, for the efficient use of its resources. This paper addresses this as a multi-objective problem, carrying out an analysis of the objectives that are opposed during the planning of the tasks, which are waiting in the queue, before assigning tasks to processors. For this, we propose a method that avoids strategies such as those that use genetic operators, exhaustive searches of contiguous free processors on the target system, and the use of the strict allocation policy: First Come First Serve (FIFO). Instead, we use estimation and simulation of the joint probability distribution as a mechanism of evolution, for obtaining assignments of a set of tasks, which are selected from the waiting queue through the planning policy Random-Order-of-Service (ROS). A set of conducted experiments that compare the results of the FIFO allocation policy, with the results of the proposed method show better results in the criteria of: utilization, throughput, mean turnaround time, waiting time and the total execution time, when system loads are significantly increased.