In this paper, a study on task assignment strategies for a complex real-time network system is presented. Firstly, two task assignment strategies are proposed to improve previous strategies. The proposed strategies assign tasks with meeting end-to-end real-time constraints, and also with optimizing system utilization through period modulation of the tasks. Consequently, the strategies aim at the optimizationto optimize of system performance with while still meeting real-time constraints. The proposed task assignment strategies are devised using the genetic algorithmswith heuristic real-time constraints in the generation of new populations. The strategies are differentiated by the optimization method of the two objectives-meeting end-to-end real-time constraints and optimizing system utilization: the first one has sequential genetic algorithm routines for the objectives, and the second one has one multiple objective genetic algorithm routine to find a Pareto solution. Secondly, the performances of the proposed strategies and a well-known existing task assignment strategy using the BnB(Branch and Bound) optimization are compared with one other through some simulation tests. Through the comparison of the simulation results, the most adequate task assignment strategies are proposed for some as system requirements-: the optimization of system utilization, the maximization of running tasktasks, and the minimization of the number of network node nodesnumber for a network system.