Both analysis and design optimization of real-time systems has predominantly concentrated on considering hard real-time constraints. For a large class of applications, however, this is both unrealistic and leads to unnecessarily expensive implementations. This paper addresses the problem of task priority assignment and task mapping in the context of multiprocessor applications with stochastic execution times and in the presence of constraints on the percentage of missed deadlines. We propose a design space exploration strategy based on Tabu Search together with a fast method for system performance analysis. Experiments emphasize the efficiency of the proposed analysis method and optimization heuristic in generating high quality implementations of soft real-time systems with stochastic task execution times and constraints on deadline miss ratios.