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The use of large scale distributed systems for multiple perhaps heterogeneous applications is becoming more commonplace. The organizations that are utilizing these resources must ensure that the applications are executed in a timely manner without unnecessary wasting the resources available on the distributed system. Characteristics of two distributed computing applications are presented; large scale discrete event simulation and a real-time digital signal processing activity. A stochastic processor allocation algorithm is developed for assigning processes to processors in an effective and efficient manner based upon application characteristics. In particular, a multiobjective evolutionary algorithm (MOEA) is created in order to examine Pareto results for such diverse processor allocation. The results indicate that the focus of the two distinct applications and the associated respective optimal regions have distinct differences.