This work considers the satellite data processing portion of a space-based weather monitoring system. It uses a heterogeneous distributed processing platform. There is uncertainty in the arrival time of new data sets to be processed, and resource allocation must be robust with respect to this uncertainty. The tasks to be executed by the platform are classified into two broad categories: high priority (e.g., telemetry, tracking, and control), and revenue generating (e.g., data processing and data research). In this environment, the resource allocation of the high-priority tasks must be done before the resource allocation of the revenue generating tasks. A two-part allocation scheme is presented in this research. The goal of first part is to find a resource allocation that minimizes makespan of the high-priority tasks. The robustness for the first part of the mapping is defined as the difference between this time and the expected arrival of the next data set. For the second part, the robustness of the mapping is the difference between the expected arrival time and the time at which the revenue earned is equal to the operating cost. Thus, the heuristics for the second part find a mapping that minimizes the time for the revenue (gained by completing revenue generating tasks) to be equal to the cost. Different resource allocation heuristics are designed and evaluated using simulations, and their performance is compared to a mathematical bound.