We present the design of a Resource-Aware Task Allocator (RATA) and an empirical analysis in handling real-time tasks for processing on Distributed Satellite Systems (DSS). We consider task processing performance across low Earth orbit (LEO) to Low-Medium Earth Orbit (Low-MEO) constellation sizes, under varying traffic loads. Using Single-Level Tree Network(SLTN)-based cooperative task allocation architecture, we attempt to evaluate some key performance metrics - blocking probabilities, response times, energy consumption, and resource utilization across several tens of thousands of tasks per experiment. Our resource-conscious RATA monitors key parameters such as arrival rate, resources (on-board compute, storage, bandwidth, battery) availability, satellite eclipses' influence in processing and communications. This study is an important step towards analyzing the performance under lighter to stress inducing levels of compute intense workloads to test the ultimate performance limits under the combined influence of the above-mentioned factors. Results show pronounced non-linear scaling: while capacity increases with constellation size, blocking and delay grow rapidly, whereas energy remains resilient under solar-aware scheduling. The analysis identifies a practical satellite-count limit for baseline SLTNs and demonstrates that CPU availability, rather than energy, is the primary cause of blocking. These findings provide quantitative guidance by identifying thresholds at which system performance shifts from graceful degradation to collapse.

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