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Consider a queueing system fed by traffic from $N$ independent andidentically distributed marked point processes. We establish several novelsample path large deviations results in the scaled uniform topology for such asystem with a small buffer. This includes both the heavily loaded case (theload grows as $N\rightarrow\infty$) and the previously unexplored lightlyloaded case (the load vanishes as $N\rightarrow\infty$); this latter caserequires the introduction of novel speed scalings for such queueing systems.Alongside these sample path large deviations results, we introduce a newframework to explore the range of scalings in the many sources asymptotic forthese systems.

Sample path large deviations for marked point processes in the many sources asymptotic with small buffers: Heavily and lightly loaded systems