Large deviations for stochastic fluid networks with Weibullian tails

We consider a stochastic fluid network where the external input processes are compound Poisson with heavy-tailed Weibullian jumps. Our results comprise of large deviations estimates for buffer content process in vector-valued Skorokhod space which is endowed product $$J_1$$ topology. To illustrate our framework, we provide explicit tandem queue. At heart proof recent sample-path result, and novel continuity result reflection map