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 the buffer content process in the vector-valued Skorokhod space which is endowed with the product J1 topology. To illustrate our framework, we provide explicit results for a tandem queue. At the heart of our proof is a recent sample-path large deviations result, and a novel continuity result for the Skorokhod reflection map in the product J1 topology.

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Queueing Systems

Bazhba, M., Rhee, C.-H., & Zwart, B. (2022). Large deviations for stochastic fluid networks with Weibullian tails. Queueing Systems, 102(1-2), 25–52. doi:10.1007/s11134-022-09865-5