Weighted scheduled traffic process with asymptotic fractional dynamics

This paper investigates the asymptotic behavior of a weighted scheduled traffic process, an extension of the traditional scheduled traffic model where events are subject to random perturbations and carry variable weights. Under the assumption that the perturbations follow a heavy-tailed distribution, we demonstrate that the appropriately rescaled process converges weakly to a fractional Brownian motion. Applications of this framework span diverse fields such as queueing theory, telecommunications, finance, and healthcare, where the model provides insights into workload accumulation, network traffic variability, and transaction flow dynamics.